Southwest Quantum Information and Technology

Tenth Annual Meeting, February 14-17, 2008
University of New Mexico, Santa Fe, New Mexico

Full Program | Thursday Tutorials | Friday | Saturday | Sunday

SESSION 14: Breakout II - Quantum Information A
Session Chair:
12:00-12:30	Bei Zeng, Massachusetts Institute of Technology
	Codeword Stabilized Quantum Codes
	Abstract. Quantum error correction 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. However, such codes are strictly suboptimal in some settings---there exist nonadditive codes which encode a larger logical space than possible with a stabilizer code of the same length and capable of tolerating the same number of errors. There are only a handful of such examples, and their constructions have proceeded in an ad hoc fashion, each code working for seemingly different reasons. We present a unifying approach to quantum error correcting code design, namely, the codeword stabilized quantum codes, that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. In addition to elucidating nonadditive codes, this unified perspective promises to shed new light on additive codes as well. Our codes are described by two objects: First, the codeword stabilizer that can be taken to describe a graph state, and which transforms the quantum errors to be corrected into effectively classical errors. And second, a classical code capable of correcting the induced classical error model. With a fixed stabilizer state, finding a quantum code is reduced to finding a classical code that corrects the (perhaps rather exotic) induced error model. We use this framework to generate new codes with superior parameters ((n,K,d)) to any previously known, the number of physical qubits being n, the dimension of the encoded space K, and the code distance d. In particular, we find ((10,18,3)) and ((10,20,3)) codes. We also show how to construct encoding circuits for all codes within our framework.
12:30-13:00	Raisa Karasik, University of California, Berkeley
	Decoherence-free subspaces and incoherently generated coherences
	Abstract. A decoherence-free subspace (DFS) is a collection of states that is immune to the dominant noise effects created by the environment. DFS is usually studied for states involving two or more particles and is considered a prominent candidate for quantum memory and quantum information processing. We present rigorous criteria for the existence of DFS in finite-dimensional systems coupled to the Markovian reservoirs. This allows us to identify a new special class of decoherence free states that relies on rather counterintuitive phenomenon, which we call an “incoherent generation of coherences.” We provide examples of physical systems that support such states.
13:00-13:30	Sergio Boixo, University of New Mexico
	Quantum-limited metrology with product states
	Abstract. We study the performance of generalized quantum metrology protocols that involve estimating an unknown coupling constant in a nonlinear k-body Hamiltonian. We obtain the theoretical lower bound on the uncertainty in the estimate of the parameter. For arbitrary initial states, the lower bound scales as 1/n^k, and for initial product states, it scales as 1/n^(k-1/2). We show that the latter scaling can be achieved using simple, separable measurements. We analyze in detail the case of a quadratic Hamiltonian (k=2), implementable with Bose-Einstein condensates. We formulate a simple model, based on the evolution of angular-momentum coherent states, which explains the O(n^(-3/2)) scaling for k=2; the model shows that the entanglement generated by the quadratic Hamiltonian does not play a role in the enhanced sensitivity scaling. We show that phase decoherence does not affect the O(n^(-3/2)) sensitivity scaling for initial product states.
13:30-14:00	Ali Rezakhani, University of Southern California Center for Quantum Information Science and Technology
	Superoperator Dynamics Approach for Identification and Control of Hamiltonian Systems
	Abstract. Characterization and control of open quantum systems are among the fundamental tasks/challenges in quantum physics and quantum information science. In particular, there is much interest in the identification of quantum systems which have unknown interactions with their embedding environment. Quantum process tomography is known to be a general method for characterization of quantum dynamical processes, through an inversion of experimental data obtained from a complete set of state tomographies. In an earlier work we demonstrated that the utilization of quantum error detection techniques leads to the direct estimation of all independent parameters of a superoperator. Motivated by that approach, we now introduce new dynamical equations for superoperators â€“ leading to novel ways for Hamiltonian identification and control of open quantum systems. As an application, we show that this method could lead to efficient identification of certain properties of some sparse Hamiltonians. We also briefly discuss some possible applications to open-loop/learning control of Hamiltonian systems.