Quantum Error Mitigation Relying on Permutation Filtering

Xiong, Yifeng; Ng, Soon Xin; Hanzo, Lajos

doi:10.48550/arxiv.2107.01458

Cited by 6 publications

(10 citation statements)

References 36 publications

(60 reference statements)

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“…where {𝛾 𝑘 } 𝑅 𝑘=0 are the constants determined by (26). One can easily check that plugging the above expressions in the form of Definition 1 leads to (27).…”

Section: Richardson Extrapolationmentioning

confidence: 99%

“…Classical processing of these measurement outcomes can then retrieve the desired computational output (e.g., ground state energy of a Hamiltonian in quantum chemistry [5,[9][10][11]). Surging interest in these techniques has resulted in diverse approaches, such as zero-error noise extrapolation [12][13][14][15][16][17], probabilistic error cancellation [12,[18][19][20], and virtual distillation [21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

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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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“…where {𝛾 𝑘 } 𝑅 𝑘=0 are the constants determined by (26). One can easily check that plugging the above expressions in the form of Definition 1 leads to (27).…”

Section: Richardson Extrapolationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fundamental limits of quantum error mitigation

Takagi

Endo²,

Minagawa

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Recently, VD-inspired methods were proposed which further reduce required qubit counts [17,18] and conceptually unify VD with both ZNE and subspace expansion techniques enabling error mitigation beyond the noise floor [26][27][28].…”

Section: Virtual Distillationmentioning

confidence: 99%

Unifying and benchmarking state-of-the-art quantum error mitigation techniques

Bultrini¹,

Gordon²,

Czarnik³

et al. 2021

Preprint

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Error mitigation is an essential component of achieving practical quantum advantage in the near term, and a number of different approaches have been proposed. In this work, we recognize that many state-of-the-art error mitigation methods share a common feature: they are data-driven, employing classical data obtained from runs of different quantum circuits. For example, Zero-noise extrapolation (ZNE) uses variable noise data and Clifford-data regression (CDR) uses data from near-Clifford circuits. We show that Virtual Distillation (VD) can be viewed in a similar manner by considering classical data produced from different numbers of state preparations. Observing this fact allows us to unify these three methods under a general data-driven error mitigation framework that we call UNIfied Technique for Error mitigation with Data (UNITED). In certain situations, we find that our UNITED method can outperform the individual methods (i.e., the whole is better than the individual parts). Specifically, we employ a realistic noise model obtained from a trapped ion quantum computer to benchmark UNITED, as well as state-of-the-art methods, for problems with various numbers of qubits, circuit depths and total numbers of shots. We find that different techniques are optimal for different shot budgets. Namely, ZNE is the best performer for small shot budgets (10 5 ), while Clifford-based approaches are optimal for larger shot budgets (10 6 − 10 8 ), and for our largest considered shot budget (10 10 ), UNITED gives the most accurate correction. Hence, our work represents a benchmarking of current error mitigation methods, and provides a guide for the regimes when certain methods are most useful.

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“…Note added.-Shortly after completion of this work, the reference [43] appeared as a preprint, which consider a method similar to the power subspace corresponding to Eq. ( 5).…”

mentioning

confidence: 99%

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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Quantum Error Mitigation Relying on Permutation Filtering

Cited by 6 publications

References 36 publications

Fundamental limits of quantum error mitigation

Fundamental limits of quantum error mitigation

Unifying and benchmarking state-of-the-art quantum error mitigation techniques

Generalized quantum subspace expansion

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