A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations to a universal set by the addition of `magic' quantum states. In this context, we develop a general framework to discuss the value of the available, non-ideal magic resources, relative to those ideally required. We single out a quantity, the Quantum-assisted Robustness of Magic (QRoM), which measures the overhead of simulating the ideal resource with the non-ideal ones through quasiprobability-based methods. This extends error mitigation techniques, originally developed for Noisy Intermediate Scale Quantum (NISQ) devices, to the case where qubits are logically encoded. The QRoM shows how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit and enables the construction of explicit protocols, interpolating between classical simulation and an ideal quantum computer.
Error Mitigation From a Single Unmodified Error-Corrected Circuit
Qedma Quantum Computing（Qedma量子计算）；The Benin School of Computer Science and Engineering, Hebrew University（希伯来大学本计算机科学与工程学院）；Faculty of Mathematics and Computer Science, Weizmann Institute of Science（魏茨曼科学研究所数学与计算机科学系）；Department of Physics, Technion（以色列理工学院物理系）
We propose a method to assist fault mitigation in quantum computation through the use of sensors co-located near physical qubits. Specifically, we consider using transition edge sensors co-located on silicon substrates hosting superconducting qubits to monitor for energy injection from ionizing radiation, which has been demonstrated to increase decoherence in transmon qubits. We generalize from these two physical device concepts and explore the potential advantages of co-located sensors to assist fault mitigation in quantum computation. In the simplest scheme, co-located sensors beneficially a…
Open quantum system dynamics of random unitary type may in principle be fully undone. Closely following the scheme of environment-assisted error correction proposed by Gregoratti and Werner [M. Gregoratti and R. F. Werner, J. Mod. Opt. 50(6), 915-933 (2003)], we explicitly carry out all steps needed to invert a phase-damping error on a single qubit. Furthermore, we extend the scheme to a mixed-state environment. Surprisingly, we find cases for which the uncorrected state is closer to the desired state than any of the corrected ones.
Several techniques have been recently introduced to mitigate errors in near-term quantum computers without the overhead required by quantum error correcting codes. While most of the focus has been on gate errors, measurement errors are significantly larger than gate errors on some platforms. A widely used {\it transition matrix error mitigation} (TMEM) technique uses measured transition probabilities between initial and final classical states to correct subsequently measured data. However from a rigorous perspective, the noisy measurement should be calibrated with perfectly prepared initial st…
We show a significant reduction of errors for an architecture of quantum annealers (QA) where bosonic modes mediate the interaction between qubits. These systems have a large redundancy in the subspace of solutions, supported by arbitrarily large bosonic occupations. We explain how this redundancy leads to a mitigation of errors when the bosonic modes operate in the ultrastrong coupling regime. Numerical simulations also predict a large increase of qubit coherence for a specific annealing problem with mediated interactions. We provide evidences that noise reduction occurs in more general types…
Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of pre-existing entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQECC from any classical linear code, unlike standard QECCs which can only be constructed from dual-containing codes. Operator quantum error-correcting codes (OQECCs) allow certain errors to be corrected (or prevented) passively, reducing the complexity of the correction procedure. We combine these two extensions of standard quantum error correction into a unified entanglement-assisted quantum err…
Noisy intermediate-scale quantum (NISQ) computers could solve quantum-mechanical simulation problems that are beyond the capabilities of classical computers. However, NISQ devices experience significant errors which, if not corrected, can render physical quantities measured in these simulations inaccurate or meaningless. Here we describe a method of reducing these errors which is tailored to quantum algorithms for simulating fermionic systems. The method is based on executing quantum circuits in the model of fermionic linear optics, which are known to be efficiently simulable classically, to i…
Improving gate performance is vital for scalable quantum computing. The universal quantum computing also requires the gate fidelity to reach a high level. For superconducting quantum processor, which operates in the microwave band, the single-qubit gates are usually realized with microwave driving. The crosstalk between microwave pulses is a non-negligible error source. In this article, we propose an error mitigation scheme to address this crosstalk issue for single-qubit gates. There are three steps in our method. First, by controlling the detuning between qubits, the microwave induced classi…
