Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session R27: Focus Session: Quantum Error Correction and Decoherence Control II |
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Sponsoring Units: GQI Chair: Andrew Landahl, Sandia National Laboratories Room: 329 |
Wednesday, March 20, 2013 2:30PM - 3:06PM |
R27.00001: Magic state distillation with low overhead Invited Speaker: Sergey Bravyi Most of error correcting codes used in fault-tolerant quantum computing permit an efficient implementation of high-fidelity encoded Clifford gates and Pauli measurements. On the other hand, implementation of encoded non-Clifford gates such as the $\pi/8$-rotation $T$ usually requires distillation of certain quantum software states known as ``magic states" and substantially increases the space and time overheads. To reduce the distillation overhead we propose a new family of stabilizer codes with an encoding rate $1/3$ that permit a transversal implementation of the $T$-gate on all logical qubits. The new codes are used to construct protocols for distilling high-quality magic states by Clifford group gates and Pauli measurements. The distillation overhead scales as $O(\log^\gamma{(1/\epsilon)})$, where $\epsilon$ is the output accuracy and $\gamma=\log_2{(3)}\approx 1.6$. Our techniques lead to a two-fold overhead reduction for distilling magic states with accuracy $\epsilon \sim 10^{-12}$ compared with the best previously known protocol. [Preview Abstract] |
Wednesday, March 20, 2013 3:06PM - 3:18PM |
R27.00002: Multilevel distillation of magic states for quantum computing Cody Jones We develop a procedure for distilling magic states used in universal quantum computing which requires substantially fewer resources than prior schemes. Our distillation circuit is based on a family of concatenated quantum codes with a transversal Hadamard operation which can distill the eigenstate of the Hadamard operator. A crucial result of this design is that low-fidelity magic states can be consumed to purify high-fidelity magic states to even higher fidelity, which we call ``multilevel distillation.'' We show numerically that there exist multilevel protocols such that the average number of magic states consumed to distill from error rate $\epsilon_{\mathrm{in}} = 0.01$ to $\epsilon_{\mathrm{out}}$ in the range $10^{-5}$ to $10^{-40}$ is about $14\log_{10}(1/\epsilon_{\mathrm{out}}) - 40$; the efficiency of multilevel distillation dominates all other reported protocols when distilling Hadamard magic states from initial infidelity 0.01 to any final infidelity below $10^{-7}$. These methods are an important advance for magic-state distillation circuits in high-performance quantum computing. [Preview Abstract] |
Wednesday, March 20, 2013 3:18PM - 3:30PM |
R27.00003: ABSTRACT WITHDRAWN |
Wednesday, March 20, 2013 3:30PM - 3:42PM |
R27.00004: Direct-to-Toffoli Magic-state Distillation Bryan Eastin In recently proposed quantum computing architectures, approximately 90\% of the required resources are consumed during the distillation of single-qubit magic-states for use in performing Toffoli gates. In this talk I describe how the overhead for magic-state distillation can be reduced by merging distillation with the implementation of Toffoli gates. The resulting routines distill single-qubit magic-states directly to Toffoli ancillae, each of which can be used without further magic to perform a Toffoli gate. [Preview Abstract] |
Wednesday, March 20, 2013 3:42PM - 3:54PM |
R27.00005: Magic state distillation protocols with noisy Clifford gates Peter Brooks A promising approach to universal fault-tolerant quantum computation is to implement the non-universal group of Clifford gates, and to achieve universality by adding the ability to prepare high-fidelity copies of certain ``magic states''. By applying state distillation protocols, many noisy copies of a magic state ancilla can be purified into a smaller number of clean copies which are arbitrarily close to the perfect state, using only Clifford operations. In practice, the Clifford gates themselves will be noisy, which can limit the efficiency of state distillation and put a floor on the achievable fidelity with the desired state. Recently, a number of new state distillation protocols have been proposed that have the potential to reduce the required resource overhead. I analyze these protocols and explore the tradeoffs between these different approaches to magic state distillation when noisy Clifford gates are taken into account. [Preview Abstract] |
Wednesday, March 20, 2013 3:54PM - 4:06PM |
R27.00006: Simulating Anyon Interference to Measure the Levin-Wen Plaquette Operator WeiBo Feng, N.E. Bonesteel, David DiVincenzo It may be possible to use the ground states of the Levin-Wen model for Fibonacci anyons as a non-Abelian surface code for fault-tolerant quantum computation [1]. To do this, it will be necessary to repeatedly measure the vertex and plaquette operators of the model to check for errors. Recently, two of us have constructed quantum circuits for performing such measurements [2]. Here we present an alternate measurement scheme based on simulating an interference experiment. This ``experiment'' can be thought of, roughly, as first inserting a pair of Fibonacci anyons with trivial total topological charge onto one edge of a plaquette, ``braiding'' one anyon all the way around the plaquette while the other remains fixed, and then either measuring the total topological charge of the two anyons or manipulating their state in a specific way. We construct explicit quantum circuits which can be used to simulate these processes and show how they can be used to measure the Levin-Wen plaquette operator on a quantum computer.\\[4pt] [1] R. Koenig, G. Kuperberg, and B.W. Reichardt, Ann. Phys. 325, 2707 (2010).\\[0pt] [2] N.E. Bonesteel and D.P. DiVincenzo, Phys. Rev. B 86, 165113 (2012). [Preview Abstract] |
