Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session Q35: Quantum Error Correction DecodersRecordings Available

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Sponsoring Units: DQI Chair: Ted Yoder, IBM Room: McCormick Place W193B 
Wednesday, March 16, 2022 3:00PM  3:12PM 
Q35.00001: A decoder for the triangular color code by matching on a Möbius strip Kaavya Sahay, Benjamin J Brown The color code is remarkable for its ability to perform faulttolerant logic gates. This motivates the design of practical decoders that minimise the resource cost of colorcode quantum computation. Here we propose a decoder for the planar color code with a triangular boundary where we match syndrome defects on a nontrivial manifold that has the topology of a Möbius strip. A basic implementation of our decoder used on the color code with hexagonal lattice geometry demonstrates a logical failure rate that is competitive with the optimal performance of the surface code, ∼p^{α√n}, with α≈6/7√3≈0.5, error rate p, and n the code length. Furthermore, by exhaustively testing over five billion error configurations, we find that a modification of our decoder that manually compares inequivalent recovery operators can correct all errors of weight ≤(d−1)/2 for codes with distance d≤13. Our decoder is derived using relations among the stabilizers that preserve global conservation laws at the lattice boundary. We present generalisations of our method to depolarising noise and faulttolerant error correction, as well as to Majorana surface codes, higherdimensional color codes and singleshot error correction. 
Wednesday, March 16, 2022 3:12PM  3:24PM Withdrawn 
Q35.00002: Robust decoding in monitored dynamics of open quantum systems with Z_{2} symmetry Yaodong Li, Matthew P A Fisher We explore a class of "open" quantum circuit models with local decoherence ("noise") and local projective measurements, each respecting a global Z_2 symmetry. The model supports a spin glass phase where the Z_2 symmetry is spontaneously broken, a paramagnetic phase characterized by a divergent susceptibility, and an intermediate "trivial" phase. Within the spin glass phase the circuit dynamics can be interpreted as a quantum repetition code, with each stabilizer of the code measured stochastically at a finite rate, and the decoherences as effective bitflip errors. Motivated by the geometry of the spin glass phase, we devise a novel decoding algorithm for recovering an arbitrary initial qubit state in the code space, assuming knowledge of the history of the measurement outcomes, and the ability of performing local Pauli measurements and gates on the final state. With this simple decoder, we find that the information of the initial encoded qubit state can be retained (and then recovered) for a time logarithmic in L for a 1d circuit, and for a time at least linear in L in 2d below a finite error threshold. We also outline a connection of the simple decoder to correlation functions in a random bond Ising model, which leads to an improved decoder that has a finite threshold in both 1d and 2d, both for T linear in L. The improved decoder has a time complexity O(L^{d+1} T), thus preferable as compared to existing ones based on a "perfect matching" of error defects. 
Wednesday, March 16, 2022 3:24PM  3:36PM 
Q35.00003: Finite Rate QLDPCGKP Coding Scheme that Surpasses the CSS Hamming Bound Nithin Raveendran, Narayanan Rengaswamy, Filip D Rozpedek, Ankur Raina, Liang Jiang, Bane Vasic Quantum error correction has recently been shown to benefit greatly from specific physical encodings of the code qubits. Many authors have considered the continuousvariable GottesmanKitaevPreskill (GKP) encoding, and then imposed an outer discretevariable surface code on these GKP qubits. Under such concatenation, the analog information from the inner GKP error correction improves the noise threshold of the outer code. However, the surface code has vanishing rate and is resource intensive. We concatenate the GKP code with generic quantum lowdensity paritycheck (QLDPC) codes and demonstrate a natural way to exploit the GKP analog information (GKPAI) in iterative decoders. We first show the noise thresholds for two QLDPC code families, and then show the improvements when the hardwarefriendly minsum decoder utilizes the GKPAI. When the GKPAI is combined with a sequential update schedule for minsum, the scheme surpasses the CSS Hamming bound for these code families. Furthermore, we observe that the GKPAI helps the decoder in escaping harmful trapping sets in the Tanner graph of the QLDPC code, thereby eliminating or significantly lowering the error floor of the logical error rate curves. 
Wednesday, March 16, 2022 3:36PM  3:48PM 
Q35.00004: Neural Network Decoders for Detecting Measurement Induced Phase Transitions in Random Clifford Circuits Hossein Dehghani, Ali Lavasani, Mohammad Hafezi, Michael J Gullans Random unitary circuits with intermittent projective measurements can host a phase transition between a pure phase and a mixed phase where the pure phase has a nonextensive in circuit size entanglement entropy and the mixed phase has an extensive in size entanglement entropy. In these circuits the mixed phase can be considered as a familiy of quantum error codes where the unitary time dynamics protects quantum entanglement from projective measurements that play the role of errors. Recently, it has been shown that these phase transitions can be locally probed via entangling reference qubits to the circuit whose purification dynamics determines the phase of the quantum circuit. In this work we study these phase transitions in random Clifford stabilizer circuits and we design a neural network (NN) decoder that by using the measurement outcomes of the qubits in the circuit can learn the state of the reference qubit. Using the dynamics of the reference qubit we demonstrate that for a given circuit our NN decoder can detect the phase of the quantum circuit without measuring the entanglement entropy which can be used in noisy intermediatescale quantum devices. 
