Fundamental limits of quantum error mitigation

Article Engineering, Electrical & Electronic

Quantum Error Mitigation Relying on Permutation Filtering

Yifeng Xiong et al.

Summary: This paper proposes a general framework called permutation filters for quantum error mitigation, which includes existing permutation-based methods and achieves substantial improvements under narrowband quantum noise.

IEEE TRANSACTIONS ON COMMUNICATIONS (2022)

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Article Physics, Multidisciplinary

Generalized Quantum Subspace Expansion

Nobuyuki Yoshioka et al.

Summary: This article introduces a novel quantum subspace expansion method for handling errors in quantum computers. By utilizing the extended subspace, the impact of noise on the spectra of a given Hamiltonian can be efficiently mitigated.

PHYSICAL REVIEW LETTERS (2022)

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Article Computer Science, Information Systems

Maximal Gap Between Local and Global Distinguishability of Bipartite Quantum States

Willian H. G. Correa et al.

Summary: This article proves a tight and close-to-optimal lower bound on the effectiveness of local quantum measurements and explains how to discriminate any two bipartite quantum states using local measurements with an upper limit on the error probability.

IEEE TRANSACTIONS ON INFORMATION THEORY (2022)

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Article Quantum Science & Technology

Quantum Error Mitigation as a Universal Error Reduction Technique: Applications from the NISQ to the Fault-Tolerant Quantum Computing Eras

Yasunari Suzuki et al.

Summary: In the early stages of fault-tolerant quantum computing, limitations in quantum devices and classical decoding units restrict the available code distance and magic state count. This study integrates quantum error correction and quantum error mitigation into an efficient architecture, effectively increasing the code distance and T-gate count at the cost of constant sampling overheads. Experimental results show a reduction in the required number of physical qubits by 80% and 45% in different regimes. Additionally, when the achievable code distance is around 11, the scheme allows for more than 10(3) times the number of logical operations.

PRX QUANTUM (2022)

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Article Optics

Dual-state purification for practical quantum error mitigation

Mingxia Huo et al.

Summary: The paper introduces a practical protocol for quantum error mitigation by virtually purifying quantum states with reduced errors. By combining dual-state purification and tomography purification, the fidelity of the purified state can be increased. The protocol demonstrates reduced errors on a cloud quantum computer, especially for larger circuits with a decreasing rescaling factor as the number of qubits and circuit depth increases.

PHYSICAL REVIEW A (2022)

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Article Quantum Science & Technology

Operational applications of the diamond norm and related measures in quantifying the non-physicality of quantum maps

Bartosz Regula et al.

Summary: This paper introduces an operational approach to quantitatively study the non-physicality of linear maps, focusing on approximation with quantum channels. It presents two measures to quantify the cost of simulating maps with physically implementable channels and the advantages of non-completely-positive maps in discrimination-based quantum games. The results reduce to the diamond norm, giving this norm new operational meanings in the characterization of linear maps and showing applications in positive map approximations, quantification of non-Markovianity, and bounding error mitigation costs.

QUANTUM (2021)

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Article Physics, Multidisciplinary

The dominant eigenvector of a noisy quantum state

Balint Koczor

Summary: The research introduces error suppression techniques through derangements and virtual distillation, promising practical applications for quantum devices. The study finds that the main eigenvector of noisy quantum states differs from the ideal computational state, but the difference is not significant. This understanding is crucial for effectively leveraging noisy quantum devices.

NEW JOURNAL OF PHYSICS (2021)

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Article Physics, Multidisciplinary

Error Mitigation for Universal Gates on Encoded Qubits

Christophe Piveteau et al.

Summary: The Eastin-Knill theorem states the impossibility of a universal set of transversal gates for any quantum error-correcting code; implementing noisy encoded T gates remains a challenge and may hinder practical applications in the near future; combining error correction and error mitigation methods allows for the implementation of Clifford + T circuits on small error-corrected devices, potentially surpassing state-of-the-art classical simulation algorithms.

PHYSICAL REVIEW LETTERS (2021)

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Article Physics, Multidisciplinary

Error Mitigation and Quantum-Assisted Simulation in the Error Corrected Regime

M. Lostaglio et al.

Summary: The article introduces a standard approach to quantum computing by promoting a set of classical operations to a universal set with the addition of magic quantum states, and introduces a new concept of quantum-assisted robustness of magic (QROM) to measure the value of magic resources. The QROM technique shows how adding noisy magic resources can enhance classical quasiprobability simulations of a quantum circuit.

PHYSICAL REVIEW LETTERS (2021)

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Article Multidisciplinary Sciences

Noise-induced barren plateaus in variational quantum algorithms

Samson Wang et al.

