Generalized quantum subspace expansion

Yoshioka, Nobuyuki; Hakoshima, Hideaki; Matsuzaki, Yuichiro; Tokunaga, Yuuki; Suzuki, Yasunari; Endo, Suguru

doi:10.48550/arxiv.2107.02611

Cited by 6 publications

(11 citation statements)

References 35 publications

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“…This framework encompasses a broad class of error-mitigation strategies proposed so far [12,13,18,21,22,[29][30][31][32][33]. The value of 𝐾 may become large, in which case there is much flexibility in how one allocates the available samples into 𝐾 experiments and 𝑀 repetitions in the procedure in Table I.…”

Section: 𝑄 𝐾mentioning

confidence: 99%

“…Doing so could point at ways to enhance noise extrapolation or virtual distillation by finding means of partially integrating pre-knowledge. Indeed, recent hybrid approaches [32,[48][49][50] are equipped with such properties and thus can be good candidates for the optimal strategies. We leave a thorough analysis of these protocols using our framework as potential future work.…”

Section: Measuring Optimality and Future Directionsmentioning

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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Section: 𝑄 𝐾mentioning

confidence: 99%

Section: Measuring Optimality and Future Directionsmentioning

confidence: 99%

Fundamental limits of quantum error mitigation

Takagi

Endo²,

Minagawa

et al. 2021

Preprint

Self Cite

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“…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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“…A relatively large number of QEM techniques have been proposed in recent literature [8][9][10][11][12][13][14][15]. Some authors have defined common frameworks which encapsulate one or more of these techniques [16,17]. At its core, any QEM technique uses additional quantum resources (qubits, gates, and/or samples) in a clever way to approximate what would happen in an ideal device.…”

Section: Introductionmentioning

confidence: 99%

Logical shadow tomography: Efficient estimation of error-mitigated observables

Hu¹,

LaRose²,

You³

et al. 2022

Preprint

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We introduce a technique to estimate error-mitigated expectation values on noisy quantum computers. Our technique performs shadow tomography on a logical state to produce a memory-efficient classical reconstruction of the noisy density matrix. Using efficient classical post-processing, one can mitigate errors by projecting a general nonlinear function of the noisy density matrix into the codespace. The subspace expansion and virtual distillation can be viewed as special cases of the new framekwork. We show our method is favorable in the quantum and classical resources overhead. Relative to subspace expansion which requires O 2 N samples to estimate a logical Pauli observable with [[N, k]] error correction code, our technique requires only O 4 k samples. Relative to virtual distillation, our technique can compute powers of the density matrix without additional copies of quantum states or quantum memory. We present numerical evidence using logical states encoded with up to sixty physical qubits and show fast convergence to error-free expectation values with only 10 5 samples under 1% depolarizing noise.

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Generalized quantum subspace expansion

Cited by 6 publications

References 35 publications

Fundamental limits of quantum error mitigation

Fundamental limits of quantum error mitigation

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

Logical shadow tomography: Efficient estimation of error-mitigated observables

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