All Abstracts | Poster Abstracts | Talk Abstracts | Tutorial Abstracts

1. Scalable Traps for Quantum Information Processing with Ions*

Jason Amini, National Institute of Standards and Technology

(Session 5 : Friday from 5:00-7:00)

Abstract. J. M. Amini, C. Ospelkaus, H. Uys, C. E. Langer [a], J. Britton, K. R. Brown, D. Leibfried, S. Seidelin [b], A. VanDevender, J. H. Wesenberg [c], and D. J. Wineland. Two of the key goals for the ion trap community are scaling ion traps to hold and manipulate the numbers of qubits needed for complex algorithms and improving the quality of all operations. We will cover some of the developments at NIST on microfabricated surface-electrode traps using optimized modular design components, including a new 'Y' junction design, and using novel magnetic gates. * supported by IARPA and the NIST Quantum Information Program. [a] Current address: Lockheed Martin Space Systems Company, Littleton, CO, USA. [b] Current address: University of Grenoble, France. [c] Current address: Oxford University, U.K.A.

2. Fault-tolerant quantum computation with color codes

Jonas Anderson, University of New Mexico

(Session 5 : Friday from 5:00-7:00)

Abstract. Concatenated coding is a well-studied route to fault-tolerant quantum computation, but suffers from low accuracy thresholds (on the order of one part in 10,000) or high resource overheads (millions of physical qubits per logical qubit to achieve thresholds on the order of one percent). Kitaev's surface codes offer a new route to fault tolerance with more modest overheads and thresholds approaching 1%. The recently discovered color codes share many properties with surface codes, such as the ability to perform syndrome extraction locally in two dimensions. Some families of color codes admit a transversal implementation of the entire Clifford group. It is expected that color codes have a threshold near that of the surface codes, however the precise value of this threshold is not currently known. In this poster we investigate a particular class of planar color codes on the 4.8.8 lattice known as triangular codes. We develop a fault-tolerant error-correction strategy for these codes in which repeated syndrome measurements on this lattice generate a three-dimensional space-time combinatorial structure. We then develop an integer program (IP) that analyzes this structure and determines the most likely set of errors consistent with the observed syndrome values. We have implemented this IP for simulated noise on small versions of these triangular codes; our goal is to obtain an estimate on the threshold for fault-tolerant quantum memory with the 4.8.8 triangular color codes. Because the threshold for magic state distillation is likely to be higher than this value and because logical CNOT gates can be performed by code deformation in a single block instead of between pairs of blocks, the threshold for fault-tolerant quantum memory for these codes is also the threshold for fault-tolerant quantum computation with them.

3. The Role of Coherence in Photosynthetic Energy Transfer

Alan Aspuru-Guzik, Harvard University

(Session 11 : Sunday from 9:15-9:45)

Abstract. Recently, direct evidence of long-lived coherence has been experimentally demonstrated for the dynamics of the Fenna-Matthews-Olson (FMO) protein complex at 77K [Engel et al., Nature 446, 782 (2007)]. It was suggested that quantum coherence was important for exploring many relaxation pathways simultaneously. I will talk about our recent work in developing methods for exploring that question and analyzing the different contributions of the different processes to the efficiency of energy transfer in the complex. We generalized the concept of continuous-time quantum walks to a Liouville space formalism. This helped us analyze these contributions and report that at room temperature, this complex has contribution of coherent dynamics of about 10%. Relaxation processes are responsible for 80% of the efficiency. The quantum transport efficiency can actually be enhanced by the dynamical interplay of the system Hamiltonian with the pure dephasing dynamics induced by a fluctuating environment. This occurs in an intermediate regime between fully coherent hopping and highly incoherent transport. I will finalize with a short discussion of this environment-assisted quantum transport regime.

4. Precision Metrology using Double-Pass Continuous Quantum Measurement

Ben Baragiola, University of New Mexico

(Session 5 : Friday from 5:00-7:00)

Abstract. We summarize an ongoing study of continuously measured double-pass quantum systems relevant for quantum-limited metrology. Numerical calculations of the quantum Fisher information for the exact quantum filter indicate improved uncertainty scaling over single-pass geometry, yet quantum Kalman filters show no enhancement. We investigate other approximate filters which we hope will close this gap.

5. Dynamical Decoupling in a Model Quantum Memory

Michael Biercuk, NIST - Ion Storage Group

(Session 10 : Saturday from 4:00-4:30)

Abstract. We present results on the application of Dynamical Decoupling (DD) pulse sequences for the suppression of phase errors in a qubit array consisting of a laser-cooled crystal of trapped Beryllium ions. We study various DD sequences including CPMG and the recently discovered Uhrig DD sequence. Our results demonstrate the ability of UDD and CPMG to strongly suppress phase errors in the presence of ambient magnetic field noise, and show strong agreement with theoretical predictions for qubit decoherence. We also generate noise artifically and compare the efficacy of these DD sequences in Ohmic, 1/f and 1/f^2 noise environments -- making our qubit array a model quantum system capable of emulating solid state noise environments. Finally, we demonstrate real-time experimental optimization of DD pulse sequences without any required knowledge of the ambient noise environment.

6. Transport and heating in an X-junction ion trap array

Brad Blakestad, National Institute of Standards and Technology

(Session 5 : Friday from 5:00-7:00)

Abstract. Trapped ions are a useful system for studying the elements of quantum information processing. Simple algorithms have been demonstrated; but scaling to much larger tasks requires the ability to manipulate many qubits. To achieve this, ions could be distributed over separate trap zones in an array, where information would be shared between zones by moving the ions [1]. Multi-dimensional arrays incorporating junctions would allow arbitrary ions, selected from various locations, to be reliably grouped together for multi-qubit gates. Suppression of heating incurred during transport will minimize the time required for ion recooling. We report transport of Be+ ions through an ``X-junction" trap array with near unit probability and low heating (< 10 quanta). We demonstrate the preservation of qubit coherence during such transport. We also study a particular radio-frequency (RF) noise heating mechanism due to RF pseudopotential gradients, which are common in junction designs. * Supported by IARPA and the NIST Quantum Information Program [1] D. Kielpinski, C. Monroe and D.J. Wineland. Nature 417, 709 (2002)

7. Quantum computing through decoherence

Sergio Boixo, California Institute of Technology

(Session 10 : Saturday from 4:30-5:00)

Abstract. A computation in adiabatic quantum computing is achieved by traversing a path of nondegenerate eigenstates of a continuous family of Hamiltonians. We introduce a method that traverses a discretized form of the path: at each step we evolve with the instantaneous Hamiltonian for a random time. The resulting decoherence approximates a projective measurement onto the desired eigenstate, achieving a version of the quantum Zeno effect. For bounded error probability, the average evolution time required by our method is O(L^2 /D), where L is the length of the path of eigenstates and D the minimum spectral gap of the Hamiltonian. The randomization also works in the discrete-time case, where a family of unitary operators is given, and each unitary can be used a finite amount of times. Applications of this method for unstructured search and quantum sampling are considered. We discuss the quantum simulated annealing algorithm to solve combinatorial optimization problems. This algorithm provides a quadratic speed-up (in the gap) over its classical counterpart implemented via Markov chain Monte Carlo.

8. Creating and manipulating quantum decoherence-free, or noiseless, systems of qudits

Mark Byrd, Southern Illinois University

(Session 10 : Saturday from 3:30-4:00)

Abstract. Qudits are promising candidates for many quantum information processing tasks. They can be more entangled than qubits, can share a larger fraction of the entanglement in some cases, and may be required for some quantum information processing tasks. I will show how to make entangled qutrit states using photons which form a decoherence-free subspace and show how, in principle, we can manipulate qudit decoherence-free subspaces comprised of quDits.

9. Development of a Silicon Physical Qubit and Single Logical Qubit Design

Malcolm Carroll, Sandia National Laboratories

(Session 1 : Thursday from 6:45-7:15)

Abstract. An overview will be given of both experimental and theoretical development of a single error corrected logical qubit using silicon based hardware. The physical qubit research centers on demonstrating a basic qubit fabricated in an accumulation mode silicon metal oxide semiconductor (MOS) structure. The experimental component of the logical qubit focuses on the classical-quantum circuit interface and its impact on error correction. The logical qubit effort includes both hardware development, such as cryogenic complementary metal oxide semiconductor (CMOS), and a theoretical component, which examines a quantum error correction circuit architecture. The theoretical analysis accounts for more realistic constraints suggested by the physical qubit research while providing insight and feed-back about choices of lay-out, transport and error code choice. We note that some insight drawn from constraints of working in a cryostat may be more generally useful to other quantum computing architectures using cryogenics. In summary, the goal of this combined engineering effort is to more completely understand the design of a single solid-state logical qubit and work towards development of the required silicon qubit hardware elements (e.g., single qubit and read-out) with which to build it.

10. Trapped Ion Quantum Computation with Transverse Phonon Modes

Ming-Shien Chang, University of Maryland

(Session 5 : Friday from 5:00-7:00)

Abstract. Trapped Ion Quantum Computation with Transverse Phonon Modes
M.-S. Chang, K. Kim, S. Korenblit, K. R. Islam, L.-M. Duan†, and C. Monroe JQI and Department of Physics, University of Maryland, College Park, MD 20742
†Department of Physics, University of Michigan, Ann Arbor, MI 48109

Trapped ion systems remain as one of the most promising candidates [1] for practical quantum information processing (QIP). Recent theoretical studies suggested that using transverse collective motion as the quantum bus [2] has several potential advantages over longitudinal normal modes adopted in previous demonstrations. First, the transverse modes are more tightly bound than axial modes for any number of ions and are hence less sensitive to motional decoherence. Second, the closely-spaced spectrum of the transverse modes allows ions to couple through multiple modes simultaneously. This opens up an avenue to tailor the many-body ion coupling strengths for exploring nontrivial spin Hamiltonians [3], and enables entangling gates with arbitrary speed by applying composite laser pulses. We will report the recent experimental progress of this scheme with trapped Ytterbium ions in a linear Paul trap, and its application for quantum simulations of Heisenberg-like spin Hamiltonians. We will also discuss the scalability of this approach for trapped ion QIP.

