Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session P44: Quantum Error CorrectionFocus

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Sponsoring Units: GQI Chair: Jacob Taylor, University of Maryland / NIST Room: 347 
Wednesday, March 16, 2016 2:30PM  2:42PM 
P44.00001: A universal faulttolerant gate set for the 5qubit quantum code Theodore Yoder, Ryuji Takagi, Isaac Chuang While the smallest singleerror correcting classical code encodes one bit in just three, the smallest such quantum code requires five qubits to protect one qubit. Yet, the 5qubit quantum code is widely regarded as useless when it comes to encoded quantum computation, as it supports just one nonPauli transversal gate, the $K=SH$ gate where $H$ is Hadamard and $S$ is the phase gate. However, transversal gates, though convenient, are not all there is to faulttolerant computation. Here we develop nontransversal, faulttolerant logical gates for the 5qubit quantum code, including logical controlledZ (CZ) and logical controlledcontrolledZ (CCZ). With $K$, we can then create faulttolerant CNOT and Toffoli gates. Together, logical Toffoli and $K$ imply that the 5qubit code is capable of universal, faulttolerant quantum computation. Moreover, we achieve our results without magic states. Indeed, no ancillary qubits beyond those needed for errorcorrection are necessary in any of our faulttolerant constructions. We also report faulttolerance thresholds for our new gates, calculated by exact computer simulation. In some cases, our logical gates on the 5qubit code have better thresholds than the analogous constructions on the next smallest quantum code, the 7qubit code. [Preview Abstract] 
Wednesday, March 16, 2016 2:42PM  2:54PM 
P44.00002: Quantum faulttolerant thresholds for universal concatenated schemes Christopher Chamberland, Tomas JochymO'Connor, Raymond Laflamme Faulttolerant quantum computation uses ancillary qubits in order to protect logical data qubits while allowing for the manipulation of the quantum information without severe losses in coherence. While different models for faulttolerant quantum computation exist, determining the ancillary qubit overhead for competing schemes remains a challenging theoretical problem. In this work, we study the faulttolerance threshold rates of different models for universal faulttolerant quantum computation. Namely, we provide different threshold rates for the 105qubit concatenated coding scheme for universal computation without the need for state distillation. We study two error models: adversarial noise and depolarizing noise and provide lower bounds for the threshold in each of these error regimes. Establishing the threshold rates for the concatenated coding scheme will allow for a physical quantum resource comparison between our faulttolerant universal quantum computation model and the traditional model using magic state distillation.~ [Preview Abstract] 
Wednesday, March 16, 2016 2:54PM  3:06PM 
P44.00003: Critical parameters of a noise model that affect fault tolerant quantum computation on a single qubit Pavithran Iyer, Marcus P da Silva, David Poulin In this work, we aim to determine the parameters of a single qubit channel that can tightly bound the logical error rate of the Steane code. We do not assume any a priori structure for the quantum channel, except that it is a CPTP map and we use a concatenated Steane code to encode a single qubit. Unlike the standard Monte Carlo technique that requires many iterations to estimate the logical error rate with sufficient accuracy, we use techniques to compute the complete effect of a physical CPTP map, at the logical level. Using this, we have studied the predictive power of several physical noise metrics on the logical error rate, and show, through numerical simulations with random quantum channels, that, on their own, none of the natural physical metrics lead to accurate predictions about the logical error rate. We then show how machine learning techniques help us to explore which features of a random quantum channel are important in predicting its logical error rate. [Preview Abstract] 
Wednesday, March 16, 2016 3:06PM  3:42PM 
P44.00004: Doubled Color Codes Invited Speaker: Sergey Bravyi Combining protection from noise and computational universality is one of the biggest challenges in the faulttolerant quantum computing. Topological stabilizer codes such as the 2D surface code can tolerate a high level of noise but implementing logical gates, especially nonClifford ones, requires a prohibitively large overhead due to the need of state distillation. In this talk I will describe a new family of 2D quantum error correcting codes that enable a transversal implementation of all logical gates required for the universal quantum computing. Transversal logical gates (TLG) are encoded operations that can be realized by applying some singlequbit rotation to each physical qubit. TLG are highly desirable since they introduce no overhead and do not spread errors. It