Wednesday, March 20, 2013 4:06PM - 4:42PM |
R27.00007: Optimal control in presence of decoherence and measurement imperfections: Pure state preparation problem Invited Speaker: Alireza Shabani Quantum control is a key component in the mathematical toolbox for designing fault-tolerant quantum processors. It becomes important to find optimal control protocols for realistic experimental conditions. In this talk, I focus on quantum feedback control for preparing pure states as ideal resources for quantum computation and communication. I discuss how the optimal protocols under experimental imperfections can be different from the ones found under theoretical simplifications. The problem of our study is motivated by superconducting circuit QED proposals for quantum computation. [Preview Abstract] |
Wednesday, March 20, 2013 4:42PM - 4:54PM |
R27.00008: Surface code with decoherence: An analysis of three superconducting architectures Joydip Ghosh, Austin G. Fowler, Michael R. Geller We consider a realistic, multi-parameter error model and develop a methodology to connect logical error rates of a surface code architecture with single qubit coherence time (T1 or T2) for any realistic set of intrinsic parameters, such as state preparation, gate, and readout errors. The amplitude and phase damping are mapped to a diagonal Pauli ``depolarization'' channel via the Pauli twirl approximation. Three existing superconducting architectures are chosen and a numerical Monte Carlo simulation is performed to obtain the logical error rates. A leading order analytic model is also constructed that estimates the scaling behavior of logical error rates below threshold for small distances. Our results suggest that large-scale fault-tolerant quantum computation should be possible with existing state-of-the-art superconducting devices. [Preview Abstract] |
Wednesday, March 20, 2013 4:54PM - 5:06PM |
R27.00009: Surface Code Threshold in the Presence of Correlated Errors Eduardo Novais, Eduardo Mucciolo We study the fidelity of the surface code in the presence of correlated errors induced by the coupling of physical qubits to a bosonic environment. By mapping the time evolution of the system after one quantum error correction cycle onto a statistical spin model, we show that the existence of an error threshold is related to the appearance of an order-disorder phase transition in the statistical model in the thermodynamic limit. This allows us to relate the error threshold to bath parameters and to the spatial range of the correlated errors. [Preview Abstract] |
Wednesday, March 20, 2013 5:06PM - 5:18PM |
R27.00010: Surface code fidelity decay in the presence of a bosonic bath Pejman Jouzdani, Eduardo Mucciolo, Eduardo Novais The surface code is a promising quantum computing environment that provides topological protection against errors, ensuring that the distance of the code grows as the physical sizes of the system increases. It has been recently proposed that a surface code in contact with a bosonic bath experiences an effective evolution that induces an constrained Ising-like interaction between qubits. As the coupling to the bosonic bath increases, the system may undergo a transition where the fidelity decays substantially after one quantum error correction cycle even for non-error syndromes. We investigate the manifestation of such a transition by evaluating numerically the fidelity of a surface code qubit system with the proposed Ising interaction. We carry out exact calculations for small systems and perform a finite-size scaling analysis using a cluster mean-field approach. We find a significant change in the fidelity at coupling constant values compatible with the mean-field transition point. Calculations performed with complex coupling constants yield the same behavior for the fidelity. [Preview Abstract] |
Wednesday, March 20, 2013 5:18PM - 5:30PM |
R27.00011: Fast decoder for local quantum codes using Groebner basis Jeongwan Haah Based on arXiv:1204.1063. A local translation-invariant quantum code has a description in terms of Laurent polynomials. As an application of this observation, we present a fast decoding algorithm for translation-invariant local quantum codes in {\em any} spatial dimensions using the straightforward division algorithm for multivariate polynomials. The running time is $O(n \log n)$ on average, or $O(n^2 \log n)$ on worst cases, where $n$ is the number of physical qubits. The algorithm improves a subroutine of the renormalization-group decoder by Bravyi and Haah (arXiv:1112.3252) in the translation-invariant case. [Preview Abstract] |
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