This work is supported by the DARPA OLE Program under ARO Award W911NF-07-1-0576, IARPA under ARO contract W911NF-08-1-0355, and the NSF PIF Program under grant PHY-0601255.

[1] J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995); Wineland, D. J. et al., J. Res. Natl Inst. Stand. Technol. 103, 259-328 (1998); Blatt R., Wineland D., Nature 453, 1008-1015 (2008).
[2] S.-L. Zhu, C. Monroe, and L.-M. Duan, Phys. Rev. Lett. 97, 050505 (2006).
[3] D. Porras and J. I. Cirac, Phys. Rev. Lett. 92, 207901 (2004)

11. Gapped Two-body Hamiltonian whose Unique Ground State is Universal for One-way Quantum Computation

Xie Chen, Massachusetts Institute of Technology

(Session 9 : Saturday from 4:00-4:30)

Abstract. Many-body entanglement of quantum states is one of the essential resources which make quantum algorithmic speedup over classical computers possible for certain computational problems. However, generating and maintaining in a controlled way any known type of many-body entanglement that enables quantum computation is usually hard. Here we provide an alternative scheme for quantum computation which protects its entanglement resource in the gapped ground state of a naturally occurring Hamiltonian. We demonstrate how arbitrary quantum computation may be efficiently simulated by measuring each particle in the 'tri-Cluster state', a unique ground state of gapped local Hamiltonian that involves only nearest-neighbor interactions on two-dimensional Hexagonal lattice. In this way we have provided an experimentally more feasible approach for quantum computation.

12. The relationship between continuous- and discrete-time quantum walk

Andrew Childs, University of Waterloo

(Session 11 : Sunday from 8:30-9:15)

Abstract. Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or discrete time. However, whereas a continuous-time random walk can be obtained as the limit of a sequence of discrete-time random walks, the two types of quantum walk appear fundamentally different, owing to the need for extra degrees of freedom in the discrete-time case. In this talk, I describe a precise correspondence between continuous- and discrete-time quantum walks on arbitrary graphs. This provides a description of continuous-time quantum walk as a certain limit of discrete-time quantum walks, and also leads to improved methods for simulating Hamiltonian dynamics. In particular, there is a simulation whose complexity grows linearly with the total evolution time and that does not necessarily require the Hamiltonian to be sparse.

13. Continuous measurement of a quantum phase transition in a collective atomic system weakly coupled to a single optical mode

Robert Cook, University of New Mexico

(Session 7 : Saturday from 2:30-3:00)

Abstract. We consider an atomic ensemble that is dispersively coupled to a high finesse optical cavity. The application of cavity assisted Raman transitions generate two body interactions that are symmetrically distributed across the entire ensemble. If the cavity mode rapidly decays to an external field, adiabatic elimination of the cavity produces effective atomic dynamics that are equivalent to a dissipative Lipkin-Meshkov-Glick model, which exhibits a zero temperature quantum phase transition. In the framework of quantum stochastic calculus, we derive the propagator that describes the effective coupling between the collective atomic spin and the external field. We then derive a filter that describes the atomic state conditioned on a continuous measurement of the external field. Finally, we simulate this measurement as the system is tuned though its critical parameter range.

14. The Great Hunt for Small Subsystem Codes

Gregory Crosswhite, University of Washington

(Session 5 : Friday from 5:00-7:00)

Abstract. Thanks to the hard work of experimentalists, it is increasingly becoming practical to engineer small physical systems with arbitrary 2-local interactions. As a result, it becomes increasingly important for theorists to answer the question: what exactly can be done with such systems? Put another way, what quantum error correcting or detecting codes are there that can be built using a small number of qubits with 2-local interactions? Note that these codes will in general not be stabilizer codes -- since the interactions may not commute -- but will instead be subsystem codes, a more general case. Towards this end, in this poster we shall present the results of our own systematic search for subsystem quantum codes using small numbers of qubits and 2-local interactions.

15. Preparation and detection of a 137Ba+ hyperfine qubit

Matt Dietrich, University of Washington

(Session 6 : Saturday from 11:00-11:30)

Abstract. We report the initialization and state detection of 137Ba+ hyperfine qubits. We load 137Ba+ into a linear Paul trap by direct photoionization with a Xe discharge lamp. The qubit is initialized by optically pumping into the magnetic field insensitive hyperfine ground state (F=2 m_f=0). State selective shelving to the metastable D5/2 state is accomplished by adiabatic rapid passage using a 1762 nm fiber laser stabilized to a high-finesse cavity, a process which is used for high efficiency state detection. Single qubit rotations are accomplished by RF pulses at the hyperfine splitting (8.037 GHz). Rabi flops excited by individual ultrafast laser pulses have been demonstrated and future plans include using these pulses to generate controlled-phase gates between two ions on sub-microsecond time scale.

16. Large Scale Quantum Computation in a Linear Ion Trap

Luming Duan, University of Michigan

(Session 6 : Saturday from 8:30-9:15)

Abstract. Among the approaches to quantum computation, the trapped ion system remains as one of the leading candidates. The linear Paul trap provides the most convenient architecture for quantum gate operations over a few ions, and the basic requirements for quantum computation have been demonstrated in this setup. However, scaling up this system to a large number of qubits so far remains a formidable challenge because of several obstacles, including the instability of the linear structure and the difficulties of the sideband cooling and addressing for a large ion array. The recent approach to scalable ion trap computation thus has to use a more complicated architecture where the ions are shuttled over different trapping regions. Here, we propose a way to implement large-scale quantum computation in a linear trap by overcoming all the theoretical obstacles. Through excitation of the transverse photon modes in an anharmonic trap, we show that high-fidelity quantum gates can be achieved on ions in a large linear architecture under the Doppler temperature without the requirement of sideband resolving.

17. Restrictions on Transversal Encoded Quantum Gate Sets

Bryan Eastin, National Institute of Standards and Technology

(Session 3 : Friday from 2:30-3:00)

Abstract. Transversal gates play an important role in the theory of fault-tolerant quantum computation due to their simplicity and robustness to noise. By definition, transversal operators do not couple physical subsystems within the same code block. Consequently, such operators do not spread errors within code blocks and are, therefore, fault tolerant. Nonetheless, other methods of ensuring fault tolerance are required, as it is invariably the case that some encoded gates cannot be implemented transversally. This observation has led to a long-standing conjecture that transversal encoded gate sets cannot be universal. In this talk, I discuss new results showing that the ability of a quantum code to detect an arbitrary error on any single physical subsystem is incompatible with the existence of a universal, transversal encoded gate set for the code.

18. Resource Requirements for Fault-Tolerant Quantum Simulation: The Transverse Ising Model Ground State

Samuel Gasster, The Aerospace Corporation

(Session 9 : Saturday from 5:00-5:30)

Abstract. Craig R. Clark, Kenneth R. Brown, Tzvetan S. Metodi, Samuel D. Gasster The cost, in both computational space and time, of calculating the energy of the ground state of the transverse Ising model on a fault-tolerant quantum computer is estimated using the Quantum Logic Array (QLA) architecture model. The QLA is a homogeneous, scalable, tile-based quantum architecture design employing concatenated quantum error correction for the construction of logical qubits and gates, based on experimentally viable ion-trap device technology parameters and components. The error correction requirements for calculating the energy on the QLA architecture are comparable to those for factoring large integers via Shor's quantum factoring algorithm number due to the exponential scaling of the computational time steps with the precision. As a result, a fault-tolerant QLA-based quantum computer which can factor 1024-bit integers can also be used to calculate the Ising ground-state energy with precision of up to 7 decimal digits.

19. Strong NP-Hardness of the Quantum Separability Problem

Sevag Gharibian, Institute for Quantum Computing, University of Waterloo

(Session 8 : Saturday from 4:00-4:30)

Abstract. Quantum entanglement is generally believed to be a valuable resource in the theory of quantum computing. The problem of determining whether an arbitrary quantum state is entangled, dubbed the Quantum Separability problem, has hence received much attention over the past decade. In 2003, Gurvits showed that the Quantum Separability problem is NP-hard, with one caveat - one must allow instances in which the input quantum state is exponentially close (with respect to dimension, and in Euclidean distance) to the border of the set of separable (equivalently, unentangled) quantum states. This leaves open the question - is the Quantum Separability problem "weakly" NP-hard, i.e. can it be solved efficiently if one is promised that the input state is at least an inverse polynomial distance away from the border of the separable set? In this talk, we answer this question negatively by showing that the Quantum Separability problem is in fact "strongly" NP-hard. This is accomplished by combining previous work by Gurvits and a recent non-ellipsoidal reduction of Liu to show that the Weak Membership problem over the set of separable quantum states is strongly NP-hard. Based on this result, we observe an immediate lower bound on the maximum distance possible between a bound entangled state and the separable set (assuming P != NP). Time permitting, we also demonstrate that determining whether a completely positive trace-preserving linear map (i.e. a quantum channel) is entanglement-breaking is NP-hard.

20. Relationship between 3-qubit entanglement and nonlocality

Shohini Ghose, Wilfrid Laurier University

(Session 4 : Friday from 4:00-4:30)

Abstract. Multiqubit entanglement is a crucial ingredient for large-scale quantum information processing and has been the focus of several recent studies. Entanglement between qubits can lead to violations of Bell-type inequalities that are satisfied by local hidden variable models, indicating the nonlocal nature of the correlations between qubits. For 2-qubit pure states, bipartite entanglement is simply related to the Bell-CHSH nonlocality parameter. No such analytical relation between multipartite entanglement and nonlocality has yet been obtained for systems of three or more qubits. We have derived relationships between genuine tripartite entanglement and nonlocality for families of 3-qubit GHZ-class pure states. We quantify tripartite entanglement by the 3-tangle and derive its relationship to the Svetlichny inequality for testing tripartite nonlocality. For the class of generalized GHZ states, although the 3-tangle is always non-zero, we identify some states that do not violate the Svetlichny inequality. Furthermore, we show that states known as the maximal slice states always violate the Svetlichny inequality and analogous to the 2-qubit case, the amount of violation increases with the 3-tangle. We find that the generalized GHZ states and the maximal slice states have unique tripartite entanglement and nonlocality properties in the set of all pure states.