Summary: The study demonstrates that local Pauli noise can render VQAs untrainable. It shows that noise-induced barren plateaus cause the gradient to exponentially vanish during the training process.

NATURE COMMUNICATIONS (2021)

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Article Quantum Science & Technology

Physical Implementability of Linear Maps and Its Application in Error Mitigation

Jiaqing Jiang et al.

Summary: Completely positive and trace-preserving maps characterize physically implementable quantum operations, while general linear maps including positive but not completely positive maps play fundamental roles in quantum information theory but cannot be physically implemented. This work introduces a systematic framework using the quasi-probability decomposition technique to simulate or approximate the action of general linear maps with physically implementable operations. The physical implementability measure quantifies the cost of simulating a given map using physically implementable quantum operations and is efficiently computable by semidefinite programs.

QUANTUM (2021)

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Article Quantum Science & Technology

Error mitigation with Clifford quantum-circuit data

Piotr Czarnik et al.

Summary: A novel error-mitigation method for gate-based quantum computers is proposed in this study, which generates training data in quantum circuits and fits a linear ansatz to predict noise-free observables for arbitrary circuits. The method achieves an order-of-magnitude error reduction under various conditions.

QUANTUM (2021)

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Article Quantum Science & Technology

Quantum-enhanced analysis of discrete stochastic processes

Carsten Blank et al.

Summary: Discrete stochastic processes (DSP) are widely used in modeling the dynamics of probabilistic systems, often analyzed using Monte-Carlo methods. A quantum algorithm for calculating the characteristic function of a DSP has been proposed, which grows linearly with the number of time steps and guarantees optimal variance without the need for importance sampling.

NPJ QUANTUM INFORMATION (2021)

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Article Physics, Multidisciplinary

Optimal resource cost for error mitigation

Ryuji Takagi

Summary: The study focuses on the potential and limitations of near-term quantum devices, introducing a framework for quantum error mitigation to evaluate the optimal resource cost. The research methodology includes assessing the optimal cost of noise mitigation and improving bounds for noise models, offering operational meaning to resource measures.

PHYSICAL REVIEW RESEARCH (2021)

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Article Optics

Mitigating measurement errors in multiqubit experiments

Sergey Bravyi et al.

Summary: Reducing measurement errors in multiqubit quantum devices is critical for performing quantum algorithms. This study demonstrates error mitigation through classical postprocessing and introduces two error-mitigation schemes based on different noise models. Experimental demonstration on IBM Quantum devices shows the effectiveness of the proposed techniques.

PHYSICAL REVIEW A (2021)

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Article Optics

Relationship between costs for quantum error mitigation and non-Markovian measures

Hideaki Hakoshima et al.

Summary: This study investigates quantum error mitigation (QEM) for non-Markovian noise and reveals a clear relationship between costs for QEM and non-Markovian measures. Several non-Markovian noise models are used as examples to bridge the theoretical framework with concrete physical systems. This discovery may lead to improved QEM strategies for realistic quantum devices in non-Markovian environments.

PHYSICAL REVIEW A (2021)

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Article Multidisciplinary Sciences

Decoding quantum errors with subspace expansions

Jarrod R. McClean et al.

NATURE COMMUNICATIONS (2020)

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Article Multidisciplinary Sciences

Error-mitigated quantum gates exceeding physical fidelities in a trapped-ion system

Shuaining Zhang et al.

NATURE COMMUNICATIONS (2020)

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Review Physics, Multidisciplinary

Quantum computational chemistry

Sam McArdle et al.

REVIEWS OF MODERN PHYSICS (2020)

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Article Optics

Zero-noise extrapolation for quantum-gate error mitigation with identity insertions

Andre He et al.

PHYSICAL REVIEW A (2020)

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Article Quantum Science & Technology

Variational Quantum Fidelity Estimation

M. Cerezo et al.

QUANTUM (2020)

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Article Computer Science, Information Systems

Sampling Overhead Analysis of Quantum Error Mitigation: Uncoded vs. Coded Systems

Yifeng Xiong et al.

IEEE ACCESS (2020)

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Article Multidisciplinary Sciences

Error mitigation extends the computational reach of a noisy quantum processor

Abhinav Kandala et al.

NATURE (2019)

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Article Physics, Multidisciplinary

Error-Mitigated Digital Quantum Simulation

Sam McArdle et al.

PHYSICAL REVIEW LETTERS (2019)

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Review Chemistry, Multidisciplinary

Quantum Chemistry in the Age of Quantum Computing

Yudong Cao et al.

