Errors in quantum logic gates are usually modeled by quantum process matrices (CPTP maps). But process matrices can be opaque, and unwieldy. We show how to transform a gate's process matrix into an error generator that represents the same information more usefully. We construct a basis of simple and physically intuitive elementary error generators, classify them, and show how to represent any gate's error generator as a mixture of elementary error generators with various rates. Finally, we show how to build a large variety of reduced models for gate errors by combining elementary error generators and/or entire subsectors of generator space. We conclude with a few examples of reduced models, including one with just $9N^2$ parameters that describes almost all commonly predicted errors on an N-qubit processor.
Quantum error mitigation (QEM) has been proposed as an alternative method of quantum error correction to compensate errors in quantum systems without qubit overhead. While Markovian gate errors on digital quantum computers have been mainly considered previously, it is indispensable to discuss a relationship between QEM and non-Markovian errors because non-Markovian noise effects inevitably exist in most of the solid-state systems. In this work, we investigate the QEM for non-Markovian noise, and show that there is a clear relationship between costs for QEM and non-Markovian measures. As exampl…
Error Propagation Theory for Variational Non-Markovian Open Quantum Dynamics
Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China（中国科学技术大学微尺度物质科学国家研究中心）；State Key Laboratory of Porous Materials for Separation and Conversion & MOE Key Laboratory of Computational Physical Sciences & Department of Chemistry, Fudan University（复旦大学化学系多孔材料分离转化国家重点实验室及计算物理科学教育部重点实验室）；Hefei National Laboratory（合肥国家实验室）
Hamiltonian quantum computing, such as the adiabatic and holonomic models, can be protected against decoherence using an encoding into stabilizer subspace codes for error detection and the addition of energy penalty terms. This method has been widely studied since it was first introduced by Jordan, Farhi, and Shor (JFS) in the context of adiabatic quantum computing. Here we extend the original result to general Markovian environments, not necessarily in Lindblad form. We show that the main conclusion of the original JFS study holds under these general circumstances: assuming a physically reaso…
Non-Markovian Quantum Error Deterrence by Dynamical Decoupling in a General Environment
研究了一种动态解耦方案，用于阻止非马尔可夫（通常对应于低温、短时间和强耦合）机制中的错误，该机制适用于由多级结构构造的量子比特。我们采用最近提出的有效自旋玻色子模型[K.盐川和B. L. Hu，Phys.Rev.A70，062106（2004）]作为量子布朗振子模型的低温极限，其中可以获得具有色噪声的一般环境的精确解。在我们的解耦方案中，一个训练的强脉冲对被用来发展的相互作用哈密顿量瞬间。使用此方案，我们表明，动态解耦方法可以抑制$1/f$噪声与更慢，因此更容易访问的脉冲比以前的研究，但它仍然未能解耦超欧姆类型的环境。
We investigate the distribution of errors on a computationally useful entangled state generated via the repeated emission from an emitter undergoing strongly non-Markovian evolution. For emitter-environment coupling of pure-dephasing form, we show that the probability that a particular patten of errors occurs has a bound of Markovian form, and thus accuracy threshold theorems based on Markovian models should be just as effective. This is the case, for example, for a charged quantum dot emitter in a moderate to strong magnetic field. Beyond the pure-dephasing assumption, though complicated erro…
In this study, we explore the non-Markovian cost function for quantum error mitigation (QEM) and the representation of two-qubit operators using Dirac Gamma matrices, central to the structure of relativistic quantum mechanics. The primary focus of quantum computing research, particularly with noisy intermediate-scale quantum (NISQ) devices, is on reducing errors and decoherence for practical application. While much of the existing research concentrates on Markovian noise sources, the study of non-Markovian sources is crucial given their inevitable presence in most solid-state quantum computing…
The promise of quantum computing with imperfect qubits relies on the ability of a quantum computing system to scale cheaply through error correction and fault-tolerance. While fault-tolerance requires relatively mild assumptions about the nature of qubit errors, the overhead associated with coherent and non-Markovian errors can be orders of magnitude larger than the overhead associated with purely stochastic Markovian errors. One proposal to address this challenge is to randomize the circuits of interest, shaping the errors to be stochastic Pauli errors but leaving the aggregate computation un…
Generic non-Markovian quantum processes have infinitely long memory, implying an exact description that grows exponentially in complexity with observation time. Here, we present a finite memory ansatz that approximates (or recovers) the true process with errors bounded by the strength of the non-Markovian memory. The introduced memory strength is an operational quantity and depends on the way the process is probed. Remarkably, the recovery error is bounded by the smallest memory strength over all possible probing methods. This allows for an unambiguous and efficient description of non-Markovia…
Non-Markovian Noise Suppression Simplified through Channel Representation
Tsinghua University（清华大学）；Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院）；Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院量子信息中心）；Technology Innovation Institute（技术创新研究所）；A*STAR Quantum Innovation Centre (Q.InC)（A*STAR量子创新中心）；Agency for Science, Technology and Research (A*STAR)（新加坡科技研究局）；Institute of High Performance Computing (IHPC)（高性能计算研究所）；University of Oxford（牛津大学）；Imperial College London（帝国理工学院）；Quantum Motion
Adiabatic quantum computing (AQC) can be protected against thermal excitations via an encoding into error detecting codes, supplemented with an energy penalty formed from a sum of commuting Hamiltonian terms. Earlier work showed that it is possible to suppress the initial thermally induced excitation out of the encoded ground state, in the case of local Markovian environments, by using an energy penalty strength that grows only logarithmically in the system size, at a fixed temperature. The question of whether this result applies beyond the initial time was left open. Here we answer this in th…
A Lie-algebraic approach to non-Markovian quantum dynamics
The University of Hong Kong（香港大学）；Tsinghua University（清华大学）；Materials Innovation Institute for Life Sciences and Energy (MILES)（生命科学与能源材料创新研究所）；HKU-SIRI, Shenzhen（香港大学深圳研究院）