The Eastin-Knill theorem states that no quantum error correcting code can have a universal set of transversal gates. For CSS codes that can implement Clifford gates transversally it suffices to provide one additional non-Clifford gate, such as the T-gate, to achieve universality. Common methods to implement fault-tolerant T-gates like magic state distillation generate a significant hardware overhead that will likely prevent their practical usage in the near-term future. Recently methods have been developed to mitigate the effect of noise in shallow quantum circuits that are not protected by er…
We exhibit discrete memoryless quantum channels whose quantum capacity assisted by two-way classical communication, $Q_2$, exceeds their unassisted one-shot Holevo capacity $C_H$. These channels may be thought of as having a data input and output, along with a control input that partly influences, and a control output that partly reveals, which of a set of unitary evolutions the data undergoes en route from input to output. The channel is designed so that the data's evolution can be exactly inferred by a classically coordinated processing of 1) the control output, and 2) a reference system ent…
Quantum computing devices are inevitably subject to errors. To leverage quantum technologies for computational benefits in practical applications, quantum algorithms and protocols must be implemented reliably under noise and imperfections. Since noise and imperfections limit the size of quantum circuits that can be realized on a quantum device, developing quantum error mitigation techniques that do not require extra qubits and gates is of critical importance. In this work, we present a deep learning-based protocol for reducing readout errors on quantum hardware. Our technique is based on train…
Readout errors are among the most dominant errors on current noisy intermediate-scale quantum devices. Recently, an efficient and scaleable method for mitigating such errors has been developed, based on classical bit-flip correction. In this talk, we compare the performance of this method for IBM's and Rigetti's quantum devices, demonstrating how the method improves the noisy measurements of observables obtained on the quantum hardware. Moreover, we examine the variance amplification to the data after applying of our mitigation procedure, which is common to all mitigation strategies. We derive…
Excess noise is a major obstacle to high-performance continuous-variable quantum key distribution (CVQKD), which is mainly derived from the amplitude attenuation and phase fluctuation of quantum signals caused by channel instability. Here, an excess noise suppression scheme based on equalization is proposed. In this scheme, the distorted signals can be corrected through equalization assisted by a neural network and pilot tone, relieving the pressure on the post-processing and eliminating the hardware cost. For a free-space channel with more intense fluctuation, a classification algorithm is ad…
Quantum error mitigation techniques can reduce noise on current quantum hardware without the need for fault-tolerant quantum error correction. For instance, the quasiprobability method simulates a noise-free quantum computer using a noisy one, with the caveat of only producing the correct expected values of observables. The cost of this error mitigation technique manifests as a sampling overhead which scales exponentially in the number of corrected gates. In this work, we present a new algorithm based on mathematical optimization that aims to choose the quasiprobability decomposition in a nois…
Noise-Symmetry Optimization of Quantum Error-Corrected Metrology
School of Physics, Sun Yat-sen University（中山大学物理学院）；State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University（北京大学物理学院介观物理国家重点实验室）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）
Compiling quantum algorithms for near-term quantum computers (accounting for connectivity and native gate alphabets) is a major challenge that has received significant attention both by industry and academia. Avoiding the exponential overhead of classical simulation of quantum dynamics will allow compilation of larger algorithms, and a strategy for this is to evaluate an algorithm's cost on a quantum computer. To this end, we propose a variational hybrid quantum-classical algorithm called quantum-assisted quantum compiling (QAQC). In QAQC, we use the overlap between a target unitary $U$ and a …
Quantum Error Mitigation with Attention Graph Transformers for Burgers Equation Solvers on NISQ Hardware
Vision-Guided and Intelligent Robotics Lab (ViGIR) - EECS Department - University of Missouri - Columbia（智能机器人实验室（ViGIR）- 电子工程与计算机科学系 - 密苏里大学 - 哥伦比亚）；Department of Mechanical and Aerospace Engineering - University of Missouri - Columbia（机械与航空航天工程系 - 密苏里大学 - 哥伦比亚）
IBM Research（IBM 研究部）；Trinity Business School（三一商学院）；Donostia International Physics Center (DIPC)（圣塞巴斯蒂安国际物理中心）；Nanoscale Device Characterization Division, National Institute of Standards and Technology（美国国家标准与技术研究院纳米器件表征部门）；Centro de Física de Materiales CFM/MPC (CSIC-UPV/EHU)（材料物理中心 (西班牙国家科研委员会-巴斯克国立大学/阿尔贝塔理工大学)）；Advanced Micro Devices Inc.（超威半导体公司）