21. Diagnosis of Pulsed Squeezing in Multiple Temporal Modes

Scott Glancy, National Institute of Standards and Technology, Boulder, Colorado

(Session 5 : Friday from 5:00-7:00)

Abstract. When one makes squeezed light by downconversion of a pulsed pump laser, many temporal / spectral modes are simultaneously squeezed by different amounts. There is no guarantee that any of these modes matches the pump or the local oscillator used to measure the squeezing in homodyne detection. Therefore the state observed in homodyne detection is not pure, and many photons are present in the beam path that do not lie in the local oscillator's mode. These problems limit the fidelity of quantum information processing tasks with pulsed squeezed light. I will describe our attempts to make coherent state superpositions (sometimes called "cat states") using photon subtraction from squeezed light, the problems caused by multimode squeezing, and methods to characterize the contents of the many squeezed modes.

22. Controlling the Loss of Entanglement

Jon Grice, University of California, San Diego

(Session 5 : Friday from 5:00-7:00)

Abstract. We present an open-loop discrete time control technique to slow down the loss of entanglement of a two qubit model (the X-states studied by Eberly and Yu) undergoing specific local noises. We find the optimal policy the controller must follow to maximize entanglement after N time steps in terms of the initial state.

23. Optomechanical systems

Jack Harris, Yale University

(Session 1 : Thursday from 6:00-6:45)

Abstract. Very sensitive mechanical detectors are rapidly approaching a regime in which either the mechanical device itself or its readout should demonstrate quantum behavior. The main technical barrier to reaching this regime has been the difficulty of integrating ultrasensitive micromechanical devices with high-finesse optical cavities. Recently we have developed a robust means for addressing this issue, and have integrated a 50 nm-thick membrane (with a quality factor > 1,000,000) into an optical cavity with a finesse ~ 200,000. Although the membrane is nearly transparent, it couples to the optical cavity dispersively. This coupling is strong enough to laser-cool the membrane from room temperature to 7 mK. In addition, the dispersive nature of the optomechanical coupling allows us to realize a sensitive "displacement squared" readout of the membrane. Such a readout is a crucial requirement for measuring quantum jumps in a mechanical oscillator. We will describe these results, as well as our progress towards observing quantum effects in this system.

24. Manipulating mixed-species ion crystals in a segmented ion trap.

Jonathan Home, National Institute of Standards and Technology

(Session 5 : Friday from 5:00-7:00)

Abstract. Manipulating mixed-species ion crystals in a segmented ion trap* One of the main requirements for scalable quantum information processing is the ability to move information around the processor. In ion trap QIP, one possibility is to move the ions themselves, using control voltages applied to the electrodes of a segmented trap. In practice, ambient fluctuations in the electric field at the ion and imperfect control of electrode potentials mean that the ion's motion is excited, which degrades the performance of two-qubit logic gates. One solution is to trap two different ion species in the same potential. This allows re-initialization of the ground state of motion by laser cooling the refrigerator ion, while leaving quantum information stored in the internal state of the qubit ion intact. We describe experimental implementation of a range of manipulations of ion crystals containing Beryllium and Magnesium ions in a segmented ion trap, including ion re-ordering, separation, and ground state cooling. In addition, we have used the motion of these ion chains to characterize higher order terms in our trapping potential, which significantly change the normal modes of extended crystals. The precise level of control of the trap potential required for manipulating such crystals has implications for the design of small scale ion traps. * Supported by IARPA and the NIST Quantum Information Program

25. The Classically-Enhanced Father Protocol

Min-Hsiu Hsieh, Quantum Computation and Information Project, Solution Oriented Research for Science and Technology

(Session 12 : Sunday from 11:45-12:15)

Abstract. The classically-enhanced father protocol is an optimal protocol for a sender to transmit both classical and quantum information to a receiver by exploiting preshared entanglement and a large number of independent uses of a noisy quantum channel. We detail the proof of a quantum Shannon theorem that gives the three-dimensional capacity region containing all achievable rates that the classically-enhanced father protocol obtains. Points in the capacity region are rate triples consisting of the classical communication rate, the quantum communication rate, and the entanglement consumption rate of a particular coding scheme. The classically-enhanced father protocol is more general than any other protocol in the family tree of quantum Shannon theoretic protocols. Several previously known quantum protocols are now child protocols of the classically-enhanced father protocol. Interestingly, the classically-enhanced father protocol gives insight for constructing optimal classically-enhanced entanglement-assisted quantum error-correcting codes.

26. Upper Bounds on Fidelity Preservation with Dynamical Decoupling

Michael Hsieh, University of Southern California

(Session 5 : Friday from 5:00-7:00)

Abstract. Dynamical decoupling (DD) continues to hold promise as a relatively simple but versatile means of mitigating the influence of a noisy and uncontrolled environment on a controlled quantum system. For a qubit coupled to a bath via an entangling Hamiltonian of the most general possible form, we calculate the range of possible joint qubit-bath dynamics (specifically, the set of permissible Kraus mappings for the total composite system) as a function of the parameters of the DD control pulses under a variety of DD pulse configurations. The upper bounds on system state fidelity preservation are obtained in terms of the minimal distance between the set of attainable Kraus mappings with the ideal set describing fully decoupled dynamics.

27. Multiple-unicast communication over directed Quantum Networks

Avinash Jain, University of California, San Diego

(Session 5 : Friday from 5:00-7:00)

Abstract. We explore the possibility of network coding in multiple-unicast of quantum information over directed quantum networks. Using information-theoretic tools, we first show that over a Butterfly network, the quantum network coding does not increase the information flow over that achieved by routing. We then extend the Butterfly network to a network where quantum network coding explicitly provides gains over routing. Next we specify a criterion that any directed acyclic graph should satisfy for quantum network coding to outperform routing. We show that when this criterion is not satisfied, the quantum information flow in any 2-pair unicast communication over any directed acyclic network is bounded by sparsest multicut capacity as the fidelity of transmission approaches one.

28. Quantum Control of Large Atomic Hyperfine Manifolds

Poul Jessen, University of Arizona

(Session 2 : Friday from 9:15-9:45)

Abstract. Laboratory techniques to manipulate and observe ultracold atoms make these an attractive platform for testing new ideas in quantum control and measurement. I will review a series of experiments in which we have used tensor AC Stark shifts and magnetic fields to drive non-trivial quantum dynamics of a large spin-angular momentum associated with an atomic hyperfine ground state. The nonlinear spin Hamiltonian is sufficiently general to achieve universal quantum control over the 2F+1 dimensional state space, and allows us to generate arbitrary spin states and perform a full quantum state reconstruction of the result. We have implemented and verified time optimal controls to generate a broad variety of spin states, as well as an adiabatic scheme to generate spin-squeezed states for metrology. Most recently we have used our control and measurement tools to realize a common paradigm for quantum chaos known as the quantum kicked top. Direct observation of the phase space dynamics of this system has given an unprecedented look at quantum/classical correspondence. We are now implementing a new scheme for quantum control of an entire ground hyperfine manifold, based solely on interaction with DC, radiofrequency and microwave magnetic fields. The longer coherence times available with this approach will allow us to explore new ideas related to robust control and constructive design of unitary transformations.

29. Ion Motional Entanglement and Quantum Information Experiments at NIST*

John Jost, National Institute of Standards and Technology, Boulder

(Session 6 : Saturday from 9:15-10:45)

Abstract. I will summarize current trapped-ion quantum information processing (QIP) experiments at NIST. Quantum entanglement has been the subject of considerable research, in part due to its non intuitive nature and ubiquitous presence in QIP. For this reason it is of interest to study entanglement in a variety of systems. We demonstrate deterministic entanglement in a system pervasive in nature: mechanical oscillators. Here, the mechanical oscillators are composed of the vibrations of two Be+ - Mg+ ion pairs in spatially separate locations. The techniques demonstrated in this experiment are likely to form core components of large-scale trapped-ion QIP. Other work at NIST includes characterization of ion transport dynamics in a trap array that includes a 2-D junction, recent developments in micro-fabricated surface traps, and studies of dynamic decoupling. * supported by IARPA and the NIST Quantum Information Program

30. Entangled Mechanical Oscillators*

John Jost, National Institute of Standards and Technology, Boulder

(Session 5 : Friday from 5:00-7:00)

Abstract. J. D. Jost, J. P. Home, J. M. Amini, D. Hanneke, R. Ozeri+, C. Langer**, J. J. Bollinger, D.Leibfried & D. J. Wineland Quantum entanglement has been the subject of considerable research, in part due to its non-intuitive nature and ubiquitous presence in QIP. For this reason, it is of interest to study entanglement in a variety of systems. We demonstrate deterministic entanglement in a system pervasive in nature: mechanical oscillators. Here, the mechanical oscillators are composed of the vibrations of two Be+ - Mg+ ion pairs in spatially separate locations. In addition, we show entanglement of a spin qubit with a spatially separated mechanical oscillator. These experiments demonstrate the creation of entangled states of a mixed species chain of four trapped ions, distribution of entanglement in an ion trap array, and sympathetic recooling of logical qubits. The techniques demonstrated in this experiment form core components for large-scale trapped-ion QIP. * supported by IARPA and the NIST Quantum Information Program +Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, 76100, Israel **Lockheed Martin Littleton, CO, U.S.A.

