Lu-Ming Duan, Guang-Can Guo
A general theory of quantum error avoiding codes is established, and new light is shed on the relation between quantum error avoiding and correcting codes. Quantum error avoiding codes are found to be a special type of highly degenerate quantum error correcting codes. A combination of the ideas of correcting and avoiding quantum errors may yield better codes. We give a practical example.
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We study the performance of simple error correcting and error avoiding quantum codes together with their concatenation for correlated noise models. Specifically, we consider two error models: i) a bit-flip (phase-flip) noisy Markovian memory channel (model I); ii) a memory channel defined as a memory degree dependent linear combination of memoryless channels with Kraus decompositions expressed solely in terms of tensor products of X-Pauli (Z-Pauli) operators (model II). The performance of both the three-qubit bit flip (phase flip) and the error avoiding codes suitable for the considered error …
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.
Error-correcting codes are usually envisioned to counter errors by operating unitary corrections depending on the projective measurement results of some syndrome observables. We here propose a way to use them in a more integrated way, where the error correction is applied continuously and autonomously by an engineered environment. We focus on a proposal for the repetition code that counters bit-flip errors, and how to scale up the network encoding a logical quantum bit, towards stronger information protection. The challenge has been to devise a network architecture which allows to autonomously…
We study the performance of simple quantum error correcting codes with respect to correlated noise errors characterized by a finite correlation strength. Specifically, we consider bit flip (phase flip) noisy quantum memory channels and use repetition and noiseless quantum codes. We characterize the performance of the codes by means of the entanglement fidelity as function of the error probability and degree of memory. Finally, comparing the entanglement fidelities of repetition and noiseless quantum codes, we find a threshold for the correlation strength that allows to select the code with bet…
This is a short introduction to quantum computers, quantum algorithms and quantum error correcting codes. Familiarity with the principles of quantum theory is assumed. Emphasis is put on a concise presentation of the principles avoiding lengthy discussions.
A formulation for evaluating the performance of quantum error correcting codes for a general error model is presented. In this formulation, the correlation between errors is quantified by a Hamiltonian description of the noise process. We classify correlated errors using the system-bath interaction: local versus nonlocal and two-body versus many-body interactions. In particular, we consider Calderbank-Shor-Steane codes and observe a better performance in the presence of correlated errors depending on the timing of the error recovery. We also find this timing to be an important factor in the de…
Quantum Zeno effect versus adiabatic quantum computing and quantum annealing
研究绝热Grover搜索算法中环境耦合导致的退相干，发现量子芝诺效应通过持续测量抑制量子跃迁，从而限制量子加速，并推广到基于Landau-Zener跃迁的绝热量子算法和量子退火方案。
Correcting and extending Trotterized quantum many-body dynamics
本研究提出一种混合量子-经典拟设，通过Trotter化在量子计算机上模拟简化哈密顿量，并用经典模型修正遗漏项，实现避免SWAP门、减轻Trotter误差及扩展系统尺寸。该方法无变分参数，导数纯经典计算，规避了参数化量子电路优化难题。
Collective decoherence is possible if the departure between quantum bits is smaller than the effective wave length of the noise field. Collectivity in the decoherence helps us to devise more efficient quantum codes. We present a class of optimal quantum codes for preventing collective amplitude damping to a reservoir at zero temperature. It is shown that two qubits are enough to protect one bit quantum information, and approximately $L+ 1/2 \log_2((πL)/2)$ qubits are enough to protect $L$ qubit information when $L$ is large. For preventing collective amplitude damping, these codes are much mor…
