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

Title: 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 ( ρ m , σ ) , which is evaluated for a state ρ m 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.

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

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

Grant/Contract Number:: 89233218CNA000001; A9550-16-1-0495; PHY-1733907

OSTI ID:: 1659189

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

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

Publisher:: Quantum Science Open CommunityCopyright Statement

Country of Publication:: United States

Language:: English

References (8)

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Cited By (5)

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
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
Variational quantum algorithm for estimating the quantum Fisher information Beckey, Jacob L.; Cerezo, M.; Sone, Akira Physical Review Research, Vol. 4, Issue 1 https://doi.org/10.1103/physrevresearch.4.013083	journal	February 2022
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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Title: Variational Quantum Fidelity Estimation

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