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Variational Quantum Fidelity Estimation

Cerezo, M. and Poremba, Alexander and Cincio, Lukasz and Coles, Patrick J. (2020) Variational Quantum Fidelity Estimation. Quantum, 4 . Art. No. 248. ISSN 2521-327X. doi:10.22331/q-2020-03-26-248.

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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 mm-largest eigenvalues. Our bounds can be refined, i.e., they tighten monotonically with mm. 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.

Item Type:Article
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URLURL TypeDescription Paper
Cerezo, M.0000-0002-2757-3170
Poremba, Alexander0000-0002-7330-1539
Cincio, Lukasz0000-0002-6758-4376
Coles, Patrick J.0000-0001-9879-8425
Additional Information:© 2020 This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. Accepted in Quantum 2020-03-02; Published: 2020-03-26. We thank John Watrous and Mark Wilde for helpful correspondence. MC was supported by the Center for Nonlinear Studies at Los Alamos National Laboratory (LANL). AP was supported by AFOSR YIP award number FA9550-16-1-0495, the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant PHY-1733907), and the Kortschak Scholars program. LC was supported by the DOE through the J. Robert Oppenheimer fellowship. PJC acknowledges support from the LANL ASC Beyond Moore’s Law project. MC, LC, and PJC also acknowledge support from the LDRD program at LANL. This work was supported in part by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, Condensed Matter Theory Program.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Los Alamos National LaboratoryUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)FA9550-16-1-0495
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Kortschak Scholars ProgramUNSPECIFIED
Department of Energy (DOE)UNSPECIFIED
Record Number:CaltechAUTHORS:20200423-104102695
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:102747
Deposited By: Tony Diaz
Deposited On:23 Apr 2020 18:32
Last Modified:16 Nov 2021 18:15

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