Computing partition functions in the one-clean-qubit model
Abstract
We present a method to approximate partition functions of quantum systems using mixed-state quantum computation. For positive-semidefinite Hamiltonians, our method has an expected running-time that is almost linear in [M/( εrel Z )]2, where M is the dimension of the quantum system, Z is the partition function, and εrel is the relative precision. It is based on approximations of the exponential operator as linear combinations of certain operators related to block-encoding of Hamiltonians or Hamiltonian evolutions. The trace of each operator is estimated using a standard algorithm in the one-clean-qubit model. For large values of Z , our method may run faster than exact classical methods, whose complexities are polynomial in M . We also prove that a version of the partition function estimation problem within additive error is complete for the so-called DQC1 complexity class, suggesting that our method provides a superpolynomial speedup for certain parameter values. Overall, to attain a desired relative precision, we develop a classical procedure based on a sequence of approximations within predetermined additive errors that may be of independent interest.
- Authors:
-
[1];
[2];
[2]
- Univ. de Sherbrooke, QC (Canada). Inst. Quantique
- 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 Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1819143
- Report Number(s):
- LA-UR-19-30447
Journal ID: ISSN 2469-9926; TRN: US2214561
- Grant/Contract Number:
- 89233218CNA000001
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review A
- Additional Journal Information:
- Journal Volume: 103; Journal Issue: 3; Journal ID: ISSN 2469-9926
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; Computer science; Information science; Mathematics; Quantum computing; Optimization problems; Quantum algorithms; Quantum simulation
Citation Formats
Chowdhury, Anirban N., Somma, Rolando D., and Subaşı, Yiğit. Computing partition functions in the one-clean-qubit model. United States: N. p., 2021.
Web. doi:10.1103/physreva.103.032422.
Chowdhury, Anirban N., Somma, Rolando D., & Subaşı, Yiğit. Computing partition functions in the one-clean-qubit model. United States. https://doi.org/10.1103/physreva.103.032422
Chowdhury, Anirban N., Somma, Rolando D., and Subaşı, Yiğit. Wed .
"Computing partition functions in the one-clean-qubit model". United States. https://doi.org/10.1103/physreva.103.032422. https://www.osti.gov/servlets/purl/1819143.
@article{osti_1819143,
title = {Computing partition functions in the one-clean-qubit model},
author = {Chowdhury, Anirban N. and Somma, Rolando D. and Subaşı, Yiğit},
abstractNote = {We present a method to approximate partition functions of quantum systems using mixed-state quantum computation. For positive-semidefinite Hamiltonians, our method has an expected running-time that is almost linear in [M/( εrel Z )]2, where M is the dimension of the quantum system, Z is the partition function, and εrel is the relative precision. It is based on approximations of the exponential operator as linear combinations of certain operators related to block-encoding of Hamiltonians or Hamiltonian evolutions. The trace of each operator is estimated using a standard algorithm in the one-clean-qubit model. For large values of Z , our method may run faster than exact classical methods, whose complexities are polynomial in M . We also prove that a version of the partition function estimation problem within additive error is complete for the so-called DQC1 complexity class, suggesting that our method provides a superpolynomial speedup for certain parameter values. Overall, to attain a desired relative precision, we develop a classical procedure based on a sequence of approximations within predetermined additive errors that may be of independent interest.},
doi = {10.1103/physreva.103.032422},
journal = {Physical Review A},
number = 3,
volume = 103,
place = {United States},
year = {Wed Mar 17 00:00:00 EDT 2021},
month = {Wed Mar 17 00:00:00 EDT 2021}
}
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