Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session T40: Quantum Error Correction TheoryFocus Recordings Available

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Sponsoring Units: DQI Chair: Kyungjoo Noh, AWS Center for Quantum Computing Room: McCormick Place W196B 
Thursday, March 17, 2022 11:30AM  11:42AM 
T40.00001: Measurementfree Quantum Error Correction with a Digital Entropy Pump: Part 1 Albert T Schmitz, Michael A Perlin, Shavindra P Premaratne, Anne Y Matsuura As quantum computing has become viable in concept, attention has shifted toward addressing the challenges of largescale practical computing. This includes quantum error correction atscale, which in the current paradigm is limited in part by challenges associated with realtime measurement, decoding and control feedback with a classical processing unit. We propose a method to circumvent these challenges and eliminate any need for feedback with a classical processor for the purposes of error correction. The method transfers the entropy associated with unknown errors from data qubits to ancillas, then unconditionally resets the ancillas to their ground state in an overall process that can be recognized as a digital entropy pump. Using a stabilizer code, the entropy transfer from data qubits is achieved with gatelevel instructions that extract error syndromes, decode them and apply corresponding corrections coherently all within the quantum processor. Resetting ancillas then removes this entropy from the system through the quantum hardware’s engineered dissipative coupling to its environment. 
Thursday, March 17, 2022 11:42AM  11:54AM 
T40.00002: Measurementfree Quantum Error Correction with a Digital Entropy Pump: Part 2 Michael A Perlin, Albert T Schmitz, Shavindra P Premaratne, Anne Y Matsuura As quantum computing has become viable in concept, attention has shifted toward addressing the challenges of largescale practical computing. This includes quantum error correction atscale, which in the current paradigm is limited in part by challenges associated with realtime measurement, decoding and control feedback with a classical processing unit. We propose a method to circumvent these challenges and eliminate any need for feedback with a classical processor for the purposes of error correction. The method transfers the entropy associated with unknown errors from data qubits to ancillas, then unconditionally resets the ancillas to their ground state in an overall process that can be recognized as a digital entropy pump. Using a stabilizer code, the entropy transfer from data qubits is achieved with gatelevel instructions that extract error syndromes, decode them and apply corresponding corrections coherently all within the quantum processor. Resetting ancillas then removes this entropy from the system through the quantum hardware’s engineered dissipative coupling to its environment. 
Thursday, March 17, 2022 11:54AM  12:06PM 
T40.00003: Distance bounds for generalized bicycle codes Renyu Wang The Generalized Bicycle (GB) codes is a class of quantum errorcorrecting codes constructed from a pair of binary circulant matrices [1][2]. An important advantage of GB codes is that they have a naturally overcomplete set of lowweight stabilizer generators which is expected to improve their performance in the presence of syndrome measurement errors. Without row weight limit, GB codes with finite encoding rates and distance scaling as Ο(n/log n) exist. For GB codes with a given row weight w, upper distance bounds can be constructed by mapping them to codes local in D=w2 dimensions. We show that several large families of such codes have distances d ≥ O(n^{1/2}). Numerically, we studied distance scaling in one such family encoding a single qubit, where the distance is seen to grow as a square root of n, with the coefficient increasing with w. 
Thursday, March 17, 2022 12:06PM  12:42PM 
T40.00004: Quantum error mitigation for physical and logical qubits Invited Speaker: Sergey Bravyi It has been recently shown that a limited form of error correction for shallow quantum circuits can be achieved by combining outcomes of multiple noisy experiments in a way that negates the effect of noise. These methods, collectively known as Quantum Error Mitigation (QEM), are well suited for quantum devices available today because they introduce little or no overhead in the number of qubits. In this talk I will discuss recent progress on QEM with a focus on the quasiprobability methods. First, it is shown that QEM can be naturally integrated into the standard surface code architecture to implement logical Tgates. As a result, logical Clifford+T circuits with a number of Tgates inversely proportional to the physical noise rate can be implemented on small errorcorrected devices without magic state distillation. Secondly, I will discuss how to mitigate readout errors introduced by imperfect qubit measurements. Such errors are often the dominant factor limiting scalability of nearterm devices. 