31. Simplifying quantum double Hamitonians using perturbative gadgets

Robert Koenig, California Institute of Technology

(Session 11 : Sunday from 9:45-10:15)

Abstract. Perturbative gadgets were originally introduced to generate effective k-local interactions in the low-energy sector of a 2-local Hamiltonian. Extending this idea, we present gadgets which are specifically suited for realizing Hamiltonians exhibiting non-abelian anyonic excitations. At the core of our construction is a perturbative analysis of a widely used hopping-term Hamiltonian. We show that in the low-energy limit, this Hamiltonian can be approximated by a certain ordered product of operators. In particular, this provides a simplified realization of Kitaev's quantum double Hamiltonians.

32. Status and recent progress of remote entanglement experiments with Barium-137 ions

Nathan Kurz, University of Washington

(Session 5 : Friday from 5:00-7:00)

Abstract. Because of its visible wavelength cooling transition, relatively high natural abundance, low-lying long-lived D states for shelving readout, and stable hyperfine qubit states spaced by 8.037 GHz, barium 137 represents an excellent ionic qubit candidate. We have built the necessary apparatus and developed techniques to trap and cool this ion. To date, we have demonstrated qubit initialization into the 6S1/2|F=1, mF=0> state by optical pumping, Rabi oscillations between 6S1/2|F=1, mF=0> and 6S1/2|F=2, mF=0> states, and the ability to state-selectively shelve the qubit to the 5D3/2 state for readout. Ultrafast pulses from a mode-locked Ti:Sapphire laser on resonance with the 6P3/2 transition have been shown to excite the ion with near unit probability on a sub-picosecond time scale. When tuned on resonance with the 6P1/2 transition, these pulses will entangle the spin state of the ion with the frequency of the emitted photonic qubit to be coupled into optical fiber and mode-matched on a beam splitter with the emitted photon of an identically prepared ion to generate a remote entangled ion pair. Long-term projects include the construction of a pulse programmer to drive the 8.037 GHz hyperfine transition with phase- and envelope-controlled pulses and construction of a thulium-doped fiber amplifier to increase optical power of the shelving laser at 1762 nm to improve readout speed.

33. Recent Progress in Quantum Computing with Optically Controlled Semiconductors

Thaddeus Ladd, Stanford University

(Session 1 : Thursday from 7:45-8:15)

Abstract. I will present two recent experimental results from the Yamamoto group at Stanford. The first is the rapid initialization and subsequent coherent manipulation of a single electron spin qubit in a self-assembled InAs quantum dot using ultra-fast laser pulses. This result demonstrates a complete single qubit gate set at the highest possible clock speed for the system. The second is the generation of indistinguishable single photons from two separate semiconductor sources based on isolated donor-bound excitons in ZnSe/ZnMgSe quantum wells. This result demonstrates a tool of great importance for linear optics quantum computing; it also shows promise for mass-production of homogeneous, optically connected semiconductor qubits. I will also briefly indicate some theoretical work on implementing all-optical quantum logic and designing a complete quantum computer architecture around these elements.

34. Stable Mode Sorting by Two-Dimensional Parity of Photonic Transverse Spatial States

Cody Leary, University of Oregon Dept. of Physics and Oregon Center for Optics

(Session 5 : Friday from 5:00-7:00)

Abstract. We describe a mode sorter for two-dimensional parity of transverse spatial states of light based on an out-of-plane Sagnac interferometer. Both Hermite-Gauss (HG) and Laguerre-Gauss (LG) modes can be guided into one of two output ports according to the two-dimensional parity of the mode in question. Our interferometer sorts HG_nm input modes depending upon whether they have even or odd order n + m; it equivalently sorts LG_lp modes depending upon whether they have an even or odd value of their orbital angular momentum l. It functions efficiently at the single-photon level, and therefore can be used to sort single-photon states. Due to the inherent phase stability of this type of interferometer as compared to those of the Mach-Zehnder type, it provides a promising tool for the manipulation and filtering of higher order transverse spatial modes for the purposes of quantum information processing. For example, several similar Sagnacs cascaded together may allow, for the first time, a stable measurement of the orbital angular momentum of a true single-photon state. Furthermore, as an alternative to well-known holographic techniques, one can use the Sagnac in conjunction with a multi-mode fiber as a spatial mode filter, which can be used to produce spatial-mode entangled Bell states and heralded single photons in arbitrary first-order (n + m = 1) spatial states, covering the entire Poincare sphere of first-order transverse modes.

35. Resolved sideband cavity cooling of 88Sr+

David Leibrandt, MIT

(Session 5 : Friday from 5:00-7:00)

Abstract. Cavity cooling is a method of laser cooling which uses coherent scattering into an optical cavity to cool particles [PRL 84, 3787 (2000)]. The particle to be cooled is placed in an optical cavity and excited with a laser tuned to the red of the cavity resonance. On average, scattering events which remove a photon from the laser and put it into the optical cavity cool the particle. The cooling limit is determined by the linewidth and cooperativity of the cavity, which can be designed to allow sub-Doppler cooling. Furthermore, because the cooling limit is independent of the energy level structure of the particle, cavity cooling is in principle applicable to particles without closed optical transitions [PRL 99, 073001 (2007); PRA 77, 023402 (2008)]. In this work we describe an experiment to study cavity cooling of a single 88Sr+ ion in the previously unexplored resolved sideband regime. The ion is confined in a linear RF Paul trap with motional frequencies of 0.86, 1.2, and 1.5 MHz. Large cavity cooling rates are attained by cooling near the 422 nm S1/2 to P1/2 optical dipole transition. We use a 5 cm long, near-confocal Fabry-Perot cavity with a linewidth of 164 kHz and a cooperativity of 0.25. The theoretical cavity cooling limit is 3 motional quanta, which is slightly lower than the Doppler cooling limit for 88Sr+ on the S1/2 to P1/2 transition. Experimental results demonstrate resolved sideband cavity cooling, but with a cavity cooling rate which is several times smaller than predicted by the theory.

36. Exploring exotic matter through the quantum manipulation of dipolar atoms

Benjamin Lev, University of Illinois at Urbana-Champaign

(Session 2 : Friday from 10:15-10:45)

Abstract. Highly magnetic atoms such as dysprosium offer the ability to create strongly correlated matter in both atomic physics and quantum optics settings. In addition, these atoms will form the key ingredient in novel devices possessing unsurpassed sensitivity and resolution for the microscopy of condensed matter materials. Our group aims to develop technology to perform laser cooling---and subsequent trapping in atom chips and optical lattices---of dysprosium. This will lead to three research projects: the investigation of quantum liquid crystal physics in 2D fermoinic dipolar lattices; the exploration of non-equilibrium quantum phase transitions in many body cavity QED; and the development of atom chip microscopy at the 10^-10 magnetic flux quantum level.

37. Optical lattice-based addressing and control of long-lived neutral-atom qubits

Nathan Lundblad, Joint Quantum Institute/NIST/Univ. of Maryland

(Session 2 : Friday from 10:45-11:15)

Abstract. Quantum computational platforms are driven by competing needs: the isolation of the quantum system from the environment to prevent decoherence, and the ability to control the system with external fields. For example, neutral-atom optical-lattice architectures provide environmental isolation through the use of "clock" states that are robust against changing external fields, yet those same external fields are inherently useful for qubit addressing. Here we demonstrate a technique to address a spatially dense field-insensitive qubit register. A subwavelength-scale effective magnetic-field gradient permits the addressing of particular "marked" elements of the lattice register, leaving unmarked qubits unaffected, with little worry about crosstalk or leakage. We demonstrate this technique with rubidium atoms, and show that we can robustly perform single-qubit rotations on qubits located at addressed lattice sites. This precise coherent control is an important step forward for lattice-based neutral-atom quantum computation, and is applicable to state transfer and qubit isolation in other architectures using field-insensitive qubits.

38. Quantum limited metrology with (β0〉 + 0β〉)/√2 states

Vaibhav Madhok, University Of New Mexico

(Session 5 : Friday from 5:00-7:00)

Abstract. We show how to achieve Heisenberg-limited sensitivity using states of the form (β0〉 + 0β〉)/√2 where | β〉 is a coherent state, in a two-arm interferometer. We describe appropriate measurements to achieve the above limit and discuss a scheme for making such states and measurements. We compare these states with "NOON" states and with other methods for achieving the Heisenberg-limited sensitivity.

39. Creation of Pure-State Photon Pairs and Single Photon Wavelength Translation in Photonic Crystal Fibers

Hayden McGuinness, University of Oregon

(Session 5 : Friday from 5:00-7:00)

Abstract. H. J. McGuinness and M. G. Raymer Oregon Center for Optics University of Oregon Tailor-made photonic crystal fibers (PCFs) allow for unprecedented control over important properties such as fiber dispersion, while also producing tight light confinement and nearly endlessly single mode behavior. It is possible to engineer a PCF which, with judicious choice of pumping scheme, spontaneously produces two-photon states with spectral correlations (“entanglement”) ranging from almost complete correlation to almost no correlation, without the need for spectral post filtering. Of special interest are pure, uncorrelated states, which could be a resource in quantum information processing. Under a different pumping scheme it is possible to translate photon states from one wavelength to another with theoretically one hundred percent efficiency and with no additional noise. The translation can occur over a few up to several hundred nanometers, for example, from telecom to visible wavelengths, and visa versa. We study these types of photon state creation and translation theoretically and experimentally.

40. Comparing quantum codes with a Clifford-circuit simulator

Adam Meier, University of Colorado at Boulder

(Session 5 : Friday from 5:00-7:00)

Abstract. The stabilizer formalism used in the proof of the Gottesman-Knill theorem allows classical computers to simulate efficiently a class of quantum circuits known as Clifford circuits. Within this class, the circuits needed to encode and decode additive quantum codes are of particular interest due to the large portion of time most designs for quantum computers spend on encoding and decoding. By modeling these processes on a classical computer under different error models, we can compare different quantum codes in a very practical and pertinent way. We present progress on our design of a fast Clifford-circuit simulator and some results for codes based on Galois fields of prime-power order. This work is in collaboration with K. Costello, B. Eastin, S. Glancy and E. Knill.

