Mitsuru Hamada
A conjugate code pair is defined as a pair of linear codes either of which contains the dual of the other. A conjugate code pair represents the essential structure of the corresponding Calderbank-Shor-Steane (CSS) quantum code. It is known that conjugate code pairs are applicable to (quantum) cryptography. We give a construction method for efficiently decodable conjugate code pairs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a concatenated code independently, our method uses information about the likelihood of errors having occurred at lower levels to maximize the probability of correctly interpreting error syndromes. Results of simulations of our method applied to the [[4,1,2]] subsystem code indicate that it can correct a number of discrete errors up to half of the distance of the c…
We discuss a method to construct quantum codes correcting amplitude damping errors via code concatenation. The inner codes are chosen as asymmetric Calderbank-Shor-Steane (CSS) codes. By concatenating with outer codes correcting symmetric errors, many new codes with good parameters are found, which are better than the amplitude damping codes obtained by any previously known construction.
We introduce the concept of generalized concatenated quantum codes. This generalized concatenation method provides a systematical way for constructing good quantum codes, both stabilizer codes and nonadditive codes. Using this method, we construct families of new single-error-correcting nonadditive quantum codes, in both binary and nonbinary cases, which not only outperform any stabilizer codes for finite block length, but also asymptotically achieve the quantum Hamming bound for large block length.
In this work, a quantum error correction (QEC) procedure with the concatenated five-qubit code is used to construct a near-perfect effective qubit channel (with a error below $10^{-5}$) from arbitrary noise channels. The exact performance of the QEC is characterized by a Choi matrix, which can be obtained via a simple and explicit protocol. In a noise model with five free parameters, our numerical results indicate that the concatenated five-qubit code is general: To construct a near-perfect effective channel from the noise channels, the necessary size of the concatenated five-qubit code depend…
In this paper we present several classes of asymptotically good concatenated quantum codes and derive lower bounds on the minimum distance and rate of the codes. We compare these bounds with the best-known bound of Ashikhmin--Litsyn--Tsfasman and Matsumoto. We also give a polynomial-time decoding algorithm for the codes that can decode up to one fourth of the lower bound on the minimum distance of the codes.
Entanglement-assisted continuous-variable concatenated codes for encoding qubits or oscillators
提出两种纠缠辅助级联码：将GKP内码与EA稳定子外码级联，或将GKP外码与EA稳定子内码级联，以降低逻辑错误概率并抑制正交误差方差。
Concatenated coding provides a general strategy to achieve the desired level of noise protection in quantum information storage and transmission. We report the implementation of a concatenated quantum error-correcting code able to correct against phase errors with a strong correlated component. The experiment was performed using liquid-state nuclear magnetic resonance techniques on a four spin subsystem of labeled crotonic acid. Our results show that concatenation between active and passive quantum error-correcting codes offers a practical tool to handle realistic noise contributed by both ind…
Approximate level-by-level maximum-likelihood decoding based on the Chase algorithm for high-rate concatenated stabilizer codes
本文提出基于Chase算法的近似逐层最大似然解码器，用于高率拼接稳定器码，以提升在比特翻转噪声下的解码性能。
Bidirectional Decoding for Concatenated Quantum Hamming Codes
本文提出一种双向解码方法，用于提升拼接量子汉明码在位翻转噪声下的纠错性能，将阈值从1.56%提高到4.35%，并保持更高的码距扩展能力。
Efficient Concatenated Bosonic Code for Additive Gaussian Noise
针对玻色编码解码复杂的问题，提出用GKP编码检测丢弃易错量子比特并级联量子奇偶校验编码处理残余错误，采用线性时间解码器且性能显著优于标准解码器。
Protecting quantum information from the detrimental effects of decoherence and lack of precise quantum control is a central challenge that must be overcome if a large robust quantum computer is to be constructed. The traditional approach to achieving this is via active quantum error correction using fault-tolerant techniques. An alternative to this approach is to engineer strongly interacting many-body quantum systems that enact the quantum error correction via the natural dynamics of these systems. Here we present a method for achieving this based on the concept of concatenated quantum error …
Qubit-oscillator concatenated codes: decoding formalism & code comparison
该研究针对玻色码与量子比特码的最优级联问题，为四类码的三种级联方案开发了高效最大似然译码器，经加性高斯白噪声测试验证，部分含GKP稳定子码的级联方案性能更优，还提出了无额外压缩的新型GKP稳定子码及其多能级版本。
Subsystem many-hypercube codes: High-rate concatenated codes with low-weight syndrome measurements
本文提出基于多超立方体码的子系统量子码，通过保持高编码率的同时实现恒定权重的综合征测量，提升解码性能。
We derive the effective channel for a logical qubit protected by an arbitrary quantum error-correcting code, and derive the map between channels induced by concatenation. For certain codes in the presence of single-bit Pauli errors, we calculate the exact threshold error probability for perfect fidelity in the infinite concatenation limit. We then use the control theory technique of balanced truncation to find low-order non-asymptotic approximations for the effective channel dynamics.
