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Title: Continuous Matrix Product States for Quantum Fields: An Energy Minimization Algorithm

Authors:
; ;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1361225
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 118; Journal Issue: 22; Related Information: CHORUS Timestamp: 2017-06-02 22:12:31; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English

Citation Formats

Ganahl, Martin, Rincón, Julián, and Vidal, Guifre. Continuous Matrix Product States for Quantum Fields: An Energy Minimization Algorithm. United States: N. p., 2017. Web. doi:10.1103/PhysRevLett.118.220402.
Ganahl, Martin, Rincón, Julián, & Vidal, Guifre. Continuous Matrix Product States for Quantum Fields: An Energy Minimization Algorithm. United States. doi:10.1103/PhysRevLett.118.220402.
Ganahl, Martin, Rincón, Julián, and Vidal, Guifre. Fri . "Continuous Matrix Product States for Quantum Fields: An Energy Minimization Algorithm". United States. doi:10.1103/PhysRevLett.118.220402.
@article{osti_1361225,
title = {Continuous Matrix Product States for Quantum Fields: An Energy Minimization Algorithm},
author = {Ganahl, Martin and Rincón, Julián and Vidal, Guifre},
abstractNote = {},
doi = {10.1103/PhysRevLett.118.220402},
journal = {Physical Review Letters},
number = 22,
volume = 118,
place = {United States},
year = {Fri Jun 02 00:00:00 EDT 2017},
month = {Fri Jun 02 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on June 2, 2018
Publisher's Accepted Manuscript

Citation Metrics:
Cited by: 4works
Citation information provided by
Web of Science

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  • We investigate properties of the states of a scalar field in a Robertson-Walker space-time constructed by an energy-minimization requirement. It is shown that in general the anticommutator expectation value of these states will not possess the Hadamard form. We present a simple example in which we can give a closed form for such an expectation value. The implications of this result for renormalization theory in quantum field theory on curved space-time are discussed.
  • Cited by 28
  • Matrix product states provide a natural entanglement basis to represent a quantum register and operate quantum gates on it. This scheme can be materialized to simulate a quantum adiabatic algorithm solving hard instances of an NP-complete problem. Errors inherent to truncations of the exact action of interacting gates are controlled by the size of the matrices in the representation. The property of finding the right solution for an instance and the expected value of the energy (cost function) are found to be remarkably robust against these errors. As a symbolic example, we simulate the algorithm solving a 100-qubit hard instance,more » that is, finding the correct product state out of {approx}10{sup 30} possibilities. Accumulated statistics for up to 60 qubits seem to point at a subexponential growth of the average minimum time to solve hard instances with highly truncated simulations of adiabatic quantum evolution.« less
  • We demonstrate how to simulate both discrete and continuous stochastic evolutions of a quantum many-body system subject to measurements using matrix product states. A particular, but generally applicable, measurement model is analyzed and a simple representation in terms of matrix product operators is found. The technique is exemplified by numerical simulations of the antiferromagnetic Heisenberg spin-chain model subject to various instances of the measurement model. In particular, we focus on local measurements with small support and nonlocal measurements, which induce long-range correlations.