Variational Quantum Fidelity Estimation

Cerezo de la Roca, Marco Vinicio Sebastian; Poremba, Alexander; Cincio, Lukasz; Coles, Patrick Joseph

doi:10.22331/q-2020-03-26-248

Variational Quantum Fidelity Estimation

Journal Article · Thu Mar 26 00:00:00 EDT 2020 · Quantum

DOI:https://doi.org/10.22331/q-2020-03-26-248· OSTI ID:1659189

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Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
California Institute of Technology (CalTech), Pasadena, CA (United States)

Computing quantum state fidelity will be important to verify and characterize states prepared on a quantum computer. In this work, we propose novel lower and upper bounds for the fidelity F(ρ,σ) based on the ``truncated fidelity'' F( ρm ,σ) , which is evaluated for a state ρm obtained by projecting ρ onto its m -largest eigenvalues. Our bounds can be refined, i.e., they tighten monotonically with m . To compute our bounds, we introduce a hybrid quantum-classical algorithm, called Variational Quantum Fidelity Estimation, that involves three steps: (1) variationally diagonalize ρ , (2) compute matrix elements of σ in the eigenbasis of ρ , and (3) combine these matrix elements to compute our bounds. Our algorithm is aimed at the case where σ is arbitrary and ρ is low rank, which we call low-rank fidelity estimation, and we prove that no classical algorithm can efficiently solve this problem under reasonable assumptions. Finally, we demonstrate that our bounds can detect quantum phase transitions and are often tighter than previously known computable bounds for realistic situations.

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: National Science Foundation (NSF); US Air Force Office of Scientific Research (AFOSR); USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1659189

Report Number(s):: LA-UR--19-25585

Journal Information:: Quantum, Journal Name: Quantum Vol. 4; ISSN 2521-327X

Publisher:: Quantum Science Open CommunityCopyright Statement

Country of Publication:: United States

Language:: English

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Variational quantum algorithms Cerezo, M.; Arrasmith, Andrew; Babbush, Ryan Nature Reviews Physics, Vol. 3, Issue 9 https://doi.org/10.1038/s42254-021-00348-9	journal	August 2021
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Variational quantum Gibbs state preparation with a truncated Taylor series Wang, Youle; Li, Guangxi; Wang, Xin arXiv https://doi.org/10.48550/arxiv.2005.08797	text	January 2020
Reformulation of the No-Free-Lunch Theorem for Entangled Data Sets Sharma, Kunal; Cerezo, M.; Holmes, Zoë arXiv https://doi.org/10.48550/arxiv.2007.04900	text	January 2020
Quantum Algorithm for Fidelity Estimation Wang, Qisheng; Zhang, Zhicheng; Chen, Kean arXiv https://doi.org/10.48550/arxiv.2103.09076	text	January 2021

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