has been known before that a quantum code can have only a finite number of TLGs which rules out computational universality. Our scheme circumvents this nogo result by combining TLGs of two different quantum codes using the gaugefixing method pioneered by Paetznick and Reichardt. The first code, closely related to the 2D color code, enables a transversal implementation of all singlequbit Clifford gates such as the Hadamard gate and the $\pi/2$ phase shift. The second code that we call a doubled color code provides a transversal Tgate, where T is the $\pi/4$ phase shift. The Clifford+T gate set is known to be computationally universal. The two codes can be laid out on the honeycomb lattice with two qubits per site such that the code conversion requires parity measurements for sixqubit Pauli operators supported on faces of the lattice. I will also describe numerical simulations of logical Clifford+T circuits encoded by the distance3 doubled color code. Based on a joint work with Andrew Cross. [Preview Abstract] 
Wednesday, March 16, 2016 3:42PM  3:54PM 
P44.00005: Efficiently simulable approximations to realistic incoherent and coherent errors and their application to threshold estimation Mauricio Gutierrez, Kenneth Brown Classical simulations of noisy stabilizer circuits are often used to estimate the threshold of a quantum errorcorrecting code (QECC). It is not completely clear how sensitive a code's threshold is to the error model, and whether or not a Pauli channel (PC) is a good approximation for realistic nonstabilizer errors. Within the stabilizer formalism, it has been shown that for a single qubit more accurate approximations can be obtained by expanding the PC. We now examine the feasibility of employing these error approximations at the singlequbit level to obtain better estimates of a QECC's threshold. We calculate the level1 pseudothreshold for the Steane [[7,1,3]] code for several error models. At the logical level, the Pauli twirled channel (PTC) provides an extremely accurate approximation for incoherent channels. However, for coherent channels, the PTC severely underestimates the magnitude of the error. By computing the effective 1qubit process matrix for the whole circuit at low error rates, it becomes clear that this behavior is due to the stronger persistence of offdiagonal entries in the coherent channels. Therefore, if the main source of error in the quantum system is coherent, reliable stabilizer simulations should employ expanded Clifford channels. [Preview Abstract] 
Wednesday, March 16, 2016 3:54PM  4:06PM 
P44.00006: Decoder for 3D color codes KungChuan Hsu, Todd Brun Transversal circuits are important components of faulttolerant quantum computation. Several classes of quantum errorcorrecting codes are known to have transversal implementations of any logical Clifford operation. However, to achieve universal quantum computation, it would be helpful to have highperformance errorcorrecting codes that have a transversal implementation of some logical nonClifford operation. The 3D color codes~\footnote{H. Bomb\'{i}n, New J. Phys. {\bf 17}, 083002 (2015).} are a class of topological codes that permit transversal implementation of the logical $\pi /8$gate. The decoding problem of a 3D color code can be understood as a graphmatching problem on a threedimensional lattice. Whether this class of codes will be useful in terms of performance is still an open question. We investigate the decoding problem of 3D color codes and analyze the performance of some possible decoders. [Preview Abstract] 
Wednesday, March 16, 2016 4:06PM  4:18PM 
P44.00007: Highthreshold decoding algorithms for the gauge color code William Zeng, Benjamin Brown Gauge color codes are topological quantum error correcting codes on three dimensional lattices. They have garnered recent interest due to two important properties: (1) they admit a universal transversal gate set, and (2) their structure allows reliable error correction using syndrome data obtained from a measurement circuit of constant depth. Both of these properties make gauge color codes intriguing candidates for low overhead faulttolerant quantum computation. Recent work by Brown et al. calculated a threshold of ~0.31\% for a particular gauge color code lattice using a simple clustering decoder and phenomenological noise. We show that we can achieve improved threshold error rates using the efficient Wootton and Loss Markovchain Monte Carlo (MCMC) decoding. In the case of the surface code, the MCMC decoder produced a threshold close to that code's upper bound. While no upper bound is known for gauge color codes, the thresholds we present here may give a better estimate. [Preview Abstract] 
Wednesday, March 16, 2016 4:18PM  4:30PM 
P44.00008: ABSTRACT WITHDRAWN 
Wednesday, March 16, 2016 4:30PM  4:42PM 