Establishing the strong converse theorem for a communication channel confirms that the capacity of that channel, that is, the maximum achievable rate of reliable information communication, is the ultimate limit of communication over that channel. Indeed, the strong converse theorem for a channel states that coding at a rate above the capacity of the channel results in the convergence of the error to its maximum value 1 and that there is no trade-off between communication rate and decoding error. Here we prove that the strong converse theorem holds for the product-state capacity of quantum chan…
The rapidly developing quantum technologies and thermodynamics have put forward a requirement to precisely control and measure the temperature of microscopic matter at the quantum level. Many quantum thermometry schemes have been proposed. However, precisely measuring low temperature is still challenging because the obtained sensing errors generally tend to diverge with decreasing temperature. Using a continuous-variable system as a thermometer, we propose non-Markovian quantum thermometry to measure the temperature of a quantum reservoir. A mechanism to make the sensing error $δT$ scale with …
A gauge-invariant theory of small Markovian errors in quantum gate sets
Quantum Performance Laboratory, Sandia National Laboratories（桑迪亚国家实验室量子性能实验室）；Department of Physics and Astronomy, Quantum New Mexico Institute, University of New Mexico（新墨西哥大学量子新墨西哥学院物理与天文学系）；IonQ
We introduce the multipartite collision model, defined in terms of elementary interactions between subsystems and ancillae, and show that it can simulate the Markovian dynamics of any multipartite open quantum system. We develop a method to estimate an analytical error bound for any repeated interactions model, and we use it to prove that the error of our scheme displays an optimal scaling. Finally, we provide a simple decomposition of the multipartite collision model into elementary quantum gates, and show that it is efficiently simulable on a quantum computer according to the dissipative qua…
The study of memory effects in quantum channels helps in developing characterization methods for open quantum systems and strategies for quantum error correction. Two main sets of channels exist, corresponding to system dynamics with no memory (Markovian) and with memory (non-Markovian). Interestingly, these sets have a non-convex geometry, allowing one to form a channel with memory from the addition of memoryless channels and vice-versa. Here, we experimentally investigate this non-convexity in a photonic setup by subjecting a single qubit to a convex combination of Markovian and non-Markovia…
We measure and quantify non-Markovian effects in IBM's Quantum Experience. Specifically, we analyze the temporal correlations in a sequence of gates by characterizing the performance of a gate conditioned on the gate that preceded it. With this method, we estimate (i) the size of fluctuations in the performance of a gate, i.e., errors due to non-Markovianity; (ii) the length of the memory; and (iii) the total size of the memory. Our results strongly indicate the presence of non-trivial non-Markovian effects in almost all gates in the universal set. However, based on our findings, we discuss th…
Analysis of Superradiance-Based Quantum Metrology under Independent Markovian Pure Dephasing
School of Fundamental Science and Technology, Keio University（庆应义塾大学基础理工学部）；Department of Electrical, Electronic, and Communication Engineering, Faculty of Advanced Science and Engineering, Chuo University（中央大学理工学府电气电子通信工程系）；Department of Physics, Simon Fraser University（西蒙菲莎大学物理系）；Center for Spintronics Research Network, Keio University（庆应义塾大学自旋电子学研究网络中心）
With continuing improvements on the quality of fabricated quantum devices, it becomes increasingly crucial to analyze noisy quantum process in greater details such as characterizing the non-Markovianity in a quantitative manner. In this work, we propose an experimental protocol, termed Spectral Transfer Tensor Maps (SpecTTM), to accurately predict the RHP non-Markovian measure of any Pauli channels without state-preparation and measurement (SPAM) errors. In fact, for Pauli channels, SpecTTM even allows the reconstruction of highly-precised noise power spectrum for qubits. At last, we also disc…
Quantum error correction is instrumental in protecting quantum systems from noise in quantum computing and communication settings. Pauli channels can be efficiently simulated and threshold values for Pauli error rates under a variety of error-correcting codes have been obtained. However, realistic quantum systems can undergo noise processes that differ significantly from Pauli noise. In this paper, we present an efficient hard decoding algorithm for optimizing thresholds and lowering failure rates of an error-correcting code under general completely positive and trace-preserving (i.e., Markovi…
We study the exact open system dynamics of single qubit gates during a measurement-based quantum computation considering non-Markovian environments. We obtain analytical solutions for the average gate fidelities and analyze it for amplitude damping and dephasing channels. We show that the average fidelity is identical for the X-gate and Z-gate and that neither fast application of the projective measurements necessarily implies high gate fidelity, nor slow application necessarily implies low gate fidelity. Indeed, for highly non-Markovian environments, it is of utmost importance to know the bes…
Randomized compiling reduces the effects of errors on quantum computers by tailoring arbitrary Markovian errors into stochastic Pauli noise. Here we prove that randomized compiling also tailors non-Markovian errors into local stochastic Pauli noise and investigate the technique's limitations. We show through analysis and numerical results that randomized compiling alters errors in three distinct helpful ways. First, it prevents the coherent accumulation of errors (including hard to remove crosstalk effects) across gate cycles by destroying intercycle coherent correlations. Second, it converts …
Max-Planck-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
Non-Markovian effects are important in modeling the behavior of open quantum systems arising in solid-state physics, quantum optics as well as in study of biological and chemical systems. The non-Markovian environment is often approximated by discrete bosonic modes, thus mapping it to a Lindbladian or Hamiltonian simulation problem. While systematic constructions of such modes have been previously proposed, the resulting approximation lacks rigorous and general convergence guarantees. In this letter, we show that under some physically motivated assumptions on the system-environment interaction…