Wednesday, March 16, 2022 3:48PM  4:00PM 
Q35.00005: Interpretation of UnionFind Decoder on Weighted Graphs and Application to XZZX Surface Code Yue Wu, Namitha Liyanage, Shruti Puri, Lin Zhong UnionFind (UF) and MinimumWeight Perfect Matching (MWPM) are popular decoder designs for surface codes. The former has significantly lower time complexity than the latter. On the other hand UF is considered somewhat inferior to MWPM, in terms of decoding accuracy. In this work we present an interpretation of UF decoder on weighted graphs. This interpretation provides an explanation of why UF and MWPM decoders perform closely: UF decoder is an approximate implementation of the blossom algorithm used for MWPM. This interpretation also shows that UF decoder should work very well with the XZZX code when noise in the underlying hardware is strongly biased. With analytics and numerical simulations, we show that the accuracy of the UF decoder is identical to that of MWPM for XZZX surface code when noise is infinitely biased and measurements are perfect. When circuitlevel noise is taken into account then the UF decoder has a threshold of only 6% less than that of the MWPM decoder. In a practical setting with noise bias of 100, the threshold of UF decoder is 2% less with perfect measurements and 9% less with circuitlevel noise than that of the MWPM decoder. 
Wednesday, March 16, 2022 4:00PM  4:12PM 
Q35.00006: The decoding of surface codes with twists Sophia Lin The standard surface code consists of weight4 and weight2 stabilizers, and can be efficiently decoded by a Minimum Weight Perfect Matching (MWPM) decoder. Some variants of surface code contain a twist, a stabilizer (usually weight5) with a PauliY measurement. The inclusion of twists allow for easy implementation of Clifford gates. However, the resulting codes are nonCSS, giving rise to a challenge in decoding. We study how adding a twist to surface code affects the decoding, with a focus on Litinski’s edgetracked code. 
Wednesday, March 16, 2022 4:12PM  4:24PM 
Q35.00007: Fast decoder for generic quantum codes via machine learning Anirudh Lanka, Prithviraj Prabhu, Todd A Brun Decoders for quantum errorcorrecting codes must use minimal resources to correct errors faster than they appear. We reduce this spacetime requirement using neural networks and evolutionary algorithms to construct quantum decoders for generic stabilizer codes. In offline training, a map from syndromes to errors is optimized based on a cost function of the error locations. The trained network is then used to decode the syndrome bits in constant time for a given physical noise model. These techniques are tested on several block codes, small lowdensity parity check (LDPC) codes, and topological codes in both noiseless and noisy measurement regimes, and the performance and resource use are measured. 
Wednesday, March 16, 2022 4:24PM  4:36PM 
Q35.00008: Morphing quantum codes Michael Vasmer, Aleksander Kubica We introduce a morphing procedure that can be used to generate new quantum codes from existing quantum codes. In particular, we morph the 15qubit ReedMuller code, producing a [[10,1,2]] code with a faulttolerant logical T gate (the smallest code to our knowledge with this property). In addition, we construct a family of hybrid toriccolor (HTC) codes by morphing the color code. Our code family inherits the faulttolerant gates of the original color code, implemented via constantdepth local unitaries. We use this property to construct toric codes with faulttolerant multiqubit controlZ gates. We also provide an effcient decoding algorithm for HTC codes in 2D, and numerically benchmark its performance for phaseflip noise. We expect that morphing may also be a useful technique for modifying other code families such as triorthogonal codes. 