Long-distance quantum communication using concatenated ring graph codes
针对长距离量子通信需处理传输损耗和操作错误但现有级联码硬件需求高的问题，提出基于级联环图码和线性光学贝尔态测量的单向量子中继器架构，物质量子比特数随级联深度线性扩展，单量子比特错误率ε>10⁻³时仍能以千赫兹速率实现>10⁴千米通信。
Learning to Decode Concatenated Quantum Codes with Hierarchical Message Passing
该研究提出分层消息传递神经框架解码级联量子码，在[[15,7,3]]量子汉明码上提升去极化伪阈值，在多超立方体码上降低逻辑-CNOT失效率，为级联码设计提供通用解码工具。
We propose a method for universal fault-tolerant quantum computation using concatenated quantum error correcting codes. Namely, other than computational basis state preparation as required by the DiVincenzo criteria [1], our scheme requires no special ancillary state preparation to achieve universality, as opposed to schemes such as magic state distillation. The concatenation scheme exploits the transversal properties of two different codes, combining them to provide a means to protect against low-weight arbitrary errors. We give the required properties of the error correcting codes to ensure …
Simple logical quantum computation with concatenated symplectic double codes
该研究基于辛双构造提出级联辛双码，仅用物理单量子比特门和量子比特重标记即可实现丰富逻辑门，结合注入折叠横门完成完整Clifford群，模拟显示其在近先进物理错误率下性能良好，是中大规模量子计算机底层计算码的有力候选。
Quantum error correction and fault-tolerance make it possible to perform quantum computations in the presence of imprecision and imperfections of realistic devices. An important question is to find the noise rate at which errors can be arbitrarily suppressed. By concatenating the 7-qubit Steane and 15-qubit Reed-Muller codes, the 105-qubit code enables a universal set of fault-tolerant gates despite not all of them being transversal. Importantly, the CNOT gate remains transversal in both codes, and as such has increased error protection relative to the other single qubit logical gates. We show…
Deterministic generation of concatenated graph codes from quantum emitters
针对光子量子技术中光子损耗的核心挑战，提出利用双量子发射器或单带存储量子发射器的多光子发射生成级联图码的方案，可在高损耗、标准融合门且无辅助光子的场景下实现容错融合基量子计算。
We analyze the properties of a 2D topological code derived by concatenating the [[4, 2, 2]] code with the toric/surface code, or alternatively by removing check operators from the 2D square-octagon or 4.8.8 color code. We show that the resulting code has a circuit-based noise threshold of $\sim 0.41\%$ (compared to $\sim 0.6\%$ for the toric code in a similar scenario), which is higher than any known 2D color code. We believe that the construction may be of interest for hardware in which one wants to use both long-range two-qubit gates as well as short-range gates between small clusters of qub…
Graphs are closely related to quantum error-correcting codes: every stabilizer code is locally equivalent to a graph code, and every codeword stabilized code can be described by a graph and a classical code. For the construction of good quantum codes of relatively large block length, concatenated quantum codes and their generalizations play an important role. We develop a systematic method for constructing concatenated quantum codes based on "graph concatenation", where graphs representing the inner and outer codes are concatenated via a simple graph operation called "generalized local complem…
We analyze the resource overhead of recently proposed methods for universal fault-tolerant quantum computation using concatenated codes. Namely, we examine the concatenation of the 7-qubit Steane code with the 15-qubit Reed-Muller code, which allows for the construction of the 49 and 105-qubit codes that do not require the need for magic state distillation for universality. We compute a lower bound for the adversarial noise threshold of the 105-qubit code and find it to be $8.33\times 10^{-6}.$ We obtain a depolarizing noise threshold for the 49-qubit code of $9.69\times 10^{-4}$ which is comp…
Entanglement-assisted concatenated quantum codes (EACQCs), constructed by concatenating two quantum codes, are proposed. These EACQCs show several advantages over the standard concatenated quantum codes (CQCs). Several families of EACQCs that, unlike standard CQCs, can beat the nondegenerate Hamming bound for entanglement-assisted quantum error correction codes (EAQECCs) are derived. Further, a number of EACQCs with better parameters than the best known standard quantum error correction codes (QECCs) and EAQECCs are also derived. In particular, several catalytic EACQCs with better parameters t…