41. Quantum Control of Hyperfine Spins with Coherent Electromagnetic Fields

Seth Merkel, University of New Mexico

(Session 5 : Friday from 5:00-7:00)

Abstract. With long coherence times and well characterized control fields from the "quantum optics toolbox", cold neutral atoms provide a useful platform in which to explore methods and techniques for quantum information processing and quantum control. In this poster we study the use of coherent electromagnetic fields to control ultracold neutral alkali atoms in their electronic ground state. In cesium-133, the two hyperfine manifolds comprise a 16 dimensional state space that we can manipulate with rf/microwave magnetic fields. These fields lead to evolutions that are controllable in the Lie algebraic sense and have a relatively simple geometric structure. We look at three protocols for quantum control in this poster: state preparation (mapping a fiducial state to an arbitrary target state), generating unitary maps from state preparations, and robust state preparations using composite pulse techniques from NMR.

42. Control of Atomic Wave Functions in Optical Lattices

Brian Mischuck, University of New Mexico

(Session 5 : Friday from 5:00-7:00)

Abstract. The coherent transport of atoms in optical lattices is essential for quantum computation and quantum simulations involving controlled collisions between the atoms. Such coherence is typically limited by inhomogeneities and background fields. By applying the techniques of quantum control, we study protocols for robustly evolving the motional wave function in the ground band using applied external fields, and well-designed lattices. We examine explicit constructions for synthesizing specific unitary maps.

43. Ion Trap Photonic Quantum Networks

Christopher Monroe, JQI and University of Maryland

(Session 6 : Saturday from 10:15-11:00)

Abstract. The local manipulation and entanglement of nearby atomic ion qubits through their Coulomb interaction is now established as one of the most reliable ways to build entangled states. Trapped ions can also be coupled through a photonic channel, allowing for various remote probabilistic ion-ion entanglement protocols. Recent experiments have shown entanglement, a Bell inequality violation, teleportation, and operation of a two-qubit quantum gate between two ions separated by 1 meter. Despite the probabilistic nature of this ion/photon network, it can be efficiently scaled to much larger numbers of ions for distributed large-scale quantum computing and long-distance quantum communication, especially when accompanied by local Coulomb-mediated deterministic quantum gates. Future work will couple photons emitted from trapped ions into optical cavities, and perhaps interface trapped ion qubits with other optically-active qubits such as quantum dots.

44. Dynamical Control of Cs Atoms in an Optical Lattice using Microwave Manipulation

Enrique Montano, University of Arizona

(Session 5 : Friday from 5:00-7:00)

Abstract. Enrique Montaño, Jae Hoon Lee, Poul Jessen College of Optical Sciences, University of Arizona, Tucson, AZ Brian Mischuck, Ivan Deutch Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM Many schemes for quantum information processing in optical lattices require quantum coherent transport of the atomic qubits. Such transport usually relies on tunneling or dynamical changes in the lattice potential. We are developing a new, more controllable and potentially far more robust approach based on µw transitions between the sites of a spinor lattice. As a first step, we have demonstrated the ability to coherently transfer a qubit between well-defined vibrational states at neighboring lattice sites. We will explore the types of dynamical control this can lead to in our spinor lattice system. In a lattice composed of counter propagating beams with orthogonal, linear polarizations (the lin-90˚-lin configuration) a µw field will couple each site equally to its neighbors, and the spatial wavefunction of an atom will spread out over the sites in a continuous-time random walk. In a lin-theta≠90˚-lin lattice the symmetry is broken and each site is coupled to a single neighboring site either to the left or to the right, depending on the choice of theta. With this configuration, controlled transport over the entire lattice can be constructed from a series of pairwise couplings.

45. Induced Nonlinear Interactions and Parameter Estimation in Cold Atoms

Heather Partner, University of New Mexico

(Session 5 : Friday from 5:00-7:00)

Abstract. Recent progress in both theory and experiment have suggested that nonlinear interactions could provide improved uncertainty scaling for quantum precision measurements. It is our goal to translate these ideas into a functional experimental design, specifically in atomic magnetometry. We discuss our plans to perform double-passed continuous measurements on the collective spin of cooled atoms in a fountain configuration, with the aim of investigating improvements over single-pass geometries.

46. Quantum Fidelity and Thermal Phase Transitions

Haitao Quan, Los Alamos National Laboratory

(Session 1 : Thursday from 8:15-8:45)

Abstract. We study the quantum fidelity approach to characterize thermal phase transitions. Specifically, we focus on the mixed-state fidelity induced by a perturbation in temperature. We consider the behavior of fidelity in two types of second-order thermal phase transitions (based on the type of non-analiticity of free energy), and we find that usual fidelity criteria for identifying critical points is more applicable to the case of $\lambda$ transitions (divergent second derivatives of free energy). Our study also reveals that for fixed perturbations, the sensitivity of fidelity at high temperatures (where thermal fluctuations wash out information about the transition) is reduced. From the connection to thermodynamic quantities we propose slight variations to the usual fidelity approach that allow us to overcome these limitations. In all cases we find that fidelity remains a good pre-criterion for testing thermal phase transitions, and we use it to analyze the non-zero temperature phase diagram of the Lipkin-Meshkov-Glick model.

47. Magnetic Resonance Force Microscopy with spin noise

Shesha Raghunathan, University of Southern California

(Session 5 : Friday from 5:00-7:00)

Abstract. A promising technique for measuring single electron spins is magnetic resonance force microscopy (MRFM), in which a micro-cantilever with a permanent magnetic tip is resonantly driven by a single oscillating spin. If the quality factor of the cantilever is high enough, this signal will be amplified over time to the point that it can be detected by optical or other techniques. An important requirement, however, is that this measurement process occur on a time scale short compared to any noise which disturbs the orientation of the measured spin. We describe a model of spin noise for the MRFM system, and show how this noise is transformed to become time-dependent by going to the usual rotating frame. We simplify the description of the spin-cantilever system by approximating the cantilever wavefunction as a gaussian wavepacket, and show that the resulting approximation closely matches the full quantum behavior. We then examine the problem of detecting the signal for a cantilever with thermal noise and spin with spin noise, deriving a condition for this to be a useful measurement.

48. Source and Detector Technologies for Optical Quantum Information

Radhika Rangarajan, University of Illinois Urbana Champaign

(Session 5 : Friday from 5:00-7:00)

Abstract. Scalable quantum computation and quantum communication require the ability to create and detect multiple qubits with high fidelity. We report on our progress in developing both source and detector technologies high-brightness high-fidelity polarization entangled sources and high-efficiency photon-number resolving detectors. High-fidelity pulsed entanglement sources are essential for various quantum communication protocols, including quantum teleportation. By using temporal and spatial compensation, we can generate high-fidelity entanglement from pulsed and diode laser sources. We have demonstrated for the first time a robust, high quality, large aperture source of degenerate and non-degenerate Type-I entangled photons using BiBO, a highly nonlinear non-hygroscopic biaxial crystal, with a diode laser source. We also report on our progress in developing a high-fidelity Type-I source using an ultrafast pulsed source. On the detector front, we report on our current status in developing Visible Light Photon Counters (VLPCs) and Solid State Photo-Multipliers (SSPMs). VLPCs and SSPMs are photon number resolving detectors that have high quantum efficiency. Past measured efficiency for both the detectors were limited to less than 88% due to in-coupling losses. We are currently working to improve the overall performance of these detectors by a) reducing coupling losses and blocking infrared background, b) using improved low-noise electronics, and c) incorporating novel cryogenic designs.

49. Two-qubit quantum logic gates via optical Feshbach resonances in alkaline-earth-like atoms

Iris Reichenbach, University of New Mexico

(Session 2 : Friday from 11:15-11:45)

Abstract. The ability to implement quantum information processing in neutral atoms hinges critically on the ability to coherently control both the internal states and the interactions between two such atoms. We show that alkaline-earth-like atoms are uniquely suited to the task of quantum computing, due to their rich but controllable internal structure, including the nuclear spin, and their very narrow 1S0 -> 3P1 intercombination transition, which makes the application of optical Feshbach resonances possible. Optical Feshbach resonances allow for fine tuning of the interaction strength over a wide range, even making it possible to completely turn off the interaction, thus improving the coherence time. Theoretical modeling of the optical Feshbach resonance on the example of 171Yb shows their potential in the implementation of two qubit gates through nuclear spin exchange.

50. Quantum Information as Complementary Classical Information

Joseph Renes, Technical University of Darmstadt

(Session 5 : Friday from 5:00-7:00)

Abstract. Since the breakthrough by Calderbank, Shor, and Steane on the existence of quantum error-correcting codes, an oft-used notion in quantum information theory is that we can treat quantum information essentially as a strange combination of two types of classical information, pertaining to two complementary observables "amplitude" and "phase". Correcting errors afflicting either of these observables is sufficient to restore the quantum information to its original state. This approach is also appealing on a more fundamental level, as it suggests that the important differences between classical and quantum information processing originate from the phenomenon of complementarity, which is at the heart of the difference between classical and quantum mechanics. However, the central results of quantum information theory established recently, such as the achieveable rate of quantum communication over a noisy channel, follow a different approach termed decoupling which has a natural origin in the study of quantum cryptography. We show that the decoupling-based results can be concretely established in the complementary classical information picture. By adopting an information-theoretic approach to complementarity, we are able to construct entanglement distillation protocols which straightforwardly seek to distill amplitude and phase correlations without venturing into decoupling. This gives new and intuitive proofs of both the noisy channel coding theorem and the asymptotic rates of both secret-key distillation and state merging. Joint work with J.-C. Boileau.