CHEMICAL REVIEWS (2019)

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Article Multidisciplinary Sciences

Quantum computation with universal error mitigation on a superconducting quantum processor

Chao Song et al.

SCIENCE ADVANCES (2019)

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Article Multidisciplinary Sciences

Quantum supremacy using a programmable superconducting processor

Frank Arute et al.

NATURE (2019)

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Article Optics

Experimental error mitigation via symmetry verification in a variational quantum eigensolver

R. Sagastizaba et al.

PHYSICAL REVIEW A (2019)

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Article Physics, Mathematical

Ultimate Data Hiding in Quantum Mechanics and Beyond

Ludovico Lami et al.

COMMUNICATIONS IN MATHEMATICAL PHYSICS (2018)

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Article Physics, Multidisciplinary

Cloud Quantum Computing of an Atomic Nucleus

E. F. Dumitrescu et al.

PHYSICAL REVIEW LETTERS (2018)

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Article Physics, Multidisciplinary

Practical Unitary Simulator for Non-Markovian Complex Processes

Felix C. Binder et al.

PHYSICAL REVIEW LETTERS (2018)

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Article Multidisciplinary Sciences

Quantum majorization and a complete set of entropic conditions for quantum thermodynamics

Gilad Gour et al.

NATURE COMMUNICATIONS (2018)

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Article Quantum Science & Technology

Quantum Computing in the NISQ era and beyond

John Preskill

QUANTUM (2018)

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Article Optics

Low-cost error mitigation by symmetry verification

X. Bonet-Monroig et al.

PHYSICAL REVIEW A (2018)

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Article Multidisciplinary Sciences

Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets

Abhinav Kandala et al.

NATURE (2017)

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Article Physics, Multidisciplinary

Error Mitigation for Short-Depth Quantum Circuits

Kristan Temme et al.

PHYSICAL REVIEW LETTERS (2017)

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Article Multidisciplinary Sciences

Fundamental limits of repeaterless quantum communications

Stefano Pirandola et al.

NATURE COMMUNICATIONS (2017)

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Article Optics

Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states

Jarrod R. McClean et al.

PHYSICAL REVIEW A (2017)

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Article Physics, Mathematical

Relative entropy convergence for depolarizing channels

Alexander Mueller-Hermes et al.

JOURNAL OF MATHEMATICAL PHYSICS (2016)

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Article Physics, Multidisciplinary

Colloquium: Non-Markovian dynamics in open quantum systems

Heinz-Peter Breuer et al.

REVIEWS OF MODERN PHYSICS (2016)

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Article Optics

Simulating single photons with realistic photon sources

Xiao Yuan et al.

PHYSICAL REVIEW A (2016)

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Article Multidisciplinary Sciences

The second laws of quantum thermodynamics

Fernando Brandao et al.

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA (2015)

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Article Computer Science, Theory & Methods

Universal optimal quantum correlator

Francesco Buscemi et al.

INTERNATIONAL JOURNAL OF QUANTUM INFORMATION (2014)

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Article Multidisciplinary Sciences

A variational eigenvalue solver on a photonic quantum processor

Alberto Peruzzo et al.

NATURE COMMUNICATIONS (2014)

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Article Computer Science, Information Systems

Entanglement Cost of Quantum Channels

Mario Berta et al.

IEEE TRANSACTIONS ON INFORMATION THEORY (2013)

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Article Optics

SWAP test and Hong-Ou-Mandel effect are equivalent

Juan Carlos Garcia-Escartin et al.

PHYSICAL REVIEW A (2013)

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Article Physics, Mathematical

Distinguishability of Quantum States Under Restricted Families of Measurements with an Application to Quantum Data Hiding

William Matthews et al.

COMMUNICATIONS IN MATHEMATICAL PHYSICS (2009)

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Article Physics, Mathematical

Asymptotic error rates in quantum hypothesis testing

K. M. R. Audenaert et al.

COMMUNICATIONS IN MATHEMATICAL PHYSICS (2008)

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Article Multidisciplinary Sciences

Enhanced sensitivity of photodetection via quantum illumination

Seth Lloyd

SCIENCE (2008)

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Article Physics, Multidisciplinary

Efficient quantum circuits for Schur and Clebsch-Gordan transforms

Dave Bacon et al.

PHYSICAL REVIEW LETTERS (2006)

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Article Physics, Multidisciplinary

Quantum metrology

V Giovannetti et al.

PHYSICAL REVIEW LETTERS (2006)

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Article Physics, Multidisciplinary

Direct estimations of linear and nonlinear functionals of a quantum state

AK Ekert et al.

PHYSICAL REVIEW LETTERS (2002)

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Fundamental limits of quantum error mitigation

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