Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: Quantum eigenvalue estimation via time series analysis

Abstract

We present an efficient method for estimating the eigenvalues of a Hamiltonian H from the expectation values of the evolution operator for various times. For a given quantum state ρ, our method outputs a list of eigenvalue estimates and approximate probabilities. Each probability depends on the support of ρ in those eigenstates of H associated with eigenvalues within an arbitrarily small range. The complexity of our method is polynomial in the inverse of a given precision parameter ε, which is the gap between eigenvalue estimates. Unlike the well-known quantum phase estimation algorithm that uses the quantum Fourier transform, our method does not require large ancillary systems, large sequences of controlled operations, or preserving coherence between experiments, and is therefore more attractive for near-term applications. The output of our method can be used to estimate spectral properties of H and other expectation values efficiently, within additive error proportional to ε.

Authors:
ORCiD logo [1]
+ Show Author Affiliations
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1634958
Report Number(s):
LA-UR-19-26913
Journal ID: ISSN 1367-2630; TRN: US2201320
Grant/Contract Number:  
89233218CNA000001
Resource Type:
Accepted Manuscript
Journal Name:
New Journal of Physics
Additional Journal Information:
Journal Volume: 21; Journal Issue: 12; Journal ID: ISSN 1367-2630
Publisher:
IOP Publishing
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; computer science; information science; mathematics; quantum computing; quantum simulation; phase estimation

Citation Formats

Somma, Rolando Diego. Quantum eigenvalue estimation via time series analysis. United States: N. p., 2019. Web. doi:10.1088/1367-2630/ab5c60.
Copy to clipboard
Somma, Rolando Diego. Quantum eigenvalue estimation via time series analysis. United States. https://doi.org/10.1088/1367-2630/ab5c60
Copy to clipboard
Somma, Rolando Diego. Mon . "Quantum eigenvalue estimation via time series analysis". United States. https://doi.org/10.1088/1367-2630/ab5c60. https://www.osti.gov/servlets/purl/1634958.
Copy to clipboard
@article{osti_1634958,
title = {Quantum eigenvalue estimation via time series analysis},
author = {Somma, Rolando Diego},
abstractNote = {We present an efficient method for estimating the eigenvalues of a Hamiltonian H from the expectation values of the evolution operator for various times. For a given quantum state ρ, our method outputs a list of eigenvalue estimates and approximate probabilities. Each probability depends on the support of ρ in those eigenstates of H associated with eigenvalues within an arbitrarily small range. The complexity of our method is polynomial in the inverse of a given precision parameter ε, which is the gap between eigenvalue estimates. Unlike the well-known quantum phase estimation algorithm that uses the quantum Fourier transform, our method does not require large ancillary systems, large sequences of controlled operations, or preserving coherence between experiments, and is therefore more attractive for near-term applications. The output of our method can be used to estimate spectral properties of H and other expectation values efficiently, within additive error proportional to ε.},
doi = {10.1088/1367-2630/ab5c60},
journal = {New Journal of Physics},
number = 12,
volume = 21,
place = {United States},
year = {2019},
month = {12}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1088/1367-2630/ab5c60
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal

Figures / Tables:

Figure 1 Figure 1: The quantum phase estimation algorithm for estimating the eigenvalues of a unitary operator U. QFT is the quantum Fourier transform and the filled circles denote operations controlled on the states ∣1$\rangle$ of corresponding ancilla qubits. The number of these ancilla qubits, m, depends on the desired precision inmore » the estimation. Projective measurements on the ancilla qubits provide the eigenvalue estimates.« less
All figures and tables (6 total)
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

Simulated Quantum Computation of Molecular Energies
journal, September 2005

Optimal Hamiltonian Simulation by Quantum Signal Processing
journal, January 2017

Quantum Algorithm for Linear Systems of Equations
journal, October 2009

Optimal quantum measurements of expectation values of observables
journal, January 2007

Hamiltonian Simulation by Qubitization
journal, July 2019

Efficient Quantum Algorithms for Simulating Sparse Hamiltonians
journal, December 2006

  • Berry, Dominic W.; Ahokas, Graeme; Cleve, Richard
  • Communications in Mathematical Physics, Vol. 270, Issue 2
  • DOI: 10.1007/s00220-006-0150-x

A variational eigenvalue solver on a photonic quantum processor
journal, July 2014

