Southwest Quantum Information and Technology

Sixteenth Annual Meeting, February 20-22, 2014
Santa Fe, New Mexico

Full Program | Thursday | Friday | Saturday | All Sessions

SESSION 9a: Break-out 1: Quantum Computation and Fault Tolerance
4:00pm - 4:30pm	Itay Hen, University of Southern California
	Period Finding with Adiabatic Quantum Computation
	Abstract. We outline an efficient quantum-adiabatic algorithm that solves Simon's problem, in which one has to determine the `period', or xor-mask, of a given black-box function. We show that the proposed algorithm is exponentially faster than its classical counterpart and has the same complexity as the corresponding circuit-based algorithm. Together with other related studies, this result supports a conjecture that the complexity of adiabatic quantum computation is equivalent to the circuit-based computational model in a stronger sense than the well-known, proven polynomial equivalence between the two paradigms. We also discuss the importance of the algorithm and its implications for the existence of an optimal-complexity adiabatic version of Shor's integer factorization algorithm and the experimental implementation of the latter.
4:30pm - 5:00pm	Joydip Ghosh, University of Calgary
	Understanding the effects of leakage in superconducting quantum error detection circuits
	Abstract. The majority of quantum error detection and correction protocols assume that the population in a qubit does not leak outside of its computational subspace. For many existing approaches, however, the physical qubits do possess more than two energy levels and consequently are prone to such leakage events. Analyzing the effects of leakage is therefore essential to devise optimal protocols for quantum gates, measurement, and error correction. In this talk, I discuss the role of leakage in a two-qubit superconducting quantum error detection circuit. We simulate the repeated ancilla-assisted measurement of a single Z operator for a data qubit, record the outcome at the end of each measurement cycle, and explore the signature of leakage events in the obtained readout statistics. An analytic model is also developed that closely approximates the results of our numerical simulations. We find that leakage leads to destructive features in the quantum error detection scheme, making additional hardware and software protocols necessary.
5:00pm - 5:30pm	Mauricio Gutierrez, Georgia Institute of Technology
	The effect of realistic noise models on quantum error correction thresholds
	Abstract. Classical simulations of noisy stabilizer circuits are often used to estimate the threshold of a quantum error-correcting code (QECC). In this context, it is common to model the noise as a depolarizing channel by inserting Pauli gates randomly throughout the circuit [1]. However, it is not clear how sensitive a code's threshold is to the noise model, and whether or not a depolarizing channel is a good approximation for realistic non-stabilizer errors. Within the stabilizer formalism, we have shown that for a single qubit more accurate approximations can be obtained by including in the noise model Clifford operators and Pauli operators conditional on measurement [2]. Independent work by Magesan et al. has also shown the utility of adding Clifford operators to error models [3]. We now examine the feasibility of employing these error approximations at the single-qubit level to obtain better estimates of a QECC's threshold. For several codes and various noise models, we simulate an error-correction step and compute the pseudo-threshold by determining the noise strength above which encoding reduces the qubit fidelity. We compare the pseudo-threshold values for the real noise with its Pauli and expanded Pauli approximations. In most cases, the expanded Pauli channel provides a significantly better approximation to the real pseudo-threshold suggesting that our expanded error models will lead to more accurate stabilizer-based threshold estimations for realistic noise models. [1] A.M. Steane, Phys. Rev. A 68, 042322 (2003) [2] M. Gutiérrez, L. Svec, A. Vargo, and K. R. Brown, Phys. Rev. A. 87, 030302(R) (2013) [3] E. Magesan, D. Puzzuoli, C. E. Granade, D. G. Cory, Phys. Rev. A 87, 012324 (2013)
5:30pm - 6:00pm	Jonas Anderson, Université de Sherbrooke
	Towards an Efficient Decoder for Quantum LDPC Codes
	Abstract. Quantum low-density parity-checking (LDPC) codes can greatly reduce the overhead associated with fault-tolerant quantum computation (FTQC) by providing a nonzero-rate code family with low-weight stabilizer generators. In principle this means that as the code distance grows so does the number of encoded qubits thus allowing FTQC with constant overhead [1]. Exact decoding of classical LDPC codes is computationally difficult, but approximate decoders such as the belief propagation (BP) decoder are known to work well. For quantum LDPC codes much less is known and BP without modifications is plagued with issues due to degeneracy and short cycles in the Tanner graph. Here we improve upon the work of Poulin and Chung [2] by modifying BP to correct for some of the effects of message passing on a Tanner graph with cycles. Our technique uses nonlinear message weights to offset the additional correlations picked up due to cycles. For physical error rates an order of magnitude below pseudothreshold, arguably the most important regime for FTQC, we improve upon the best-known decoding schemes by an order of magnitude. We will also discuss ideas to further improve upon these schemes. [1] Daniel Gottesman, “What is the Overhead Required for Fault-Tolerant Quantum Computation?” arxiv.org/1310.2984. [2] David Poulin and Yeojin Chung, “On the iterative decoding of sparse quantum codes” Quantum Information and Computation, Vol. 8, No. 10 (2008) 0987–1000.