Thursday, March 17, 2022 12:42PM  12:54PM 
T40.00005: Computing Ground State Properties with Early FaultTolerant Quantum Computers Ruizhe Zhang, Guoming Wang, Peter Johnson Significant effort in applied quantum computing has been devoted to the problem of ground state energy estimation for molecules and materials. Yet, for many applications of practical value, additional properties of the ground state must be estimated. These include Green's functions used to compute electron transport in materials and the oneparticle reduced density matrices used to compute electric dipoles of molecules. In this paper, we propose a quantumclassical hybrid algorithm to efficiently estimate such ground state properties with high accuracy. The quantum portion of the algorithm employs a simple, lowdepth quantum circuit and the classical portion contains a novel postprocessing procedure to extract the information of the ground state property from quantum sample data. We provide an analysis of various costs (circuit repetitions, maximal evolution time, and expected total runtime) as a function of target accuracy, spectral gap, and initial ground state overlap. This algorithm suggests a concrete approach to using early faulttolerant quantum computers for carrying out industryrelevant molecular and materials calculations. 
Thursday, March 17, 2022 12:54PM  1:06PM 
T40.00006: Implementing encoded Grover's Algorithm on NISQ devices Bibek B Pokharel, Daniel A Lidar Recent access to these NISQ devices has allowed for experimental tests of both quantum algorithms and error suppression methods. We implement unstructured search encoded in the [[4,2,2]] code on various superconducting and iontrap platforms. We supplement the error detection with Bayesian measurement error mitigation. In line with theoretical expectations, we find that the code detects single qubit errors and leads to statistically significant improvement in algorithmic performance. In particular, the encoded twoqubit Grover search outperforms the unencoded version for all possible marked states. 
Thursday, March 17, 2022 1:06PM  1:18PM Withdrawn 
T40.00007: Improved upper bounds on the stabilizer rank of magic states Hammam A Qassim, David Gosset, Hakop Pashayan In this work we improve the runtime of recent classical algorithms for strong simulation of quantum circuits composed of Clifford and T gates. The improvement is obtained by establishing a new upper bound on the stabilizer rank of $m$ copies of the magic state $T\rangle=\sqrt{2}^{1}(0\rangle+e^{i\pi/4}1\rangle)$ in the limit of large $m$. In particular, we show that $T\rangle^{\otimes m}$ can be exactly expressed as a superposition of at most $O(2^{\alpha m})$ stabilizer states, where $\alpha\leq 0.3963$, improving on the best previously known bound $\alpha \leq 0.463$. This furnishes, via known techniques, a classical algorithm which approximates output probabilities of an $n$qubit Clifford + T circuit $U$ with $m$ uses of the T gate to within a given inverse polynomial relative error using a runtime $\mathrm{poly}(n,m)2^{\alpha m}$. We also provide improved upper bounds on the stabilizer rank of symmetric product states $\psi\rangle^{\otimes m}$ more generally; as a consequence we obtain a strong simulation algorithm for circuits consisting of Clifford gates and $m$ instances of any (fixed) singlequbit $Z$rotation gate with runtime $\text{poly}(n,m) 2^{m/2}$. We suggest a method to further improve the upper bounds by constructing linear codes with certain properties. 
Thursday, March 17, 2022 1:18PM  1:30PM 
T40.00008: Coherent error and stochastic error in surface code Yuanchen Zhao, Dong E Liu We compare single qubit coherent error model with stochastic error model obtained by Pauli twirl approximation in surface code. We find that the surface code under coherent error satisfies generalized KL criterion and falls into the category of approximate QEC. The extra term in the generalized KL criterion corresponds to the coherent part of the error channel at logical level. It is already known that, when code distance is large and coherent rotation angle is small, the coherent error channel converges towards probabilistic quantum channel at the logical level after syndrome measurement. Then, we conclude that the generalized KL criterion of this model also approaches normal KL criterion in that situation. We then study the success probability of QEC under such coherent errors, and confirm that the exact success probability under coherent error is smaller than the results using Pauli twirling approximation at physical level. 
