Virtual Distillation for Quantum Error Mitigation

Huggins, William J.; McArdle, Sam; O’Brien, Thomas E.; Lee, Joonho; Rubin, Nicholas C.; Boixo, Sergio; Whaley, Birgitta; Babbush, Ryan; McClean, Jarrod R.

doi:10.1103/physrevx.11.041036

Cited by 122 publications

(136 citation statements)

References 51 publications

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“…Quantum circuit of a possible implementation of the ESD/VD error suppression approach [23,24]. Reproduced from [23].…”

Section: Problem Definitionmentioning

confidence: 99%

“…While reference [24] mostly focuses on the n = 2 scenario and proposes a resource efficient variant that does not require an ancilla qubit when n = 2, reference [23] presents explicit constructions of the approach for n 2. A possible implementation is illustrated in figure 2 which uses a controlled-derangement operation and allows one to measure expectation values of the form Tr[ρ n O]/Tr[ρ n ] with respect to an observable O.…”

Section: Error Suppressionmentioning

confidence: 99%

“…Similarly, the 'noise floor' was defined in reference [24] to express the discrepancy between the 'virtual' quantum state ρ n and the ideal computational state ρ id in the limit of a large number of copies via the trace distance T(ρ n , ρ id ). We prove in appendix B that this noise floor is equivalent to the coherent mismatch up to a square-root as…”

Section: Error Suppressionmentioning

confidence: 99%

“…Reference [24] argued that the coherent mismatch is zero if the error channel maps only to orthogonal states. Indeed such special density matrices are an instance of the general class when ρ err and ρ id commute as discussed above.…”

Section: Error Suppressionmentioning

confidence: 99%

“…Given a noisy quantum state ρ, how well does its dominant eigenvector approximate the state that one would obtain from a perfect, noise-free computation? It was already noted in references [23,24] that even incoherent errors will in general introduce a drift in the dominant eigenvector. This drift was named 'coherent mismatch' and 'noise floor' by the two works.…”

Section: Introductionmentioning

confidence: 96%

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The dominant eigenvector of a noisy quantum state

Koczor

2021

New J. Phys.

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Although near-term quantum devices have no comprehensive solution for correcting errors, numerous techniques have been proposed for achieving practical value. Two works have recently introduced the very promising error suppression by derangements (ESD) and virtual distillation (VD) techniques. The approach exponentially suppresses errors and ultimately allows one to measure expectation values in the pure state as the dominant eigenvector of the noisy quantum state. Interestingly this dominant eigenvector is, however, different than the ideal computational state and it is the aim of the present work to comprehensively explore the following fundamental question: how significantly different are these two pure states? The motivation for this work is two-fold. First, comprehensively understanding the effect of this coherent mismatch is of fundamental importance for the successful exploitation of noisy quantum devices. As such, the present work rigorously establishes that in practically relevant scenarios the coherent mismatch is exponentially less severe than the incoherent decay of the fidelity—where the latter can be suppressed exponentially via the ESD/VD technique. Second, the above question is closely related to central problems in mathematics, such as bounding eigenvalues of a sum of two matrices (Weyl inequalities)—solving of which was a major breakthrough. The present work can be viewed as a first step towards extending the Weyl inequalities to eigenvectors of a sum of two matrices—and completely resolves this problem for the special case of the considered density matrices.

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“…Quantum circuit of a possible implementation of the ESD/VD error suppression approach [23,24]. Reproduced from [23].…”

Section: Problem Definitionmentioning

confidence: 99%

Section: Error Suppressionmentioning

confidence: 99%

Section: Error Suppressionmentioning

confidence: 99%

Section: Error Suppressionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

See 3 more Smart Citations

The dominant eigenvector of a noisy quantum state

Koczor

2021

New J. Phys.

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Variational Quantum‐Neural Hybrid Error Mitigation

Zhang,

Wan,

Hsieh

et al. 2023

Adv Quantum Tech

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Quantum error mitigation (QEM) is crucial for obtaining reliable results on quantum computers by suppressing quantum noise with moderate resources. It is a key factor for successful and practical quantum algorithm implementations in the noisy intermediate scale quantum (NISQ) era. Since quantum‐classical hybrid algorithms can be executed with moderate and noisy quantum resources, combining QEM with quantum‐classical hybrid schemes is one of the most promising directions toward practical quantum advantages. This work shows how the variational quantum‐neural hybrid eigensolver (VQNHE) algorithm, which seamlessly combines the expressive power of a parameterized quantum circuit with a neural network, is inherently noise resilient with a unique QEM capacity, which is absent in vanilla variational quantum eigensolvers (VQE). The study carefully analyzes and elucidates the asymptotic scaling of this unique QEM capacity in VQNHE from both theoretical and experimental perspectives. Finally, a variational basis transformation is proposed for the Hamiltonian to be measured under the VQNHE framework, yielding a powerful tri‐optimization setup, dubbed as VQNHE++. VQNHE++ can further enhance the quantum‐neural hybrid expressive power and error mitigation capacity.

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