51. Measurement-Based Quantum Computation in Realistic Spin-1 Chains

Joseph Renes, Technical University of Darmstadt

(Session 9 : Saturday from 3:30-4:00)

Abstract. The excitement surrounding meausrement-based quantum computation comes not just from the intriguing theoretical result that the power of a quantum computer can be attributed to the nature of the initial state, but also the more practical feature that it might be possible to find or engineer physical systems which would naturally provide such initial states as ground states. Since no system can be controlled or engineered perfectly, it is therefore vital to develop methods which characterize how suitable a given physical system is for this purpose. Moreover, this must be done in a way which circumvents the apparent need to evaluate the result for arbitrary computational measurement sequences, as these grow exponentially in number. We study this problem at the single-qubit level for the hybrid scheme recently introduced by Brennen and Miyake [1] using gapped one-dimensional spin-1 AKLT chains. Here individual qubit gates are performed by measurement while two-qubit gates are performed by dynamically coupling different chains. Brennen and Miyake describe a implementations using either atoms or polar molecules in optical lattices, where the gap is expected to help suppress decoherence. We show that the approach taken by Doherty and Bartlett to characterize the computational power of nearly-cluster state quantum computers [2] can be profitably adapted to this case, avoiding the exponential counting trap mentioned above. By numerical and perturbative analysis we find that arbitrary single-qubit operations can be faithfully executed over a reasonbly wide parameter range of bilinear-biquadratic Hamiltonians near the AKLT point. Furthermore, we find that the Doherty-Bartlett approach leads directly to the use of string order parameters, showing a connection between computational questions and the traditional theoretical study of condensed matter, where these parameters arise. Joint work with Stephen Bartlett, Gavin Brennen, and Akimasa Miyake. [1] Brennen and Miyake, Phys. Rev. Lett. 101, 010502 (2008). [2] Doherty and Bartlett, arXiv:0802.4314v1 [quant-ph].

52. Comparison between continuous wave and pulsed laser EQKD

Patrick Rice, Los Alamos National Lab

(Session 12 : Sunday from 11:15-11:45)

Abstract. Entangled quantum key distribution (EQKD) is a secure protocol that is based on fundamental quantum mechanics and is not vulnerable to these threats. The primary figure of merit for QKD systems is the ability to generate secret bits. However, to date, methods that have been developed to simulate the secret bit rate generation for EQKD systems have been limited by techniques that do not provide a complete description of the quantum state produced by the source. In this talk, I show a complete description and comparison of the secret bit rate for continuous-wave and pulsed laser EQKD systems. In particular, I highlight the relevant Poissonian and thermal photon statistics that affect the EQKD secret bit rate and use practical system parameters and configurations to show regimes where one expects optimal performance for each case.

53. Quantum State Reconstruction and Random Evolution

Carlos Riofrio, University of New Mexico

(Session 5 : Friday from 5:00-7:00)

Abstract. In order to perform quantum state reconstruction, the set of measured observables must be informationally complete. In this poster, we explore the performance of the reconstruction algorithm developed by Silberfarb et al. (PRL 95, 030402 (2005)) under the asumption that the quantum system undergoes random evolution. We show that in that case, although the measurements do not span the space of all density matrices, we are able to reconstruct the set of all pure states and almost-all mixed states with very high fidelities. We find that this is only possible after the inclusion of the physical constraint of positivity. Using as an example the quantum states stored in the ground-electronic hyperfine manifold (F=3) of an ensemble of Cs 133 atoms controlled by radio-frequency magnetic fields, we give a possible physical realization of this protocol provided that the dynamics exhibits a classically chaotic phase space. For this purpose, we chose the well studied quantum kicked top dynamics.

54. Non-Markovian Environmental Contributions to the Efficiency of Energy Transfer

Cesar Rodriguez-Rosario, Harvard University

(Session 10 : Saturday from 5:00-5:30)

Abstract. Non-Markovian environmental effects have been experimentally observed in the Fenna-Matthews-Olson photosynthetic complex, but their role is not understood. We study the dynamical contribution of the environment to the efficiency of energy transfer by considering a non-Markovian environment and its interplay with the system Hamiltonian. We focus on the role of memory effects of different orders in time, and their competition that affect the energy transfer by defining the efficiency of the non-Markovian process. This efficiency measure has applications to the study of the quantum transport efficiency and engineering of light-harvesting devices.

55. Practical entanglement swapping with imperfect parametric down conversion sources and inaccurate detectors

Artur Scherer, Institute for Quantum Information Science at the University of Calgary in Alberta, Canada

(Session 5 : Friday from 5:00-7:00)

Abstract. Entanglement swapping between photon pairs is a fundamental building block in schemes using quantum relays and quantum memories to overcome the range limits of long distance quantum key distribution. Its practical realization, however, suffers from experimental deficiencies due to imperfect entangled-pairs parametric down conversion (PDC) sources and inaccurate detectors. We provide a model for practical entanglement swapping that takes into account the multi-pair nature of all PDC sources as well as detector inefficiencies and dark count events. In particular, we calculate the resultant mixed entangled quantum state given two imperfect PDC sources and the result of a Bell measurement with faulty detectors. We investigate how the entanglement present in the final state of the remaining modes is affected by the practical deficiencies. This allows us to suggest the implications of the imperfections on schemes using entanglement swapping as a fundamental tool. To test the predictions of our model, comparison with experiments on entanglement swapping is provided. We gratefully acknowledge the support of General Dynamics Canada, iCORE, CIFAR, MITACS, NSERC and Quantum Works in preparing this work.

56. Heisenberg limited phase estimation with mode-entangled coherent states

Anil Shaji, The University of New Mexico

(Session 7 : Saturday from 1:00-1:30)

Abstract. We investigate phase estimation in a Mach-Zehnder type interferometer using the ``0BB0" state which is a mode-entangled state formed by superposing a state with the vacuum in the first arm of the interferometer and a coherent state in the second arm and another state with the coherent state in the first arm and the vacuum in the second. The quantum Cramer-Rao bound on the measurement uncertainty in the estimate of an unknown phase shift between the two arms of the interferometer scales inversely with the mean photon number in the 0BB0 state (Heisenberg limited scaling). We discuss how 0BB0 states can be created and also the measurements that must be performed on the output state of the interferometer in order to find the phase shift. We compare the performance of the 0BB0 states in phase estimation with that of ``N00N" states. In the presence of photon loss, using 0BB0 states instead of N00N states, lead to lower measurement uncertainties.

57. Towards an optimal algorithm for the hidden subgroup problem of dihedral group of order 2p (p: prime greater than 2)

Asif Shakeel, University of California at San Diego

(Session 5 : Friday from 5:00-7:00)

Abstract. Pretty Good Measurement is optimal for the problem of determining order two subgroups of dihedral group consisting of the identity and a reflection. Importantly, the work of Moore and Russell provides a representation theoretic proof of that. The main result of this paper is development of a multi-query algorithm that exploits the representation of dihedral group. Bacon, Van Dam and Childs and prior to them Regev show that the solution of the subset sum problem may be central to an algorithm implementing the Pretty Good Measurement. In our work, subset sum problem surfaces in the identification of irreducible sub-representations. Rest of the computations are explicitly shown in terms of Fourier transform on dihedral group, which is implemented by abelian transforms.

58. Optical Systems for Trapped Ion Fluorescence Collection

Gang Shu, University of Washington

(Session 5 : Friday from 5:00-7:00)

Abstract. Efficient and controllable ion fluorescence collection scheme is crucial for trapped ion qubit detection and single photon sources. We designed a non-imaging optical system to work directly with photon multiplier tubes (PMTs) for our new trap with a spherical mirror. We studied the possibility of collimating the diverging beam from the in-chamber spherical mirror by an external aspherical correlator, which may even enable efficient single-mode optical fiber coupling. In order to achieve efficient and reliable detections of fluorescence from two or more adjacent ions, we carefully characterized our Andor Luca EMCCD camera and developed a LabView program to reduce the image noise and count photons from customized sensor areas, with which we get satisfactory quiet images and fast accurate counts.

59. Renewing and Uniting Two Challenges of John von Neumann and Richard Feynman: Atomic-Resolution Biomicroscopy and Simulating Quantum Physics with Computers

John Sidles, University of Washington

(Session 7 : Saturday from 1:30-2:00)

Abstract. In two renowned lectures, Richard Feynman (in 1959) challenged mathematicians, scientists, and engineers to "see the individual atoms" in biological molecules and (in 1982) to "make a simulation of nature [that is] quantum mechanical." An earlier statement of these same challenges can be found in a 1946 letter from John von Neumann to Norbert Weiner. The status of these two challenges is reviewed. Atomic-resolution biomicroscopy is treated as a problem in quantum communication whose fundamental quantum limits can be calculated by combining Feynman's formalism for quantum measurement with Shannon's formalism for information channel capacity. Modern advances in quantum information theory and simulation science suggest avenues for further analysis. The assessment concludes that both of von Neumann's and Feynman's challenges are rapidly approaching scientific and technological feasibility.

60. Experimental Quantum Control of the 133Cs Hyperfine Ground Manifold

Aaron Smith, University of Arizona

(Session 5 : Friday from 5:00-7:00)

Abstract. Aaron Smith, Brian Anderson, and Poul Jessen College of Optical Sciences, University of Arizona, Tucson, AZ In recent work our group has demonstrated complete quantum control and quantum state reconstruction for the F = 3 irreducible subspace within the electronic ground hyperfine manifold of 133Cs. The control Hamiltonian for this system was generated by a time dependent magnetic field and a laser induced AC Stark shift, where the latter necessarily brings a penalty in terms of decoherence from spontaneous photon scattering. We are currently working to extend control and measurement to the full ground hyperfine manifold, by driving the atom solely with DC, radiofrequency and microwave magnetic fields [S. Merkel et al, PRA 78, 023404 (2008)]. We will report on experimental progress towards this goal.

