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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]
  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
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. https://doi.org/10.1088/1367-2630/ab5c60.
Somma, Rolando Diego. Quantum eigenvalue estimation via time series analysis. United States. https://doi.org/10.1088/1367-2630/ab5c60
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.
@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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

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

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