In this work, we develop an efficient decoding method for graph codes, a class of stabilizer quantum error-correcting codes constructed from graph states. While optimal decoding is generally NP-hard, we propose a faster decoder exploiting the structural properties of the underlying graph states. Although distinct error patterns may yield the same syndrome, we demonstrate that the post-measurement state follows a well-defined structure determined by the projective syndrome measurement. Building on this idea, we introduce a hierarchical decoder in which each level can be solved in polynomial time. Additionally, this decoder achieves optimal decoding performance at the lower levels of the hierarchy. This strategy avoids the need for full maximum-likelihood decoding of graph codes. Numerical results illustrate the efficiency and effectiveness of the proposed approach.
We consider tensor-network stabilizer codes and show that their tensor-network decoder has the property that independent logical qubits can be decoded in parallel. As long as the error rate is below threshold, we show that this parallel decoder is essentially optimal. As an application, we verify this for the max-rate holographic Steane (heptagon) code. For holographic codes this tensor-network decoder was shown to be efficient with complexity polynomial in n, the number of physical qubits. Here we show that, by using the parallel decoding scheme, the complexity is also linear in k, the number…
Decoder Model Compatibility Provides Information beyond the Logical Gap under Drifting and Correlated Quantum Noise
University of Washington（华盛顿大学）；Pacific Northwest National Laboratory（太平洋西北国家实验室）；Fordham University（福特汉姆大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；NASA Ames Research Center（美国宇航局艾姆斯研究中心）
Surface codes are a promising method of quantum error correction and the basis of many proposed quantum computation implementations. However, their efficient decoding is still not fully explored. Recently, approaches based on machine learning techniques have been proposed by Torlai and Melko as well as Varsamopoulos et al. In these approaches, a so called high level decoder is used to post-correct an underlying decoder by correcting logical errors. A significant problem is that these methods require large amounts of training data even for relatively small code distances. The above-mentioned me…
Impacts of Decoder Latency on a Utility-Scale Quantum Computer Architecture
QB Information Technologies (1QBit)（1QB信息技术公司）；Department of Physics & Astronomy, University of Waterloo（滑铁卢大学物理与天文系）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；Quantum Machines（量子机器公司）；HPE Quantum, Hewlett Packard Labs（惠普实验室HPE量子部门）；Emergent Machine Intelligence, Hewlett Packard Labs（惠普实验室涌现人工智能部门）
Arbitrarily long quantum computations require quantum memories that can be repeatedly measured without being corrupted. Here, we preserve the state of a quantum memory, notably with the additional use of flagged error events. All error events were extracted using fast, mid-circuit measurements and resets of the physical qubits. Among the error decoders we considered, we introduce a perfect matching decoder that was calibrated from measurements containing up to size-4 correlated events. To compare the decoders, we used a partial post-selection scheme shown to retain ten times more data than ful…
Logical error estimation from syndrome data of surface-code experiments
Duke Quantum Center, Duke University（杜克量子中心，杜克大学）；Department of Electrical and Computer Engineering, Duke University（电气与计算机工程系，杜克大学）；Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid（马德里自治大学-西班牙国家科研委员会理论物理研究所，马德里自治大学）；Department of Electrical & Computer Engineering, University of Southern California（电气与计算机工程系，南加州大学）；Center for Quantum Information Science & Technology, University of Southern California（量子信息与科技中心，南加州大学）；Quantum Elements, Inc.（量子元素公司）；Department of Physics & Astronomy, University of Southern California（物理与天文学系，南加州大学）；Department of Chemistry, University of Southern California（化学系，南加州大学）；Department of Physics, Duke University（物理系，杜克大学）；Department of Chemistry, Duke University（化学系，杜克大学）
Simple, Efficient, and Generic Post-Selection Decoding for qLDPC Codes
Graduate School of China Academy of Engineering Physics（中国工程物理研究院研究生院）；International Center for Elementary Particle Physics, University of Tokyo（东京大学基础粒子物理国际中心）；Department of Applied Physics, University of Tokyo（东京大学应用物理系）
Topological quantum error-correcting codes are a promising candidate for building fault-tolerant quantum computers. Decoding topological codes optimally, however, is known to be a computationally hard problem. Various decoders have been proposed that achieve approximately optimal error thresholds. Due to practical constraints, it is not known if there exists an obvious choice for a decoder. In this paper, we introduce a framework which can combine arbitrary decoders for any given code to significantly reduce the logical error rates. We rely on the crucial observation that two different decodin…
We construct a gate and time-independent noise model that results in the output of a logical randomized benchmarking protocol oscillating rather than decaying exponentially. To illustrate our idea, we first construct an example in standard randomized benchmarking where we assume the existence of ``hidden'' qubits, permitting a choice of representation of the Clifford group that contains multiplicities. We use the multiplicities to, with each gate application, update a hidden memory of the gate history that we use to circumvent theorems which guarantee the output decays exponentially. In our fo…
Shor and Steane ancilla are two well-known methods for fault-tolerant logical measurements, which are successful on small codes and their concatenations. On large quantum low-density-parity-check (LDPC) codes, however, Shor and Steane measurements have impractical time and space overhead respectively. In this work, we widen the choice of ancilla codes by unifying Shor and Steane measurements into a single framework, called homomorphic measurements. For any Calderbank-Shor-Steane (CSS) code with the appropriate ancilla code, one can avoid repetitive measurements or complicated ancilla state pre…
A Unified Hardware-to-Decoder Architecture for Hybrid Continuous-Variable and Discrete-Variable Quantum Error Correction in LiDMaS+
College of Computing, Georgia Institute of Technology（佐治亚理工学院计算学院）；Independent Quantum Architecture Researcher & Software Developer, SchroSIM Quantum Software Project（独立量子架构研究员及软件开发者，SchroSIM量子软件项目）；Volkswagen AG（大众汽车集团）；Department of Physics, RWTH Aachen（亚琛工业大学物理系）；Department of Computational and Applied Mechanics, Federal University of Juiz de Fora（朱伊斯德福拉联邦大学计算与应用力学系）；Institut für Informatik, Fakultät für Mathematik und Informatik, TU Bergakademie Freiberg（弗莱贝格矿业技术大学数学与信息技术学院计算机科学研究所）