61. Optical One-Way Barrier for Atoms

Daniel Steck, University of Oregon

(Session 5 : Friday from 5:00-7:00)

Abstract. We demonstrate an asymmetric optical potential barrier for ultracold ⁸⁷Rb atoms using laser light tuned near the D₂ transition. Such a one-way barrier, where atoms impinging on one side are transmitted but reflected from the other, is a literal realization of Maxwell's demon and has important implications for cooling atomic species not amenable to standard laser-cooling techniques. In our experiment, atoms are confined to a far-detuned dipole trap consisting of a single focused Gaussian beam, which is divided near the focus by the barrier. The one-way barrier consists of two focused laser beams oriented normal to the dipole trap. The first barrier beam is tuned between the F = 1 → F' and the F = 2 → F' families of hyperfine transitions, and presents a barrier only for atoms in the F = 2 ground state, while letting F = 1 atoms pass. The second beam pumps the atoms to F = 2 on the reflecting side of the barrier, thus producing the asymmetry. We study experimentally the reflection and transmission dynamics of atoms in the presence of the one-way barrier.

62. A scalable, high-speed measurement-based quantum computer using trapped ions

Rene Stock, University of Toronto

(Session 5 : Friday from 5:00-7:00)

Abstract. A scalable, high-speed measurement-based quantum computer using trapped ions R. Stock, D. F. V. James Department of Physics, University of Toronto, Canada The tremendous progress achieved in the control of trapped ions has recently led to the creation of an entangled state of eight ions. The entanglement of many more ions for large-scale quantum computer seems very feasible. However, the slow entangling gate and slow readout of ions hinder fast operations and will limit the practical use of a future ion-trap quantum computer. One-way (i.e. measurement-based) quantum computing architectures offer a way out by parallelizing the slow entangling operations to create a many-body entangled state and by processing quantum information via fast readout and measurement of qubits. In this work, we investigate the challenges involved in developing a high-speed one-way quantum-computing scheme for ions. We devise an architecture for the creation of many-body entangled states and show how a 3D cluster state suitable for error correction can be efficiently mapped to 2D ion-trap architectures. We propose the projective measurement of ions via multi-photon photoionization for nanosecond measurement and operation, and discuss the viability of such a scheme for Ca ions.

63. Practical quantum metrology with Bose-Einstein condensates

Alexandre Tacla, University of New Mexico

(Session 5 : Friday from 5:00-7:00)

Abstract. We analyze in detail the recently proposed experiment [Boixo et al., Phys. Rev. Lett. 101, 040403 (2008)] for achieving better than 1/n scaling in a quantum metrology protocol using a two-mode Bose-Einstein condensate of n atoms. There were several simplifying assumptions in the original proposal that made it easy to see how a scaling approaching 1/n^3/2 may be obtained. We look at these assumptions in detail to see when they may be justified. We present numerical results that confirm our theoretical predictions for the effect of the spreading of the BEC wave function with increasing n on the scaling. Numerical integration of the coupled Gross-Pitaevskii equations for the two mode BEC also shows that the assumption that the two modes share the same spatial wave function is justified for a length of time that is sufficient to run the metrology scheme.

64. Channel-Optimized Quantum Error Correction

Soraya Taghavi, University of Southern California

(Session 8 : Saturday from 4:30-5:00)

Abstract. We develop a theory for finding quantum error correction (QEC) procedures which are optimized for given noise channels. Our theory accounts for uncertainties in the noise channel, against which our QEC procedures are robust. We demonstrate via numerical examples that our optimized QEC procedures always achieve a higher channel fidelity than the standard error correction method, which is agnostic about the specifics of the channel. Our main novel finding is that in the setting of a known noise channel the recovery ancillas are redundant for optimized quantum error correction. We show this using a general rank minimization heuristic and supporting numerical calculations. Therefore, one can further improve the fidelity by utilizing all the available ancillas in the encoding block.

65. No-Go Results for a 2D Quantum Memory Based on Stabilizer Codes

Barbara Terhal, IBM Research

(Session 3 : Friday from 1:15-2:00)

Abstract. We study the possibility of a self-correcting quantum memory based on stabilizer codes with geometrically-local stabilizer generators. We prove that the distance of such stabilizer codes in D dimensions is bounded by O(L^{D-1}) where L is the linear size of the D-dimensional lattice. In addition, we prove that in D=1 and D=2, the energy barrier separating different logical states is upper-bounded by a constant independent of L. This shows that in such systems there is no natural energy dissipation mechanism which prevents errors from accumulating. Our results are in contrast with the existence of a classical 2D self-correcting memory, the 2D Ising ferromagnet.

66. Spin squeezing in a double-pass optical-feedback geometry

Collin Trail, University of New Mexico

(Session 5 : Friday from 5:00-7:00)

Abstract. Squeezed collective atomic spin states can be generated using the Faraday effect, by passing light through an atomic sample twice, imprinting the spin component along the direction of the propagation of light on to the light on the first pass, and rotating the atoms proportionally to this spin component on the second pass, thus creating an effective nonlinearity (M. Takeuchi et al., 2005, Phys. Rev. Lett. 94, 023003). The squeezing produced is reduced by loss of light still entangled to the atoms. We show how this scheme can be improved by a quantum eraser effect, where measuring the light properly reduces it's entanglement to our atomic sample. Furthermore, we present estimates for the reduction in squeezing due to spontaneous emission, by approximating the distribution of the collective variables by a Gaussian.

67. Designing Optimal States and Transformations for Quantum Optical Communication and Metrology

Dmitry Uskov, Tulane/LSU

(Session 9 : Saturday from 4:30-5:00)

Abstract. Entangled states of light are in great demand in quantum technology today. Photonic quantum communication, information processing, and metrology are all based on exploiting special properties of non-classical multipath entangled states. Generation of such states and quantum operations on them require effective photon-photon interaction which may be produced using ancilla modes and projective measurements. We will report on our study of optimal implementations of optical measurement-assisted transformations of non-classical photonic states, by performing numerical optimization of the fidelity, success probability, and Fisher-information functions. For the first time, we have provided convincing numerical evidence that for the basic CNOT (CS) gate the maximal success probability is S = 2/27. We have numerically verified a hypothesis that maximal success probability is achieved using a minimal level of ancilla resource (for NS, CS and Toffoli gates). As a proof of principle, we demonstrated that heuristic methods of constructing optimal optical schemes are quite limited when it comes to complicated 3- and more qubit gates: using the Toffoli gate, we found a scheme that uses fewer ancilla photons and provides better success probability than the best previously known scheme.The numerical optimization method was used to address the error-correction problem. For a particular error-correction scheme, the encoding-decoding gates required construction of a CS gate coupling hyper-entangled qubits. The solution found numerically requires only three ancilla photons while providing maximal success probability. We will also report on our numerical results for optimization of Heisenberg-limited quantum phase metrology.

68. Verifying multi-partite mode entanglement of W states

Steven van Enk, University of Oregon

(Session 4 : Friday from 3:30-4:00)

Abstract. We construct a method for verifying mode entanglement of N-mode W-states. The ideal W-state contains exactly one excitation symmetrically shared between N modes, but our method takes the existence of higher numbers of excitations into account, as well as the vacuum state and other deviations from the ideal state. Moreover, our method distinguishes between full N-party entanglement and states with M-mode entanglement with M

69. Resource Handling for Quantum Networks of Arbitrary Topology

Rodney Van Meter, Keio University

(Session 8 : Saturday from 3:30-4:00)

Abstract. To date, research on entangled quantum networks has primarily focused on an abstract model consisting of a linear chain of repeaters, with a power of two number of hops of identical length and quality. We are analyzing the behavior of more complex network topologies, with more than two end nodes competing to communicate across shared links. We compare three resource management disciplines, hop-by-hop teleportation, nested entanglement swapping, and graph state-based bipartite communication. We discuss quantum equivalents to the classical network concepts of spatially and temporally multiplexed circuit switching, and packet switching. We show cases in which multiplexing raises the aggregate communication rate, and cases in which graph states help the system reach the bisection bandwidth.

70. Cryogenic surface electrode ion traps for quantum computation

Shannon Wang, Massachusetts Institute of Technology

(Session 5 : Friday from 5:00-7:00)

Abstract. Dense arrays of trapped ions provide one way of scaling up ion trap quantum information processing. However, miniaturization of ion traps is currently limited by sharply increasing motional state decoherence at sub-100μm ion-electrode distances. The ability to address individual ions and perform quantum operations in such dense, small ion traps is another important challenge. We present a cryogenic ion trap system using microfabricated traps, which addresses the heating and addressing issues. In these traps, a single trapped Sr+ ion is characterized using the temperature dependence between 10-100 K to elucidate the heating mechanism. At 6 K, heating rates are observed to be as low as two quanta per second with the ion located 100 μm above the surface; this heating rate is more than two orders of magnitude lower than the best results obtained in a comparable trap at room temperature. The cryogenic system enable novel use of superconductors as flux shields to stabilize the magnetic field, and the low heating rates enable high fidelity quantum operations. We performed coherent operations on the internal and motional state and found the classical fidelity of a Controlled-NOT gate to be 95%. We also performed some initial experiments on full process tomography of the CNOT gate. Finally, we have developed a scheme to create a local magnetic field gradient by integrating current sources onto a microfabricated surface-electrode trap, and obtained some initial experimental results on individual addressing of ions. The low heating rates and individual addressing in a cryogenic surface-electrode ion trap makes it a viable candidate system for realizing scalable quantum computation.

71. Quantum computing with atoms in a 3D optical lattice

David Weiss, Penn State

(Session 2 : Friday from 8:30-9:15)

Abstract. We have demonstrated trapping and imaging of 250 single atoms in a 3D optical lattice. The 5 micron lattice spacing is large enough that individual atoms can be addressed using lasers and microwaves in a way that does not affect the quantum coherence of other atoms. Our goal is to use these trapped atoms as qubits. So far, we fill a random half of the lattice sites, but a combination of site-selective state changes and state-selective lattice translations should allow us to verifiably fill all vacancies. We will describe our experiments to date and our plans for entangling atoms and implementing a neutral atom quantum computer.