In quantum error correction, the description of noise channel cannot be completely accurate, and fluctuation always appears in noise channel. It is found that when fluctuation of physical noise channel is considered, the average effective channel is dependent only on the average of physical noise channel, and the average of physical noise channel here plays the role of the independent error model in the previous works. Now, one may conclude that in the independent error model, the results in previous works are also valid for average channel where fluctuation exists. In some typical cases, our …
A family of quantum codes of increasing block length with positive rate is asymptotically good if the ratio of its distance to its block length approaches a positive constant. The asymptotic quantum Gilbert-Varshamov (GV) bound states that there exist $q$-ary quantum codes of sufficiently long block length $N$ having fixed rate $R$ with distance at least $N H^{-1}_{q^2}((1-R)/2)$, where $H_{q^2}$ is the $q^2$-ary entropy function. For $q < 7$, only random quantum codes are known to asymptotically attain the quantum GV bound. However, random codes have little structure. In this paper, we genera…
We consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However, we demonstrate that for concatenated block codes, the optimal decoding can be efficiently computed using a message passing algorithm. We compare the performance of the message passing algorithm to that of the widespread blockwise hard decoding technique. Our Monte Carlo results using the 5 qubit and Steane's code on a depolarizing channel demonstrate signifi…
Achievable rates for concatenated square Gottesman-Kitaev-Preskill codes
本研究通过拼接连续变量-离散变量编码，实现了GKP码在所有噪声强度下的最优速率，展示了其在位移噪声和纯损失通道中的应用潜力。
This work compares the overhead of quantum error correction with concatenated and topological quantum error-correcting codes. To perform a numerical analysis, we use the Quantum Resource Estimator Toolbox (QuRE) that we recently developed. We use QuRE to estimate the number of qubits, quantum gates, and amount of time needed to factor a 1024-bit number on several candidate quantum technologies that differ in their clock speed and reliability. We make several interesting observations. First, topological quantum error correction requires fewer resources when physical gate error rates are high, w…
Bounds on concatenated entanglement-assisted quantum error-correcting codes
本文研究了纠缠辅助量子纠错码的界限，推导了拼接码的共享纠缠表达式，并探讨了非最大纠缠EAQECC在格里斯默和普洛特金界限下的饱和条件，同时提出了相关码的构造方法。
Concatenated Steane code with single-flag syndrome checks
本研究针对[[49,1,9]]级联Steane码提出低开销保距标志容错纠错协议，通过推广WPEC技术优化门排序实现单生成子双辅助量子比特症状提取，仿真显示其伪阈值优于同设置下的[[61,1,9]] 6.6.6色码。
We discuss long code problems in the Bennett-Brassard 1984 (BB84) quantum key distribution protocol and describe how they can be overcome by concatenation of the protocol. Observing that concatenated modified Lo-Chau protocol finally reduces to the concatenated BB84 protocol, we give the unconditional security of the concatenated BB84 protocol.
One of the main problems for the future of practical quantum computing is to stabilize the computation against unwanted interactions with the environment and imperfections in the applied operations. Existing proposals for quantum memories and quantum channels require gates with asymptotically zero error to store or transmit an input quantum state for arbitrarily long times or distances with fixed error. In this report a method is given which has the property that to store or transmit a qubit with maximum error $ε$ requires gates with error at most $cε$ and storage or channel elements with erro…
A method for concatenating quantum error-correcting codes is presented. The method is applicable to a wide class of quantum error-correcting codes known as Calderbank-Shor-Steane (CSS) codes. As a result, codes that achieve a high rate in the Shannon theoretic sense and that are decodable in polynomial time are presented. The rate is the highest among those known to be achievable by CSS codes. Moreover, the best known lower bound on the greatest minimum distance of codes constructible in polynomial time is improved for a wide range.
