Mitsuru Hamada
On a class of memoryless quantum channels which includes the depolarizing channel, the highest fidelity of quantum error-correcting codes of length n and rate R is proven to be lower bounded by 1-exp[-nE(R)+o(n)] for some function E(R). The E(R) is positive below some threshold R', which implies R' is a lower bound on the quantum capacity.
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Achieving metrological limits using ancilla-free quantum error-correcting codes
该研究针对含噪声子计量中现有QEC码依赖无噪声辅助比特的难题，构造两种多探针QEC码（含可忽略辅助比特型与无辅助比特型），在马尔可夫噪声哈密顿量估计下可分别实现海森堡极限与标准量子极限的最优渐近系数。
Many quantum technologies are now reaching a high level of maturity and control, and it is likely that the first demonstrations of suppression of naturally occurring quantum noise using small topological error correcting codes will soon be possible. In doing this it will be necessary to define clear achievable metrics to measure and compare the performance of real codes. Here we consider the smallest examples of several families of topological codes: surface codes, color codes, and the gauge color code, and determine the minimum requirements to demonstrate error suppression. We use an exact de…
We derive a set of composite pulse sequences that generates CNOT gates and correct all systematic errors within the logical subspace to arbitrary order. These sequences are applicable for any two-qubit interaction Hamiltonian, and make no assumptions about the underlying noise mechanism except that it is constant on the timescale of the operation. We do assume access to error-free single-qubit gates, so single-qubit gate imperfections eventually limit the achievable fidelity. However, since single-qubit gates generally have much higher fidelities than two-qubit gates in practice, these pulse s…
Recently, there has been growing interest in using adiabatic quantum computation as an architecture for experimentally realizable quantum computers. One of the reasons for this is the idea that the energy gap should provide some inherent resistance to noise. It is now known that universal quantum computation can be achieved adiabatically using 2-local Hamiltonians. The energy gap in these Hamiltonians scales as an inverse polynomial in the problem size. Here we present stabilizer codes which can be used to produce a constant energy gap against 1-local and 2-local noise. The corresponding fault…
Tradeoffs between the information rate and fidelity of quantum error-correcting codes are discussed. Quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a general completely positive linear map, where the dimension of the underlying Hilbert space is a prime number. On such a quantum channel, the highest fidelity of a quantum error-correcting code of length $n$ and rate R is proven to be lower bounded by 1 - \exp [-n E(R) + o(n)] for some function E(R). The E(R) is positive below some threshold R', which implies R' is a lower bou…
We introduce a purely graph-theoretical object, namely the coding clique, to construct quantum errorcorrecting codes. Almost all quantum codes constructed so far are stabilizer (additive) codes and the construction of nonadditive codes, which are potentially more efficient, is not as well understood as that of stabilizer codes. Our graphical approach provides a unified and classical way to construct both stabilizer and nonadditive codes. In particular we have explicitly constructed the optimal ((10,24,3)) code and a family of 1-error detecting nonadditive codes with the highest encoding rate s…
The highest information rate at which quantum error-correction schemes work reliably on a channel, which is called the quantum capacity, is proven to be lower bounded by the limit of the quantity termed coherent information maximized over the set of input density operators which are proportional to the projections onto the code spaces of symplectic stabilizer codes. Quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a completely positive linear map on a Hilbert space of finite dimension, and the codes that are proven to have th…
Quantum error correcting codes have been shown to have the ability of making quantum information resilient against noise. Here we show that we can use quantum error correcting codes as diagnostics to characterise noise. The experiment is based on a three-bit quantum error correcting code carried out on a three-qubit nuclear magnetic resonance (NMR) quantum information processor. Utilizing both engineered and natural noise, the degree of correlations present in the noise affecting a two-qubit subsystem was determined. We measured a correlation factor of c=0.5+/-0.2 using the error correction pr…
Hypergraph product code with 0.2 constant coding rate and high code capacity noise threshold
提出TGRE-超图乘积码，具有0.2常数编码率，这是已知最高的量子稳定码，其去极化噪声信道中的码容量噪声阈值约为0.096。
An error avoiding quantum code is presented which is capable of stabilizing Grover's quantum search algorithm against a particular class of coherent errors. This error avoiding code consists of states only which are factorizable in the computational basis. Furthermore, its redundancy is smaller than the one which is achievable with a general error correcting quantum code saturating the quantum Hamming bound. The fact that this code consists of factorizable states only may offer advantages for the implementation of quantum gates in the error free subspace.