In this thesis we describe methods for avoiding the detrimental effects of decoherence while at the same time still allowing for computation of the quantum information. The philosophy of the method discussed in the first part of this thesis is to use a symmetry of the decoherence mechanism to find robust encodings of the quantum information. Stability, control, and methods for using decoherence-free information in a quantum computer are presented with a specific emphasis on decoherence due to a collective coupling between the system and its environment. Universal quantum computation on such co…
Loss-correcting fault-tolerant quantum computing architecture for neutral atoms
该研究提出一种面向中性原子的容错量子计算架构，通过协同设计布局、编译与解码，将量子比特丢失作为动态预算控制，显著降低逻辑错误率并提升容错性能。
Any physical quantum device for quantum information processing is subject to errors in implementation. In order to be reliable and efficient, quantum computers will need error correcting or error avoiding methods. Fault-tolerance achieved through quantum error correction will be an integral part of quantum computers. Of the many methods that have been discovered to implement it, a highly successful approach has been to use transversal gates and specific initial states. A critical element for its implementation is the availability of high-fidelity initial states such as |0> and the Magic State.…
Leakage is a particularly damaging error that occurs when a qubit leaves the defined computational subspace. Leakage errors limit the effectiveness of quantum error correcting codes by spreading additional errors to other qubits and corrupting syndrome measurements. The effects of leakage errors on the surface code has been studied in various contexts. However, the effects of a leaked data qubit versus a leaked ancilla qubit can be quite different. Here, we study the effects of data leakage and ancilla leakage separately. We show that data leakage is much less damaging. We show that the surfac…
Ab initio modelling of quantum dot qubits: Coupling, gate dynamics and robustness versus charge noise
本文提出一种基于实空间网格的从头算方法，用于预测量子点量子比特的交换耦合和门动力学，并通过2D近似高效模拟，同时研究电荷噪声影响并展示可提升保真度一个数量级的鲁棒脉冲序列。
Efficient Magic State Cultivation on the Surface Code
本文提出了一种在表面码上直接实现高效魔态培养的方法，显著提高了魔态生成效率并降低了错误率。
Bubble Clustering Decoder for Quantum Topological Codes
本文提出了用于量子表面码的气泡聚类（BC）解码器，通过基于缺陷中心气泡的高效聚类生成避免传统聚类生长与合并开销，作为MWPM的低延迟替代方案，在轻微性能下降下实现显著加速，其复杂度在适中错误率下与数据量子比特数呈线性关系。
We study the properties of error correcting codes for noise models in the presence of asymmetries and/or correlations by means of the entanglement fidelity and the code entropy. First, we consider a dephasing Markovian memory channel and characterize the performance of both a repetition code and an error avoiding code in terms of the entanglement fidelity. We also consider the concatenation of such codes and show that it is especially advantageous in the regime of partial correlations. Finally, we characterize the effectiveness of the codes and their concatenation by means of the code entropy …
Model-based Optimization of Superconducting Qubit Readout
针对超导量子比特测量误差高的问题，提出基于模型的读出优化方法，在17比特同步中段测量中实现1.5%单比特误差、500ns耗时，抑制测量诱导态跃迁，可扩展至数百比特以提升纠错码和近期应用性能。
Quantum $(r,δ)$-locally recoverable codes
本文提出量子$(r,δ)$-局部可恢复码，研究其构造条件及与经典码的等价性，并给出单边界及实例。
Adaptive surface code for quantum error correction in the presence of temporary or permanent defects
针对量子比特因制造或高能事件出现缺陷会破坏表面码纠错的问题，提出结合缺陷检测与区域隔离的自适应表面码方法，在有限量子比特开销下保留纠错优势，阈值受影响小，助力大规模量子计算机实现。
Exact and Efficient Stabilizer Simulation of Thermal-Relaxation Noise for Quantum Error Correction
本文提出精确且兼容稳定子的量子比特热弛豫噪声模型，通过正概率分解提升纠错性能，并在超导平台研究大规模表面码与双变量自行车码。
Noisy decoding by shallow circuits with parities: classical and quantum
研究证明正错误率下任意码都无法由 NC$^0[\oplus]$ 经典浅电路有效解码，并提出可在近半码字遭对抗性损坏时解码 Hadamard 码的量子电路。
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