Southwest Quantum Information and Technology

Eleventh Annual Meeting, February 19-22, 2009
Seattle, Washington

Full Program | Thursday | Friday | Saturday | Sunday

SESSION 9: Breakout II - Resources for Quantum Information
Session Chair:
3:30-4:00	Joseph Renes, Technical University of Darmstadt
	Measurement-Based Quantum Computation in Realistic Spin-1 Chains
	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].
4:00-4:30	Xie Chen, Massachusetts Institute of Technology
	Gapped Two-body Hamiltonian whose Unique Ground State is Universal for One-way Quantum Computation
	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.
4:30-5:00	Dmitry Uskov, Tulane/LSU
	Designing Optimal States and Transformations for Quantum Optical Communication and Metrology
	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.
5:00-5:30	Samuel Gasster, The Aerospace Corporation
	Resource Requirements for Fault-Tolerant Quantum Simulation: The Transverse Ising Model Ground State
	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.