Noise-Resilient Quantum Evolution in Open Systems through Error-Correcting Frameworks
研究利用量子纠错码在开放量子系统中保护量子态，通过微观系统-环境模型推导二阶主方程，评估五ubit码、Steane码和拓扑码在局部和集体噪声下的保真度，揭示纠错策略在不同温度下的有效性。
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.
Fault-tolerant hyperbolic Floquet quantum error correcting codes
本文提出双曲Floquet码，通过周期性两体测量实现有限编码率，并开发匹配解码器，在低错误率下以更少物理量子比特达到同等逻辑错误抑制，推进容错量子计算。
We discuss energy barriers and their relationship to self-correcting quantum memories. We introduce the solid code, a 3-d version of Kitaev's surface code, and then combine several solid codes using a technique called welding. The resulting code is a $[[O(L^3),1,O(L^{\frac{4}{3}})]]$ stabilizer code with an energy barrier of $O(L^{\frac{2}{3}})$, which is an exponential improvement over the previous highest energy barrier in 3-d. No-go results are avoided by breaking microscopic translation invariance.
Quantum steganography is the study of hiding secret quantum information by encoding it into what an eavesdropper would perceive as an innocent-looking message. Here we study an explicit steganographic encoding for Alice to hide her secret message in the syndromes of an error-correcting code, so that the encoding simulates a given noisy quantum channel. We calculate achievable rates of steganographic communication over noiseless quantum channels using this encoding. We give definitions of secrecy and reliability for the communication process, and with these assumptions derive upper bounds on th…
We derive a necessary and sufficient condition for the possibility of achieving the Heisenberg scaling in general adaptive multi-parameter estimation schemes in presence of Markovian noise. In situations where the Heisenberg scaling is achievable, we provide a semidefinite program to identify the optimal quantum error correcting (QEC) protocol that yields the best estimation precision. We overcome the technical challenges associated with potential incompatibility of the measurement optimally extracting information on different parameters by utilizing the Holevo Cramér-Rao (HCR) bound for pure …
Quantum error correction is vital for implementing universal quantum computing. A key component is the encoding circuit that maps a product state of physical qubits into the encoded multipartite entangled logical state. Known methods are typically not 'optimal' either in terms of the circuit depth (and therefore the error burden) or the specifics of the target platform, i.e. the native gates and topology of a system. This work introduces a variational compiler for efficiently finding the encoding circuit of general quantum error correcting codes with given quantum hardware. Focusing on the noi…
The field of quantum communications promises the faithful distribution of quantum information, quantum entanglement, and absolutely secret keys, however, the highest rates of these tasks are fundamentally limited by the transmission distance between quantum repeaters. The ultimate end-to-end rates of quantum communication networks are known to be achievable by an optimal entanglement distillation protocol followed by teleportation. In this work, we give a practical design for this achievability. Our ultimate design is an iterative approach, where each purification step operates on shared entan…
Stabilizer Entropy of Subspaces
研究通过稳定子熵分析子空间嵌入对魔法资源的影响，发现可通过选择合适子空间实现零或负魔法间隙，从而提高模拟效率。
We summarise important recent advances in quantum metrology, in connection to experiments in cold gases, trapped cold atoms and photons. First we review simple metrological setups, such as quantum metrology with spin squeezed states, with Greenberger-Horne-Zeilinger states, Dicke states and singlet states. We calculate the highest precision achievable in these schemes. Then, we present the fundamental notions of quantum metrology, such as shot-noise scaling, Heisenberg scaling, the quantum Fisher information and the Cramer-Rao bound. Using these, we demonstrate that entanglement is needed to s…
Quantum capacities of transducers
本文基于量子容量定义了统一的量子转换器评价标准，通过连续时间量子容量研究了最优转换方案设计，并探讨了热噪声对性能的影响。
Quantum Error Correction with Metastable States of Trapped Ions Using Erasure Conversion
本文将擦除转换技术应用于囚禁离子亚稳态量子比特，提出擦除转换方案并建立错误模型，发现在高激光功率条件下亚稳态量子比特逻辑性能优于基态量子比特。
Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg limit, which can be achieved for noiseless quantum systems, but is not achievable in general for systems subject to noise. Here we study how measurement precision can be enhanced through quantum error correction, a general method for protecting a quantum system from the damaging effects of noise. We find a necessary and sufficient condition for achieving the…