Bosonic Pauli+: Efficient Simulation of Concatenated Gottesman-Kitaev-Preskill Codes
针对级联Gottesman-Kitaev-Preskill（GKP）码缺乏高效大规模仿真工具的问题，提出可高效仿真多模式且捕捉玻色子多模式动力学的玻色子Pauli+模型（BP+），验证了其准确性并展示其通用性。
When a logical qubit is protected using a quantum error-correcting code, the net effect of coding, decoherence (a physical channel acting on qubits in the codeword) and recovery can be represented exactly by an effective channel acting directly on the logical qubit. In this paper we describe a procedure for deriving the map between physical and effective channels that results from a given coding and recovery procedure. We show that the map for a concatenation of codes is given by the composition of the maps for the constituent codes. This perspective leads to an efficient means for calculating…
The advantage of the concatenated three-qubit codes
本文提出基于三量子比特码的级联量子纠错协议，通过总结级联规则构建适用于任意独立噪声的纠错方案，在非理想门操作下以更少物理资源实现更高有效信道保真度与容错阈值。
We apply a dynamical systems approach to concatenation of quantum error correcting codes, extending and generalizing the results of Rahn et al. [1] to both diagonal and nondiagonal channels. Our point of view is global: instead of focusing on particular types of noise channels, we study the geometry of the coding map as a discrete-time dynamical system on the entire space of noise channels. In the case of diagonal channels, we show that any code with distance at least three corrects (in the infinite concatenation limit) an open set of errors. For Calderbank-Shor-Steane (CSS) codes, we give a m…
We propose an architecture of quantum-error-correction-based quantum repeaters that combines techniques used in discrete- and continuous-variable quantum information. Specifically, we propose to encode the transmitted qubits in a concatenated code consisting of two levels. On the first level we use a continuous-variable GKP code encoding the qubit in a single bosonic mode. On the second level we use a small discrete-variable code. Such an architecture has two important features. Firstly, errors on each of the two levels are corrected in repeaters of two different types. This enables for achiev…
We prove a new version of the quantum threshold theorem that applies to concatenation of a quantum code that corrects only one error, and we use this theorem to derive a rigorous lower bound on the quantum accuracy threshold epsilon_0. Our proof also applies to concatenation of higher-distance codes, and to noise models that allow faults to be correlated in space and in time. The proof uses new criteria for assessing the accuracy of fault-tolerant circuits, which are particularly conducive to the inductive analysis of recursive simulations. Our lower bound on the threshold, epsilon_0 > 2.73 \t…
We construct concatenated capacity-achieving quantum codes for noisy optical quantum channels. We demonstrate that the error-probability of capacity-achieving quantum polar encoding can be reduced by the proposed low-complexity concatenation scheme.
Staying Sober: A Shot-Free Predictor of Logical Error Rates for Concatenated Quantum Error Correcting Codes
提出一种无需采样的预测器，通过稳定子和逻辑算子计算级联量子纠错码逻辑错误率的首项，实现快速评估与比较。
We present a description of encoding/decoding for a concatenated quantum code that enables both protection against quantum computational errors and the occurrence of one quantum erasure. For this, it is presented how encoding and decoding for quantum graph codes are done, which will provide the protection against the occurrence of computational errors (external code). As internal code is used encoding and decoding via scheme of GHZ states for protection against the occurrence of one quantum erasure.
Entanglement-Assisted Concatenated Quantum Codes: Parameters and Asymptotic Performance
本文通过级联两个 EAQECC 并采用几乎 MDS、ℏ-MDS 及量子代数几何码作外码，构造多族参数更优的最大纠缠 EACQCs，并证明其可渐近达到量子 Gilbert–Varshamov 界。
High-Rate Concatenated Quantum Error-Correcting Codes for Qudits
本研究将多超立方体（MHC）码扩展至素数维度量子位元，构造了二、三级MHC码并推广逐级最小距离译码器，发现其错误阈值随维度提升，q=13时达10.0%，性能优于量子比特，为高维FTQC架构提供支撑。
A Concatenated Dual Displacement Code for Continuous-Variable Quantum Error Correction
本文提出一种拼接双位移码，通过结合高斯噪声抑制电路和外层类Steane码，有效抑制大范围位移误差，实现连续编码空间内的量子纠错。
It is an oft-cited fact that no quantum code can support a set of fault-tolerant logical gates that is both universal and transversal. This no-go theorem is generally responsible for the interest in alternative universality constructions including magic state distillation. Widely overlooked, however, is the possibility of non-transversal, yet still fault-tolerant, gates that work directly on small quantum codes. Here we demonstrate precisely the existence of such gates. In particular, we show how the limits of non-transversality can be overcome by performing rounds of intermediate error-correc…
Observation of a Fault Tolerance Threshold with Concatenated Codes
提出基于蝴蝶网络架构的广义Shor码级联容错协议，结合张量网络概率传递解码器，实现高噪声阈值状态制备并在离子阱硬件验证，理论扩展至量子存储与通用计算。
The concept of generalized concatenated quantum codes (GCQC) provides a systematic way for constructing good quantum codes from short component codes. We introduce a stabilizer formalism for GCQCs, which is achieved by defining quantum coset codes. This formalism offers a new perspective for GCQCs and enables us to derive a lower bound on the code distance of stabilizer GCQCs from component codes parameters,for both non-degenerate and degenerate component codes. Our formalism also shows how to exploit the error-correcting capacity of component codes to design good GCQCs efficiently.