Wednesday, March 16, 2022 4:36PM  4:48PM 
Q35.00009: Random Clifford Deformations of the Surface Code Arpit Dua, Aleksander Kubica, David A Huse, Liang Jiang, Steven Flammia, Michael J Gullans Clifford deformations of the surface code have been shown to have high error correction thresholds for noise biased towards dephasing. Moreover, careful tuning of the lattice geometry, i.e. shape and boundary conditions, can dramatically improve the subthreshold performance of the code with biased noise. Inspired by the improved code performance via the choice of Clifford deformation and lattice geometry, we consider random Clifford deformations of the surface code on the rotated layout. We demonstrate in the case of perfect syndrome measurements that certain random codes can outperform the best known translationinvariant deformations, i.e., the socalled ``XY'' code and ``XZZX'' codes at finite bias, in terms of subthreshold performance, while their code capacity thresholds are close to the previously highest values obtained from the XZZX code. We consider the statisticalmechanical mapping of random codes and conjecture a phase diagram of random codes with 50% thresholds at infinite bias through percolation theory arguments. We support this conjecture via tensor network decoder numerics on a large set of random code ensembles. It follows from results in bondpercolation, that for a linear system size L and at the critical point with 50% probability of Hadamard deformations, the infinitebias distance scales like O(L^1.1) 
Wednesday, March 16, 2022 4:48PM  5:00PM 
Q35.00010: Quantum error correction experiments on a 17qubit superconducting processor. Part I: Optimized calibration strategies. Hany Ali, Jorge F Marques, Olexiy O Fedorets, Matvey Finkel, Christos Zachariadis, Miguel Moreira, Wouter J Vlothuizen, Marc Beekman, Nadia Haider, Alessandro Bruno, Leonardo DiCarlo This threepart series focuses on the realization of various quantum error correction (QEC) codes on a 17transmon device designed for the distance3 surface code. The constituent weight2 to weight4 stabilizer measurements for these codes are suboptimally constructed if simply compiled from one and twoqubit gates and singlequbit readout tuned in isolation. In this first part, we present highly parallelized and orthogonal calibration methods for optimally calibrating the stabilizer measurements as parallel block units. This approach improves performance as it absorbs coherent phase errors due to residual ZZ coupling and flux crosstalk. 
Wednesday, March 16, 2022 5:00PM  5:12PM 
Q35.00011: Quantum error correction experiments on a 17qubit superconducting processor. Part II: Logical qubit performance. Jorge F Marques, Hany Ali, Olexiy O Fedorets, Boris Varbanov, Matvey Finkel, Christos Zachariadis, Miguel Moreira, Wouter J Vlothuizen, Marc Beekman, Nadia Haider, Alessandro Bruno, Barbara M Terhal, Leonardo DiCarlo In this second part, we present the realization of various QEC codes with increasing complexity on the 17transmon device. Among these are the bit and phaseflip repetition codes with distances 3, 5 and 7. These codes serve as a simple testbed for investigating decoding strategies and quantifying the link between logical and physical qubit performance. Finally, we provide an update on our progress in implementing the distance3 surface code for which the device is designed. 
Wednesday, March 16, 2022 5:12PM  5:24PM 
Q35.00012: Quantum error correction experiments on a 17qubit superconducting processor. Part III: Defect correlation analysis and decoder calibration. Boris Varbanov, Jorge F Marques, Hany Ali, Olexiy O Fedorets, Leonardo DiCarlo, Barbara M Terhal The goal of decoding is to preserve the logical qubit state by inferring physical errors through processing of the error syndrome of stabilizer measurements. In this final part, we characterize both conventional qubit errors as well as nonconventional errors, such as leakage and crosstalk, using correlations between observed syndrome defects. We then calibrate minimumweight perfect matching decoders with different sets of weights in order to minimize the logical error rate, and compare to those achieved using simple decoding strategies such as lookup tables and final majority voting. 
Wednesday, March 16, 2022 5:24PM  5:36PM 
Q35.00013: Improved singleshot decoding of higher dimensional homological product codes Oscar J Higgott, Nikolas P Breuckmann In this work we study the singleshot performance of higher dimensional homological product codes decoded using beliefpropagation and orderedstatistics decoding. We find that decoding data qubit and syndrome measurement errors together in a single stage leads to singleshot thresholds that greatly exceed all previously observed thresholds for these codes. For the 3D toric code and a phenomenological noise model, we find a sustainable threshold of 7.08%, compared to the threshold of 2.90% previously found using a twostage decoder~[Quintavalle et al., 2021]. For the 4D toric code, we observe a sustainable singleshot threshold of 4.29%. We also explore the performance of other product codes that generalise beyond the toric code, including some 4D homological product codes which we show lead to a significant reduction in qubit overhead compared the surface code for phenomenological error rates as high as 1%. 
Wednesday, March 16, 2022 5:36PM  5:48PM 
Q35.00014: Efficient Decoding of Surface Code Syndromes for Error Correction in Quantum Computing Debasmita Bhoumik Errors in surface code have typically been decoded using the popular Blossom decoder which uses Minimum Weight Perfect Matching (MWPM) algorithm. Recently, neuralnetworkbased Machine Learning (ML) techniques have been employed for this purpose. In this work, we propose a twolevel (low and high) MLbased decoding scheme, where the lowlevel decoder corrects errors on physical qubits and the highlevel decoder corrects any logical errors introduced by faulty detection of the lowlevel decoder, for symmetric and asymmetric noise models. Our results show that our proposed decoder achieves ∼10× and ∼2× higher values of pseudothreshold (physical error probability beyond which logical error probability exceeds physical error probability) and threshold (physical error probability beyond which increasing the distance of the code leads to higher logical error probability) respectively than for MWPM. We show that usage of more sophisticated ML models with higher training/testing time does not provide significant improvement in the decoder performance. Finally, data generation for training the ML decoder requires significant overhead hence lower volume of training data is desirable. We have shown that our decoder maintains a good performance with the traintest ratio as low as 40: 60.

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