Large-scale quantum computation will only be achieved if experimentally implementable quantum error correction procedures are devised that can tolerate experimentally achievable error rates. We describe a quantum error correction procedure that requires only a 2-D square lattice of qubits that can interact with their nearest neighbors, yet can tolerate quantum gate error rates over 1%. The precise maximum tolerable error rate depends on the error model, and we calculate values in the range 1.1--1.4% for various physically reasonable models. Even the lowest value represents the highest threshol…
Stabilizer codes for Heisenberg-limited many-body Hamiltonian estimation
本文研究噪声下多体哈密顿量估计的量子纠错，分析三类稳定子码在全连接 ZZZ 相互作用估计中的 n 与 t 缩放，并给出稳定子结构相关的不可行定理。
Challenges in certifying quantum teleportation: moving beyond conventional fidelity benchmark
本文指出传统保真度基准在量子隐形传态认证中存在结论不一致的局限，并通过分析Werner态及振幅阻尼信道等噪声模型，强调需要新的认证方法。
Error correction phase transition in noisy random quantum circuits
本文研究噪声随机量子电路中的信息编码，发现存在临界深度相变，并证明随机电路在深度与噪声率权衡上达到最优。
Architectures for Heterogeneous Quantum Error Correction Codes
本研究提出集成表面码与gross码的异构量子纠错架构，通过辅助总线实现码间数据移动，首次进行全系统研究，实现物理量子比特最多减少6.42倍，执行时间最多增加3.43倍。
An exact Error Threshold of Surface Code under Correlated Nearest-Neighbor Errors: A Statistical Mechanical Analysis
本文基于统计力学分析，推导出表面码在相关最近邻误差下的精确误差阈值，结合独立单量子比特误差与最近邻数据量子比特间的相关误差，提出分析约束，给出精确阈值。
Quantum synchronizable error-correcting codes are special quantum error-correcting codes that are designed to correct both the effect of quantum noise on qubits and misalignment in block synchronization. It is known that in principle such a code can be constructed through a combination of a classical linear code and its subcode if the two are both cyclic and dual-containing. However, finding such classical codes that lead to promising quantum synchronizable error-correcting codes is not a trivial task. In fact, although there are two families of classical codes that are proved to produce quant…
Near-optimal decoding algorithm for color codes using Population Annealing
本文提出一种基于群体退火的色码解码算法，通过将解码问题映射为自旋系统并估计自由能，在多种噪声模型下实现近最优阈值，且适用于表面码和qLDPC码。
Quantum communication on the bosonic loss-dephasing channel
本文反驳了玻色子损耗-退相干信道反可退化仅当损耗高于50%的猜想，证明任意损耗下退相干超临界值即反可退化，但双向经典通信可使量子通信始终实现。
The highest fidelity of quantum error-correcting codes of length n and rate R is proven to be lower bounded by 1 - exp [-n E(R)+ o(n)] for some function E(R) on noisy quantum channels that are subject to not necessarily independent errors. The E(R) is positive below some threshold R', which implies R' is a lower bound on the quantum capacity. This work is an extension of the author's previous works [M. Hamada, Phys. Rev. A, 65, 052305, 2002 (e-Print quant-ph/0109114, LANL, 2001), and M. Hamada, submitted to IEEE Trans. Inf. Theory, 2002 (e-Print quant-ph/0112103, LANL, 2001)], which presented …
The Gottesman-Kitaev-Preskill (GKP) code offers the possibility to encode higher-dimensional qudits into individual bosonic modes with, for instance, photonic excitations. Since photons enable the reliable transmission of quantum information over long distances and since GKP states subject to photon loss can be recovered to some extent, the GKP code has found recent applications in theoretical investigations of quantum communication protocols. While previous studies have primarily focused on GKP qubits, the possible practical benefits of higher-dimensional GKP qudits are hitherto widely unexpl…
Coherent error threshold for surface codes from Majorana delocalization
本文将带相干误差的表面码映射为二维Ising模型和Majorana散射网络，发现相干误差在阈值后映射到Majorana金属而非平凡绝缘体，并数值求得存储阈值ϕ_th≈0.14π，对应比特翻转率0.18，超过非相干阈值0.11。
Subsystem Symmetries and Fracton Models in Quantum Error Correction
该研究探究经典伊辛模型与量子纠错的关联，确定棋盘格码最优阈值达0.107(3)，证明分形子码是高鲁棒性量子存储器的优良候选，凸显统计力学框架的应用价值。
The local minimum degree of a graph is the minimum degree reached by means of a series of local complementations. In this paper, we investigate on this quantity which plays an important role in quantum computation and quantum error correcting codes. First, we show that the local minimum degree of the Paley graph of order p is greater than sqrt{p} - 3/2, which is, up to our knowledge, the highest known bound on an explicit family of graphs. Probabilistic methods allows us to derive the existence of an infinite number of graphs whose local minimum degree is linear in their order with constant 0.…
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