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

Abstract

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 more » 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.« less

Authors:

^[1];

^[2];

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

Publication Date:: Thu Mar 26 00:00:00 EDT 2020

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

Sponsoring Org.:: 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)

OSTI Identifier:: 1659189

Report Number(s):: LA-UR-19-25585
Journal ID: ISSN 2521-327X

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

Resource Type:: Accepted Manuscript

Journal Name:: Quantum

Additional Journal Information:: Journal Volume: 4; Journal ID: ISSN 2521-327X

Publisher:: Quantum Science Open Community

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; Mathematics; Quantum; Algorithm; Fidelity; Variational; Computing

Citation Formats


                    Cerezo de la Roca, Marco Vinicio Sebastian, Poremba, Alexander, Cincio, Lukasz, and Coles, Patrick Joseph. Variational Quantum Fidelity Estimation.  United States: N. p., 2020. 
Web.  doi:10.22331/q-2020-03-26-248.

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                    Cerezo de la Roca, Marco Vinicio Sebastian, Poremba, Alexander, Cincio, Lukasz, & Coles, Patrick Joseph. Variational Quantum Fidelity Estimation.  United States.  https://doi.org/10.22331/q-2020-03-26-248

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                    Cerezo de la Roca, Marco Vinicio Sebastian, Poremba, Alexander, Cincio, Lukasz, and Coles, Patrick Joseph. Thu .  
"Variational Quantum Fidelity Estimation".  United States.  https://doi.org/10.22331/q-2020-03-26-248.  https://www.osti.gov/servlets/purl/1659189.

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@article{osti_1659189,

  title        = {Variational Quantum Fidelity Estimation},

  author       = {Cerezo de la Roca, Marco Vinicio Sebastian and Poremba, Alexander and Cincio, Lukasz and Coles, Patrick Joseph},

  abstractNote = {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.},

  doi          = {10.22331/q-2020-03-26-248},

  journal      = {Quantum},

  number       = ,

  volume       = 4,

  place        = {United States},

  year         = {Thu Mar 26 00:00:00 EDT 2020},

  month        = {Thu Mar 26 00:00:00 EDT 2020}

}

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Works referenced in this record:

Using Quantum Computers for Quantum Simulation
text, January 2010

Brown, Katherine L.; Munro, William J.; Kendon, Vivien M.
arXiv
DOI: 10.48550/arxiv.1004.5528

Exact Ising model simulation on a quantum computer
text, January 2018

Cervera-Lierta, Alba
arXiv
DOI: 10.48550/arxiv.1807.07112

swap test and Hong-Ou-Mandel effect are equivalent
journal, May 2013

Garcia-Escartin, Juan Carlos; Chamorro-Posada, Pedro
Physical Review A, Vol. 87, Issue 5
DOI: 10.1103/physreva.87.052330

Quantum fidelity and thermal phase transitions
journal, March 2009

Quan, H. T.; Cucchietti, F. M.
Physical Review E, Vol. 79, Issue 3
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The “transition probability” in the state space of a ∗-algebra
journal, April 1976

Uhlmann, A.
Reports on Mathematical Physics, Vol. 9, Issue 2
DOI: 10.1016/0034-4877(76)90060-4

Bound on trace distance based on superfidelity
text, January 2008

Puchała, Zbigniew; Miszczak, Jarosław Adam
arXiv
DOI: 10.48550/arxiv.0811.2323

Quantum statistical zero-knowledge
preprint, January 2002

Watrous, John
arXiv
DOI: 10.48550/arxiv.quant-ph/0202111

Measuring polynomial functions of states
journal, September 2004

Brun, T. A.
Quantum Information and Computation, Vol. 4, Issue 5
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Works referencing / citing this record:

Reformulation of the No-Free-Lunch Theorem for Entangled Data Sets
text, January 2020

Sharma, Kunal; Cerezo, M.; Holmes, Zoë
arXiv
DOI: 10.48550/arxiv.2007.04900

Quantum Algorithm for Fidelity Estimation
text, January 2021

Wang, Qisheng; Zhang, Zhicheng; Chen, Kean
arXiv
DOI: 10.48550/arxiv.2103.09076

Variational quantum Gibbs state preparation with a truncated Taylor series
text, January 2020

Wang, Youle; Li, Guangxi; Wang, Xin
arXiv
DOI: 10.48550/arxiv.2005.08797

Variational quantum algorithm for estimating the quantum Fisher information
journal, February 2022

Beckey, Jacob L.; Cerezo, M.; Sone, Akira
Physical Review Research, Vol. 4, Issue 1
DOI: 10.1103/physrevresearch.4.013083

Variational quantum algorithms
journal, August 2021

Cerezo, M.; Arrasmith, Andrew; Babbush, Ryan
Nature Reviews Physics, Vol. 3, Issue 9
DOI: 10.1038/s42254-021-00348-9

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Similar Records

Title: Variational Quantum Fidelity Estimation

Abstract

Citation Formats

Using Quantum Computers for Quantum Simulation text, January 2010

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