Virtual Distillation for Quantum Error Mitigation

Contemporary quantum computers have relatively high levels of noise, making it difficult to use them to perform useful calculations, even with a large number of qubits. Quantum error correction is expected to eventually enable fault-tolerant quantum computation at large scales, but until then, it wi...

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Autores principales:	William J. Huggins, Sam McArdle, Thomas E. O’Brien, Joonho Lee, Nicholas C. Rubin, Sergio Boixo, K. Birgitta Whaley, Ryan Babbush, Jarrod R. McClean
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/47f0aaf515cc48a5a32bfac53fdebaaf
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spelling	oai:doaj.org-article:47f0aaf515cc48a5a32bfac53fdebaaf2021-11-19T16:10:57ZVirtual Distillation for Quantum Error Mitigation10.1103/PhysRevX.11.0410362160-3308https://doaj.org/article/47f0aaf515cc48a5a32bfac53fdebaaf2021-11-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.041036http://doi.org/10.1103/PhysRevX.11.041036https://doaj.org/toc/2160-3308Contemporary quantum computers have relatively high levels of noise, making it difficult to use them to perform useful calculations, even with a large number of qubits. Quantum error correction is expected to eventually enable fault-tolerant quantum computation at large scales, but until then, it will be necessary to use alternative strategies to mitigate the impact of errors. We propose a near-term friendly strategy to mitigate errors by entangling and measuring M copies of a noisy state ρ. This enables us to estimate expectation values with respect to a state with dramatically reduced error ρ^{M}/Tr(ρ^{M}) without explicitly preparing it, hence the name “virtual distillation.” As M increases, this state approaches the closest pure state to ρ exponentially quickly. We analyze the effectiveness of virtual distillation and find that it is governed in many regimes by the behavior of this pure state (corresponding to the dominant eigenvector of ρ). We numerically demonstrate that virtual distillation is capable of suppressing errors by multiple orders of magnitude and explain how this effect is enhanced as the system size grows. Finally, we show that this technique can improve the convergence of randomized quantum algorithms, even in the absence of device noise.William J. HugginsSam McArdleThomas E. O’BrienJoonho LeeNicholas C. RubinSergio BoixoK. Birgitta WhaleyRyan BabbushJarrod R. McCleanAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 4, p 041036 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 William J. Huggins Sam McArdle Thomas E. O’Brien Joonho Lee Nicholas C. Rubin Sergio Boixo K. Birgitta Whaley Ryan Babbush Jarrod R. McClean Virtual Distillation for Quantum Error Mitigation
description	Contemporary quantum computers have relatively high levels of noise, making it difficult to use them to perform useful calculations, even with a large number of qubits. Quantum error correction is expected to eventually enable fault-tolerant quantum computation at large scales, but until then, it will be necessary to use alternative strategies to mitigate the impact of errors. We propose a near-term friendly strategy to mitigate errors by entangling and measuring M copies of a noisy state ρ. This enables us to estimate expectation values with respect to a state with dramatically reduced error ρ^{M}/Tr(ρ^{M}) without explicitly preparing it, hence the name “virtual distillation.” As M increases, this state approaches the closest pure state to ρ exponentially quickly. We analyze the effectiveness of virtual distillation and find that it is governed in many regimes by the behavior of this pure state (corresponding to the dominant eigenvector of ρ). We numerically demonstrate that virtual distillation is capable of suppressing errors by multiple orders of magnitude and explain how this effect is enhanced as the system size grows. Finally, we show that this technique can improve the convergence of randomized quantum algorithms, even in the absence of device noise.
format	article
author	William J. Huggins Sam McArdle Thomas E. O’Brien Joonho Lee Nicholas C. Rubin Sergio Boixo K. Birgitta Whaley Ryan Babbush Jarrod R. McClean
author_facet	William J. Huggins Sam McArdle Thomas E. O’Brien Joonho Lee Nicholas C. Rubin Sergio Boixo K. Birgitta Whaley Ryan Babbush Jarrod R. McClean
author_sort	William J. Huggins
title	Virtual Distillation for Quantum Error Mitigation
title_short	Virtual Distillation for Quantum Error Mitigation
title_full	Virtual Distillation for Quantum Error Mitigation
title_fullStr	Virtual Distillation for Quantum Error Mitigation
title_full_unstemmed	Virtual Distillation for Quantum Error Mitigation
title_sort	virtual distillation for quantum error mitigation
publisher	American Physical Society
publishDate	2021
url	https://doaj.org/article/47f0aaf515cc48a5a32bfac53fdebaaf
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Virtual Distillation for Quantum Error Mitigation

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