Thursday, March 17, 2022 1:30PM  1:42PM 
T40.00009: Quantum Error Correction Alleviates Detectioninduced Coherent Errors Qinghong Yang, Dong E. Liu We study the performance of quantum error correction codes(QECCs) under the {\em detectioninduced coherent error} due to the imperfectness of practical implementations of stabilizer measurements, after running a quantum circuit. Considering the most promising surface code, we find that the detectioninduced coherent error will result in undetected error terms, which will accumulate and evolve into logical errors. However, we show that this kind of errors will be alleviated by increasing the code size, akin to eliminating other types of errors discussed previously. We also find that with detectioninduced coherent errors, the exact surface code becomes an approximate QECC. 
Thursday, March 17, 2022 1:42PM  1:54PM 
T40.00010: Highthreshold stabilizer code on the honeycomb lattice Basudha Srivastava, Mats Granath, Anton F Kockum We consider a topological stabilizer code on the honeycomb lattice, the XYZ^{2} code. The code is inspired by the Kitaev honeycomb model and fits in the framework of “matching codes” discussed by Wootton [J. Phys. A: Math. Theor. 48 215302 (2015)]. It utilizes weightsix (XYZXYZ) and weighttwo (XX, ZZ or YY) parity checks on a planar hexagonal grid composed of 2d^{2} qubits, with weightthree checks at the boundaries, stabilizing one logical qubit. We study the properties of the code assuming perfect stabilizer measurements using maximum likelihood decoding. For pure X, Y, or Z biased noise we can solve for the logical failure rate analytically, giving a threshold of 50%. In contrast to the rotated surface code and the XZZX code, which have code distance d^{2} only for pure Y noise, here the code distance is 2d^{2} for both pure Z and pure Y noise (for XX parity checks). The code also possesses distinctive properties in a biased noise error model which give rise to unidirectional syndromes in three directions depending on the bias. 
Thursday, March 17, 2022 1:54PM  2:06PM 
T40.00011: Fracton Topological Order at Finite Temperature Zhengzhi Wu, Xiaoyang Shen, Linhao Li, Zhehan Qin, Hong Yao As new kinds of stabilizer code models, fracton models have been promising in realizing quantum memory or quantum hard drives. However, it has been shown that the fracton topological order of many 3D fracton models occurs only at zero temperature, such as the 3+1d Xcube model or Haah code. In this work, we show that higher dimensional fracton models can support a fracton topological order below a nonzero critical temperature Tc. Focusing on a typical 4D X cube model, we show that there is a finite critical temperature Tc by analyzing its free energy from duality. We also obtained the expectation value of the ’t Hooft loops in the 4D Xcube model, which directly shows a confinementdeconfinement phase transition at finite temperature. This finitetemperature phase transition can be understood as spontaneously breaking the Z_{2 }oneform subsystem symmetry. Moreover, we propose a new nogo theorem for finitetemperature quantum fracton topological order. 
Thursday, March 17, 2022 2:06PM  2:18PM 
T40.00012: Tailoring threedimensional surface codes for biased noise Eric Huang, Arthur Pesah, Christopher T Chubb, Michael Vasmer, Arpit Dua Tailored surface codes in two dimensions have recently been shown to exhibit high error correction thresholds and subthreshold performance in presence of biased noise. 
Thursday, March 17, 2022 2:18PM  2:30PM 
T40.00013: Machine Learning for Continuous Quantum Error Correction on Superconducting Qubits Haoran Liao, Ian Convy, Birgitta Whaley, Song Zhang, Sahil Patel, William P Livingston, Irfan Siddiqi, Nam Nguyen We propose a machine learning algorithm for continuous quantum error correction that is based on the use of a recurrent neural network to identity bitflip errors from continuous noisy syndrome measurements. The algorithm is designed to operate on measurement signals deviating from the ideal behavior in which the mean value corresponds to a code syndrome value and the measurement has white noise. We analyze continuous measurements taken from a superconducting architecture using three transmon qubits to identify three significant practical examples of nonideal behavior, namely autocorrelation at temporal short lags, transient syndrome dynamics after each bitflip, and drift in the steadystate syndrome values over the course of many experiments. Based on these realworld imperfections, we generate synthetic measurement signals from which to train the recurrent neural network, and then test its proficiency when implementing active error correction, comparing this with a traditional double threshold scheme and a discrete Bayesian classifier. The results show that our machine learning protocol is able to outperform the double threshold protocol across all tests, achieving a final state fidelity comparable to the discrete Bayesian classifier. 
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