Southwest Quantum Information and Technology

Thirteenth Annual Meeting, February 17-20, 2011
Boulder, Colorado

Full Program | Thursday | Friday | Saturday | Sunday | All Sessions

SESSION 2: Quantum Error Correction
Session Chair:
5:15pm-6:00pm	Sergey Bravyi, IBM Watson Research Center
	Subsystem and stabilizer quantum codes with spatially local generators
	Abstract. Fault-tolerant quantum computation based on 2D topological quantum codes has received a considerable attention lately since it can be implemented on quantum machines with a geometrically local architecture. To better understand the potential of topological codes we derive upper bounds on the parameters of quantum codes that stem from the spatial locality constraint and find families of codes that achieve these bounds. Our analysis applies to both subspace and subsystem quantum codes. We also discuss topological subsystem codes (TSCs) proposed recently by Bombin. These codes require only the measurement of two-qubit nearest-neighbor operators for error correction. We demonstrate that TSCs can be viewed as generalizations of Kitaev's honeycomb model to 3-valent hypergraphs. This new connection provides a systematic way of constructing TSCs and analyzing their properties. Furthermore, we propose and implement some candidate decoding algorithms for one particular TSC assuming perfect error correction. Our Monte Carlo simulations indicate that this code, which we call the five-squares code, has a threshold against depolarizing noise of at least 2%.
7:30pm-8:00pm	Dave Bacon, University of Washington
	Making Error Correction Spatially Local
	Abstract. In quantum error correction quantum information is encoded across multiple subsystems in such a way that one can diagnose and fix the most likely errors that occur to the system. This error correcting step is achieved by performing a measurement that does not disturb the encoded quantum information but does diagnose what error has occurred on the system. These error diagnosing measurements are often, but not always, of observables that are non-trivial over nearly the entire quantum system containing the encoded quantum information. An example of the contrary case are topological and color quantum codes, where the diagnosing measurements involve only a small number of spatially local subsystems (that is, involve only measurements over a constant sized neighborhood on some D-dimensional lattice.) Here we show how to convert a large class of quantum error correcting codes, all stabilizer codes, into spatially local codes. These codes are subsystem codes derived from measurement based quantum computing and have properties similar to toric and surface codes.
8:00pm-8:30pm	Bryan Fong, HRL Laboratories, LLC
	Exchange-Only Computation, Leakage Reduction, and Dynamical Decoupling in the Three-Qubit Decoherence Free Subsystem
	Abstract. We describe exchange-only universal quantum computation, leakage reduction, and dynamical decoupling in the three-qubit decoherence free subsystem (DFS). We discuss the angular momentum structure of the DFS, the proper forms for the DFS CNOT and leakage reduction operators in the total angular momentum basis, and new exchange-only pulse sequences for the CNOT and leakage reduction operators. While the search for sequences is performed numerically using a genetic algorithm, the final solutions found are exact, with closed-form expressions. We also show that exchange pulses are sufficient to decouple the three-qubit DFS from its environment and describe bang-bang pulse sequences for decoupling the DFS from its bath. Sponsored by United States Department of Defense.
8:30pm-9:00pm	Gerardo Paz, University of Southern California
	Concatenated Stabilizer Dynamical Decoupling
	Abstract. We show how to integrate concatenated dynamical decoupling (CDD) techniques with quantum error correction (QEC) codes: the two main strategies to protect quantum information from the decoherence induced by unwanted interaction with the environment. It has been shown that CDD can be used as a lower level protection layer against decoherence and improves the effective error rate of a physical gate, provided one assumes certain locality conditions (local bath assumption) [Ng, Lidar, Preskill, arXiv:0911.3202]. The typical CDD protocol uses pulses from a group of non-commuting operators to decouple to arbitrary order, in the language of Magnus expansion, the state one wants to protect from the environment. In this work, in the same spirit as [Lidar, Phys. Rev. Lett. 100,160506 (2008)], we show how decouple a state encoded in some stabilizer QEC code to arbitrary order by applying pulses from the stabilizer group of the QEC code used. We demonstrate the technique for concatenated and non-concatenated QEC codes and show that, in contrast to the CDD case, (i) one can omit the local bath assumption, and (ii) has the freedom of introducing a fixed evolution for the protected quantum state. We show how to decouple a multiqubit state with a non-local system bath to arbitrary order (dictated by the distance of the QEC code).