Error mitigation and quantum-assisted simulation in the error corrected regime

Lostaglio, Matteo; Ciani, Alessandro

doi:10.48550/arxiv.2103.07526

Cited by 6 publications

(7 citation statements)

References 30 publications

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“…Thus, our work provides a toolkit for identifying fundamental bounds in the transition from error mitigation to error correction as we proceed from NISQ devices towards scalable quantum computing. This then complements presently active research in error suppression that combines the two techniques [53][54][55][56].…”

Section: Discussionmentioning

confidence: 55%

Fundamental limits of quantum error mitigation

Takagi

Endo²,

Minagawa

et al. 2021

Preprint

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The inevitable accumulation of errors in near-future quantum devices represents a key obstacle in delivering practical quantum advantage. This motivated the development of various quantum error-mitigation protocols, each representing a method to extract useful computational output by combining measurement data from multiple samplings of the available imperfect quantum device. What are the ultimate performance limits universally imposed on such protocols? Here, we derive a fundamental bound on the sampling overhead that applies to a general class of error-mitigation protocols, assuming only the laws of quantum mechanics. We use it to show that (1) the sampling overhead to mitigate local depolarizing noise for layered circuits -such as the ones used for variational quantum algorithms -must scale exponentially with circuit depth, and (2) the optimality of probabilistic error cancellation method among all strategies in mitigating a certain class of noise. We discuss how our unified framework and general bounds can be employed to benchmark and compare various present methods of error mitigation and identify situations where present error-mitigation methods have the greatest potential for improvement.

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Section: Discussionmentioning

confidence: 55%

Fundamental limits of quantum error mitigation

Takagi

Endo²,

Minagawa

et al. 2021

Preprint

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“…We emphasize that quantum error mitigation is still an active research area. For example, there is emerging interest in syncretizing error mitigation and correction techniques [74,75]. It would be interesting to explore how the proposed error mitigation framework can be enhanced via error correction.…”

Section: ⟩mentioning

confidence: 99%

Mitigating Quantum Errors via Truncated Neumann Series

Wang¹,

Chen²,

Wang³

2021

Preprint

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Quantum gates and measurements on quantum hardware are inevitably subject to hardware imperfections that lead to quantum errors. Mitigating such unavoidable errors is crucial to explore the power of quantum hardware better. In this paper, we propose a unified framework that can mitigate quantum gate and measurement errors in computing quantum expectation values utilizing the truncated Neumann series. The essential idea is to cancel the effect of quantum error by approximating its inverse via linearly combining quantum errors of different orders produced by sequential applications of the quantum devices with carefully chosen coefficients. Remarkably, the estimation error decays exponentially in the truncated order, and the incurred error mitigation overhead is independent of the system size, as long as the noise resistance of the quantum device is moderate. We numerically test this framework for different quantum errors and find that the computation accuracy is substantially improved. Our framework possesses several vital advantages: it mitigates quantum gate and measurement errors in a unified manner, it neither assumes any error structure nor requires the tomography procedure to completely characterize the quantum errors, and most importantly, it is scalable. These advantages empower our quantum error mitigation framework to be efficient and practical and extend the ability of near-term quantum devices to deliver quantum applications.

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“…Namely, we may apply the proposed method to mitigate the effect of errors due to decoding of logical qubits or insufficient number of Tgates without any characterization. This is in contrast with the previous works based on the quasi-probability method [37][38][39][40]. Third, although we focused on obtaining error-mitigated ground state or a specific eigenstate of a Hamiltonian, the solution of Eq.…”

mentioning

confidence: 92%

Generalized quantum subspace expansion

Yoshioka,

Hakoshima,

Matsuzaki

et al. 2021

Preprint

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One of the major challenges for erroneous quantum computers is undoubtedly the control over the effect of noise. Considering the rapid growth of available quantum resources that are not fully fault-tolerant, it is crucial to develop practical hardware-friendly quantum error mitigation (QEM) techniques to suppress unwanted errors. Here, we propose a novel generalized quantum subspace expansion method which can handle stochastic, coherent, and algorithmic errors in quantum computers. By fully exploiting the substantially extended subspace, we can efficiently mitigate the noise present in the spectra of a given Hamiltonian, without relying on any information of noise. The performance of our method is discussed under two highly practical setups: the quantum subspaces are mainly spanned by powers of the noisy state ρ m and a set of error-boosted states, respectively. We numerically demonstrate in both situations that we can suppress errors by orders of magnitude, and show that out protocol inherits the advantages of previous error-agnostic QEM techniques as well as overcoming their drawbacks.

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Error mitigation and quantum-assisted simulation in the error corrected regime

Cited by 6 publications

References 30 publications

Fundamental limits of quantum error mitigation

Fundamental limits of quantum error mitigation

Mitigating Quantum Errors via Truncated Neumann Series

Generalized quantum subspace expansion

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