Estimates of the quantum accuracy threshold often tacitly assume that it is possible to interact arbitrary pairs of qubits in a quantum computer with a failure rate that is independent of the distance between them. None of the many physical systems that are candidates for quantum computing possess this property. Here we study the performance of a concatenated error-detection code in a system that permits only nearest-neighbor interactions in one dimension. We make use of a new message-passing scheme that maximizes the number of errors that can be reliably corrected by the code. Our numerical r…
We present a comprehensive architectural analysis for a proposed fault-tolerant quantum computer based on cat codes concatenated with outer quantum error-correcting codes. For the physical hardware, we propose a system of acoustic resonators coupled to superconducting circuits with a two-dimensional layout. Using estimated physical parameters for the hardware, we perform a detailed error analysis of measurements and gates, including CNOT and Toffoli gates. Having built a realistic noise model, we numerically simulate quantum error correction when the outer code is either a repetition code or a…
Circuit-level benchmarks of GKP-concatenated qLDPC Codes
本研究对GKP-级联qLDPC码进行电路级基准测试，发现模拟信息BP-OSD解码优于硬判决，BB码序列在电路噪声下具有更高阈值和更低压缩需求。
In this paper, we present a new construction of asymmetric quantum codes (AQCs) by combining classical concatenated codes (CCs) with tensor product codes (TPCs), called asymmetric quantum concatenated and tensor product codes (AQCTPCs) which have the following three advantages. First, only the outer codes in AQCTPCs need to satisfy the orthogonal constraint in quantum codes, and any classical linear code can be used for the inner, which makes AQCTPCs very easy to construct. Second, most AQCTPCs are highly degenerate, which means they can correct many more errors than their classical TPC counte…
A new way of addressing loss errors is introduced which combines ideas from measurement-based quantum computation and concatenated quantum codes, allowing for universal quantum computation. It is shown that for the case where leakage is detected upon measurement, the scheme performs well under 23% loss rate. For loss rates below 10%, this approach performs better than the best scheme known up to date [Phys. Rev.Lett., 97(12):120501]. If lost qubits are tagged prior to measurement, it can tolerate up to 50% loss. The overhead per logical qubit is shown to be significantly lower than other schem…
Coherent errors, which arise from collective couplings, are a dominant form of noise in many realistic quantum systems, and are more damaging than oft considered stochastic errors. Here, we propose integrating stabilizer codes with constant-excitation codes by code concatenation. Namely, by concatenating an $[[n,k,d]]$ stabilizer outer code with dual-rail inner codes, we obtain a $[[2n,k,d]]$ constant-excitation code immune from coherent phase errors and also equivalent to a Pauli-rotated stabilizer code. When the stabilizer outer code is fault-tolerant, the constant-excitation code has a posi…
We examine general Gottesman-Kitaev-Preskill (GKP) codes for continuous-variable quantum error correction, including concatenated GKP codes, through the lens of lattice theory, in order to better understand the structure of this class of stabilizer codes. We derive formal bounds on code parameters, show how different decoding strategies are precisely related, propose new ways to obtain GKP codes by means of glued lattices and the tensor product of lattices and point to natural resource savings that have remained hidden in recent approaches. We present general results that we illustrate through…
ConiQ: Enabling Concatenated Quantum Error Correction on Neutral Atom Arrays
针对级联码（多超立方体码）在可寻址逻辑门和硬件实现上的挑战，提出基于AHA门和VAIR的ConiQ编译器，用于中性原子阵列，实现高达2000倍时空开销和10^6倍编译时间降低。
A conjugate code pair is defined as a pair of linear codes such that one contains the dual of the other. The conjugate code pair represents the essential structure of the corresponding Calderbank-Shor-Steane (CSS) quantum code. It is argued that conjugate code pairs are applicable to quantum cryptography in order to motivate studies on conjugate code pairs.
It has been known that quantum error correction via concatenated codes can be done with exponentially small failure rate if the error rate for physical qubits is below a certain accuracy threshold. Other, unconcatenated codes with their own attractive features-improved accuracy threshold, local operations-have also been studied. By iteratively distilling a certain two-qubit entangled state it is shown how to perform an encoded Toffoli gate, important for universal computation, on CSS codes that are either unconcatenated or, for a range of very large block sizes, singly concatenated.
Adaptive Syndrome Extraction
本文提出自适应综合征提取方案，仅测量可能提供有用信息的稳定子生成元，并在 [[4,2,2]] 码与超图积码级联中实时调整电路，显著降低逻辑错误率、门数和量子比特开销。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。