Universal Sampling Lower Bounds for Quantum Error Mitigation

Takagi, Ryuji; Tajima, Hiroyasu; Gu, Mile

doi:10.1103/physrevlett.131.210602

Cited by 15 publications

(4 citation statements)

References 68 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that by using fidelity instead of relative entropy a bound tighter than Eq. ( 51) can also be obtained, as discussed by Takagi, Tajima, and Gu (2023). Quek et al (2022) managed to construct a circuit structure for which the relative entropy of two different output states decreases exponentially in both circuit depth and the number of qubits, which allowed them to prove that the worst-case sampling lower bound for QEM scaled exponentially with the circuit size (instead of just depth), confirming our intuition obtained in Sec.…”

Section: B Benchmarking Qem From Other Perspectivessupporting

confidence: 72%

Quantum error mitigation

Cai,

Babbush,

Benjamin

et al. 2023

Rev. Mod. Phys.

137

View full text Add to dashboard Cite

For quantum computers to successfully solve real-world problems, it is necessary to tackle the challenge of noise: the errors that occur in elementary physical components due to unwanted or imperfect interactions. The theory of quantum fault tolerance can provide an answer in the long term, but in the coming era of noisy intermediate-scale quantum machines one must seek to mitigate errors rather than completely eliminate them. This review surveys the diverse methods that have been proposed for quantum error mitigation, assesses their in-principle efficacy, and describes the hardware demonstrations achieved to date. Commonalities and limitations among the methods are identified, while mention is made of how mitigation methods can be chosen according to the primary type of noise present, including algorithmic errors. Open problems in the field are identified, and the prospects for realizing mitigation-based devices that can deliver a quantum advantage with an impact on science and business are discussed.

show abstract

Section: B Benchmarking Qem From Other Perspectivessupporting

confidence: 72%

Quantum error mitigation

Cai,

Babbush,

Benjamin

et al. 2023

Rev. Mod. Phys.

137

View full text Add to dashboard Cite

show abstract

“…Second, it is practically important to investigate the performance of subspace methods in the context of quantum error mitigation [38]. Quantum error mitigation techniques inevitably require exponential growth in the number of measurements [73][74][75], while the exponent in the scaling heavily depends on the detail of the error mitigation methods. Thus, it is crucial to seek how the adaptive strategy benefits the trade-off relation between bias and variance.…”

Section: Discussionmentioning

confidence: 99%

Adaptive measurement strategy for quantum subspace methods

Nakamura,

Yano,

Yoshioka

2024

New J. Phys.

View full text Add to dashboard Cite

Estimation of physical observables for unknown quantum states is an important problem that underlies a wide range of fields, including quantum information processing, quantum physics, and quantum chemistry. In the context of quantum computation, in particular, existing studies have mainly focused on holistic state tomography or estimation on specific observables with known classical descriptions, while this lacks the important class of problems where the estimation target itself relies on the measurement outcome. In this work, we propose an adaptive measurement optimization method that is useful for the quantum subspace methods, namely the variational simulation methods that utilize classical postprocessing on measurement outcomes. The proposed method first determines the measurement protocol for classically simulatable states, and then adaptively updates the protocol of quantum subspace expansion (QSE) according to the quantum measurement result. As a numerical demonstration, we have shown for excited-state simulation of molecules that (i) we are able to reduce the number of measurements by an order of magnitude by constructing an appropriate measurement strategy (ii) the adaptive iteration converges successfully even for a strongly correlated molecule of H4. Our work reveals that the potential of the QSE method can be empowered by elaborated measurement protocols, and opens a path to further pursue efficient quantum measurement techniques in practical computations.

show abstract

“…Instead, the primary overhead arises from the fact that error-mitigated estimation necessarily comes at the cost of larger overall variances [95][96][97][98] . The quantity…”

Section: Theory Of Symmetry-adjusted Classical Shadowsmentioning

confidence: 99%

“…Any QEM strategy necessarily incurs a sampling overhead dependent on the amount of noise [95][96][97][98] . For global Clifford shadows, Chen et al 85 show that the sample complexity is augmented by a factor of OðF Z ðEÞ À2 Þ for estimating observables with constant Hilbert-Schmidt norm, where F Z ðEÞ ¼ 2 Àn P b2f0;1g n hhbjEjbii is the average Z-basis fidelity of E. Meanwhile for local Clifford shadows, they prove that product noise of the form…”

mentioning

confidence: 99%

Group-theoretic error mitigation enabled by classical shadows and symmetries

Zhao,

Miyake

2024

npj Quantum Inf

View full text Add to dashboard Cite

Estimating expectation values is a key subroutine in quantum algorithms. Near-term implementations face two major challenges: a limited number of samples required to learn a large collection of observables, and the accumulation of errors in devices without quantum error correction. To address these challenges simultaneously, we develop a quantum error-mitigation strategy called symmetry-adjusted classical shadows, by adjusting classical-shadow tomography according to how symmetries are corrupted by device errors. As a concrete example, we highlight global U(1) symmetry, which manifests in fermions as particle number and in spins as total magnetization, and illustrate their group-theoretic unification with respective classical-shadow protocols. We establish rigorous sampling bounds under readout errors obeying minimal assumptions, and perform numerical experiments with a more comprehensive model of gate-level errors derived from existing quantum processors. Our results reveal symmetry-adjusted classical shadows as a low-cost strategy to mitigate errors from noisy quantum experiments in the ubiquitous presence of symmetry.

show abstract

Universal Sampling Lower Bounds for Quantum Error Mitigation

Cited by 15 publications

References 68 publications

Quantum error mitigation

Quantum error mitigation

Adaptive measurement strategy for quantum subspace methods

Group-theoretic error mitigation enabled by classical shadows and symmetries

Contact Info

Product

Resources

About