P44.00009: Potts glass reflection of the decoding threshold for qudit quantum error correcting codes Yi Jiang, Alexey A. Kovalev, Leonid P. Pryadko We map the maximum likelihood decoding threshold for qudit quantum error correcting codes to the multicritical point in generalized Potts gauge glass models, extending the map constructed previously for qubit codes [1]. An $n$qudit quantum LDPC code, where a qudit can be involved in up to $m$ stabilizer generators, corresponds to a ${\mathbb Z}_d$ Potts model with $n$ interaction terms which can couple up to $m$ spins each. We analyze general properties of the phase diagram of the constructed model, give several bounds on the location of the transitions, bounds on the energy density of extended defects (nonlocal analogs of domain walls), and discuss the correlation functions which can be used to distinguish different phases in the original and the dual models. \hfill\smallskip\\[0pt] [1] A A Kovalev and L P Pryadko, Quant.\ Inf.\ \& Comp.\ {\bf 15}, 0825 (2015). [Preview Abstract] 
Wednesday, March 16, 2016 4:42PM  4:54PM 
P44.00010: Faulttolerant quantum computation in multiqubit block codes: performance and overhead Todd Brun Faulttolerant quantum computation requires that quantum information remain encoded in a quantum errorcorrecting code at all times; that a universal set of logical unitary gates and measurements is available; and that the probability of an uncorrectable error is low for the duration of the computation. Quantum computation can in principle be scaled up to unlimited size if the rate of decoherence is below a threshold. The main constructions that have been studied involve encoding each logical qubit in a separate block (either a concatenated code or a block of the surface code), which typically requires thousands of physical qubits per logical qubit, if not more. To reduce this overhead, we consider using multiqubit codes to achieve much higher storage rates. We estimate performance and overhead for certain families of codes, and ask: how large a quantum computation can be done as a function of the decoherence rate for a fixed size code block? Finally, we consider remaining open questions and limitations to this approach. [Preview Abstract] 
Wednesday, March 16, 2016 4:54PM  5:06PM 
P44.00011: Numerical Simulation of Coherent Error Correction Daniel Crow, Robert Joynt, Mark Saffman A major goal in quantum computation is the implementation of error correction to produce a logical qubit with an error rate lower than that of the underlying physical qubits. Recent experimental progress demonstrates physical qubits can achieve error rates sufficiently low for error correction, particularly for codes with relatively high thresholds such as the surface code and color code. Motivated by experimental capabilities of neutral atom systems, we use numerical simulation to investigate whether coherent error correction can be effectively used with the 7qubit color code. The results indicate that coherent error correction does not work at the 10qubit level in neutral atom array quantum computers. By adding more qubits there is a possibility of making the encoding circuits faulttolerant which could improve performance. [Preview Abstract] 
Wednesday, March 16, 2016 5:06PM  5:18PM 
P44.00012: Noise Estimation and Adaptive Encoding for Asymmetric Quantum Error Correcting Codes Jan FLORJANCZYK, Todd Brun We present a technique that improves the performance of asymmetric quantum error correcting codes in the presence of biased qubit noise channels. Our study is motivated by considering what useful information can be learned from the statistics of syndrome measurements in stabilizer quantum error correcting codes (QECC). We consider the case of a qubit dephasing channel where the dephasing axis is unknown and timevarying. We are able to estimate the dephasing angle from the statistics of the standard syndrome measurements used in stabilizer QECC's. We use this estimate to rotate the computational basis of the code in such a way that the most likely type of error is covered by the highest distance of the asymmetric code. In particular, we use the $[[15, 1, 3]]$ shortened ReedMuller code which can correct one phaseflip error but up to three bitflip errors. In our simulations, we tune the computational basis to match the estimated dephasing axis which in turn leads to a decrease in the probability of a phaseflip error. With a sufficiently accurate estimate of the dephasing axis, our memory's effective error is dominated by the much lower probability of four bitflips. [Preview Abstract] 
Wednesday, March 16, 2016 5:18PM  5:30PM 
P44.00013: Details of [[7,1,3]] Syndrome Measurements Yaakov Weinstein We explore different aspects of syndrome measurements (SM) for the [[7,1,3]] quantum error correction code. This includes determining how often to apply SM, comparing the performance of different SM, rearranging the order in which SM are applied, and exploring the effects of improving SM ancilla state construction. Finally, we attempt to formulate gates and their attached SM as superoperators. [Preview Abstract] 
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