72. Correlated photon pairs from a warm atomic ensemble of Rubidium

Tommy Willis, Joint Quantum Institute, University of Maryland

(Session 5 : Friday from 5:00-7:00)

Abstract. We produce polarization-entangled correlated photon pairs from a warm atomic vapor of Rubidium using a spontaneous four-wave mixing interaction. In the experiment we apply two pump lasers (795 nm, 1324 nm) to the atomic ensemble and observe the cross-correlation function of two photons (780 nm, 1367 nm) emitted into the phase-matched direction. We see that the pairs have non-classical polarization correlation. The temporal and spectral character of the photon pairs can be modified by changing the absorption/dispersion of the atomic vapor at the wavelength of the generated pairs.

73. Raman Optical Comb Generation in Hydrogen-filled Hollow Core Fiber

Chunbai Wu, Oregon Center for Optics, University of Oregon

(Session 5 : Friday from 5:00-7:00)

Abstract. Title: Raman Optical Comb Generation in Hydrogen-filled Hollow Core Fiber Chunbai Wu, Erin Mondloch, Cade Gledhill and M. G. Raymer Oregon Center for Optics, University of Oregon Abstract: Frequency comb generation has attracted many research efforts in recent years, with applications such as optical atomic clocks and attosecond pulse synthesis. In addition, super-continuum generation of light has been demonstrated in specially structured photonic crystal fibers. Recently, researchers at the University of Bath developed a large hollow-core (single-defect) fiber with Kagome- or square-lattice pattern cladding. [1] These fibers show high transmission spectra spanning from ultra-violet to infrared. High pressure hydrogen gas is filled in the fiber's hollow core throughout the length of the fiber, and up to 45 vibrational and rotational Raman transition lines of molecular hydrogen are observed following a high-power 10-ns IR laser pulse being coupled into the fiber. [2] The question outstanding is to what extent are the phases of these optical comb lines correlated. Perfect correlation would in principle allow deterministic phase tailoring to create attosecond pulses. A preliminary simplified model calculation indicated a high degree of correlation would exist. [2] To understand better this cascaded, coherent stimulated Raman scattering (SRS), we solve the quantum mechanical model of SRS [2,3] for the temporal evolution of first-order Stokes and anti-Stokes fields at the end of the fiber, as well as the spatial evolution of molecular polarization (collective vibrational state) stored in the hydrogen gas. (Higher order Raman lines are neglected from the equations because they are much weaker.) In the high-gain transient regime, the degree of anti-correlation between complex Stokes and anti-Stokes fields is calculated and found to equal unity throughout the duration of the pulses, even at large phase mismatch of wave vectors induced by the dispersion of the fiber. This result indicates that the generated first-order Stokes and anti-Stokes fields are nearly perfectly phase anti-correlated, although the absolute value of the phase is random due to the spontaneous initiation of the SRS process. Stokes and anti-Stokes fields are generated with opposite spectral phase. Further analysis on higher order Stokes and anti-Stokes fields is needed. In experiment, we collaborate with researchers at University of Bath (who produce the fiber). We designed a high-pressure gas chamber for filling the fiber at its ends, by using commercially-available "Swagelok" fittings. We have observed multiple Raman scattering lines from hydrogen and the team is now attempting to verify the phase coherence between them. Reference: [1] F. Couny, F. Benabid, P. S. Light, Opt. Lett. 31, 3574 (2006) [2] F. Couny, F. Benabid, P. J. Roberts, P. S. Light, M. G. Raymer, Science 318, 1118 (2007) [3] S. Ya. Kilin, Europhys. Lett. 5, 419 (1988)

74. Quantum communication with zero-capacity channels

Jon Yard, Los Alamos National Laboratory

(Session 12 : Sunday from 10:45-11:15)

Abstract. A quantum channel models a physical process in which noise is added to a quantum system via interaction with its environment. Protecting quantum systems from such noise can be viewed as an extension of the classical communication problem introduced by Shannon sixty years ago. A fundamental quantity of interest is the quantum capacity of a given channel, which measures the amount of quantum information which can be protected, in the limit of many transmissions over the channel. In this talk, I will show that certain pairs of channels, each with a capacity of zero, can have a strictly positive capacity when used together, implying that the quantum capacity does not completely characterize a channel's ability to transmit quantum information. As a corollary, I will show that a commonly used lower bound on the quantum capacity - the coherent information, or hashing bound - is an overly pessimistic benchmark against which to measure the performance of quantum error correction because the gap between this bound and the capacity can be arbitrarily large. This is joint work with Graeme Smith (IBM), published in the Sept. 26 issue of Science.

75. Entanglement verification based on SIC-POVM measurement

Jun Yin, University of Oregon

(Session 5 : Friday from 5:00-7:00)

Abstract. Maximum likelihood estimation and Bayesian methods are applied and compared to acquire certain properties (e.g., purity and entanglement) of a four-qubit system from finite measurement records. In particular, we assume a SIC-POVM is measured on each qubit. We tentatively propose a criterion for the number of SIC-POVM measurements needed to obtain reliable estimates of purity, the amount of multi-partite entanglement, and whether the state is entangled or not.

76. Duality theorem and topological properties in local stabilizer codes

Beni Yoshida, Massachusetts Institute of Technology

(Session 8 : Saturday from 5:00-5:30)

Abstract. Beni Yoshida
Massachusetts Institute of Technology

Abstract.

Topological codes offer the possibility of a naturally fault-tolerant quantum memory, and significant progress has been made with theoretical constructions in four dimensions. However, recent work (Bravyi and Terhal; Kay and Colbeck) has ruled out the possibility of such memories in two-dimensions, and left an open question about three-dimensional topological codes. Specifically, Bravyi and Terhal show that the distance of geometrically local stabilizer codes in a D-dimensional lattice of volume L^D is bounded above by O(L^{D - 1}).

Here, we present a new approach to the problem, which sharpens these bounds, by limiting consideration to topological codes whose stabilizers are geometrically local and have translational symmetry. Using this physically reasonable assumption, and assuming that the number of logical qubits is a small number which is independent of the lattice size, we find that the logical qubits must obey a duality theorem, whereby each logical qubit may be described by a pair of weight O(L^a) and O(L^{D - a}) logical operators. This gives a full set of relations between all logical operators. It follows from this theorem that the distance of such codes is bounded above by O(Lⁿ) for 2n- and (2n+1)-dimensional lattices.

This non-trivial duality clearly distinguishes systems of even and odd dimension. One surprising consequence is that for certain definitions of topological protection, encodings are possible only in systems of even dimension. This is consistent with a fact in topological quantum field theory, that the quantum Hall effect can occur only in systems of even dimension. We illustrate the implications of this observation by showing that on a two-dimensional Bravais lattice with a small number of encoded qubits, all the logical operators have O(L) weight, such that all the logical qubits are topologically protected from local errors. This also allows us to directly relate the number of encoded qubits with the topological entropy, providing insights which will be useful in designing gapped Hamiltonians with topological properties which may be useful for quantum memories.

77. Optimal experiment design for parameter estimation as applied to dipole- and exchange-coupled qubits

Kevin Young, University of California - Berkeley

(Session 7 : Saturday from 2:00-2:30)

Abstract. We consider the problem of quantum parameter estimation with the constraint that all measurements and initial states are separable. Two qubits are presumed coupled through the dipole and exchange interactions. The resulting Hamiltonian generates a unitary evolution which, when combined with arbitrary single-qubit operations, contributes to a universal set of quantum gates. However, while the functional form of the Hamiltonian is known, a particular experimental realization depends on several free parameters - in this case, the position vector relating the two qubits and the magnitude of the exchange interaction. We use the Cramer-Rao bound on the variance of any point estimator to construct an optimal series of experiments to estimate these free parameters. Our method of transforming the constrained optimal estimation problem into a convex optimization is powerful and widely applicable to other systems.

78. Generalized Concatenated Quantum Codes

Bei Zeng, Massachusetts Institute of Technology

(Session 3 : Friday from 2:00-2:30)

Abstract.

Quantum error-correcting codes play a central role in quantum computation and quantum information. While considerable understanding has now been obtained for a broad class of quantum codes, almost all of this has focused on stabilizer codes, the quantum analogues of classical additive codes. Nevertheless, there are a few known examples of nonadditive codes which outperform any possible stabilizer code. In previous work (a talk given at SQuInT 2008), my colleagues and I introduced the codeword stabilized ('CWS') quantum codes framework for understanding additive and nonadditive codes. Within this framework we found good new nonadditive codes using exhaustive or random search. However, these new codes have no obvious structure to generalize to other cases -- no nonbinary nonadditive code which outperforms any additive code has ever been found since the search space is getting too large. A systematical understanding of constructing good nonadditive CWS codes is still lacking.

In this work we provide a systematical method of constructing nonadditive CWS codes by introducing the concept of generalized concatenated quantum codes. Compared to the usual concatenated quantum code construction, the role of the basis vectors of the inner quantum code is taken on by subspaces of the inner code.

Using this generalized concatenation method, we systematically construct families of single-error-correcting nonadditive CWS codes, in both binary and nonbinary cases, which outperform any stabilizer codes. Particularly, we construct a ((90,2^{81.825},3)) qubit code as well as a ((840,3^{831.955},3)) qutrit code, which is the first known nonbinary nonadditive code that outperforms any stabilizer codes. For large block lengths, we show that these families of nonadditive codes asymptotically achieve the quantum Hamming bound. What is more, our new method can also be used to construct stabilizer codes. We show that many good stabilizer codes, e.g. quantum Hamming codes, can be constructed this way. Moreover, we found new stabilizer codes with better parameters than previously known, e.g. a [[36,26,4]] qubit code.

Based on joint work with Markus Grassl, Peter Shor, Graeme Smith, and John Smolin.