  • Peruzzo, Alberto; McClean, Jarrod; Shadbolt, Peter
  • Nature Communications, Vol. 5, Issue 1
  • DOI: 10.1038/ncomms5213

Higher order decompositions of ordered operator exponentials
journal, January 2010

  • Wiebe, Nathan; Berry, Dominic; Høyer, Peter
  • Journal of Physics A: Mathematical and Theoretical, Vol. 43, Issue 6
  • DOI: 10.1088/1751-8113/43/6/065203

Simulating Hamiltonian Dynamics with a Truncated Taylor Series
journal, March 2015

Learning the quantum algorithm for state overlap
journal, November 2018

  • Cincio, Lukasz; Subaşı, Yiğit; Sornborger, Andrew T.
  • New Journal of Physics, Vol. 20, Issue 11
  • DOI: 10.1088/1367-2630/aae94a

Quantum Algorithm Providing Exponential Speed Increase for Finding Eigenvalues and Eigenvectors
journal, December 1999

A Trotter-Suzuki approximation for Lie groups with applications to Hamiltonian simulation
journal, June 2016

  • Somma, Rolando D.
  • Journal of Mathematical Physics, Vol. 57, Issue 6
  • DOI: 10.1063/1.4952761

An efficient quantum algorithm for spectral estimation
journal, March 2017

  • Steffens, Adrian; Rebentrost, Patrick; Marvian, Iman
  • New Journal of Physics, Vol. 19, Issue 3
  • DOI: 10.1088/1367-2630/aa5e48

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
journal, October 1997

Using the matrix pencil method to estimate the parameters of a sum of complex exponentials
journal, February 1995

  • Sarkar, T. K.; Pereira, O.
  • IEEE Antennas and Propagation Magazine, Vol. 37, Issue 1
  • DOI: 10.1109/74.370583

Quantum algorithms revisited
journal, January 1998

  • Cleve, R.; Ekert, A.; Macchiavello, C.
  • Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 454, Issue 1969
  • DOI: 10.1098/rspa.1998.0164

General theory of fractal path integrals with applications to many‐body theories and statistical physics
journal, February 1991

  • Suzuki, Masuo
  • Journal of Mathematical Physics, Vol. 32, Issue 2
  • DOI: 10.1063/1.529425

Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets
journal, September 2017

  • Kandala, Abhinav; Mezzacapo, Antonio; Temme, Kristan
  • Nature, Vol. 549, Issue 7671
  • DOI: 10.1038/nature23879

Semiclassical Fourier Transform for Quantum Computation
journal, April 1996

Spectral quantum tomography
journal, September 2019

  • Helsen, Jonas; Battistel, Francesco; Terhal, Barbara M.
  • npj Quantum Information, Vol. 5, Issue 1
  • DOI: 10.1038/s41534-019-0189-0

Simulating physical phenomena by quantum networks
journal, April 2002

Quantum Algorithm for Systems of Linear Equations with Exponentially Improved Dependence on Precision
journal, January 2017

  • Childs, Andrew M.; Kothari, Robin; Somma, Rolando D.
  • SIAM Journal on Computing, Vol. 46, Issue 6
  • DOI: 10.1137/16M1087072

Entanglement-free Heisenberg-limited phase estimation
journal, November 2007

  • Higgins, B. L.; Berry, D. W.; Bartlett, S. D.
  • Nature, Vol. 450, Issue 7168
  • DOI: 10.1038/nature06257

Error mitigation extends the computational reach of a noisy quantum processor
journal, March 2019

On the Convergence Rate of Generalized Fourier Expansions
journal, January 1973

Quantum phase estimation of multiple eigenvalues for small-scale (noisy) experiments
journal, February 2019

  • O’Brien, Thomas E.; Tarasinski, Brian; Terhal, Barbara M.
  • New Journal of Physics, Vol. 21, Issue 2
  • DOI: 10.1088/1367-2630/aafb8e
    Sort by:
    [ × clear filter / sort ]

    Figures / Tables found in this record:

    Figure 1 (p. 4)figure
    Figure 2 (p. 4)figure
    Figure 3 (p. 5)figure
    Figure 4 (p. 7)figure
    Figure 5 (p. 10)figure
    Figure 6 (p. 11)figure
      [ × clear filter / sort ]
      Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

      Similar Records in DOE PAGES and OSTI.GOV collections: