Title: Quantum algorithms for open lattice field theory

Abstract

Certain aspects of some unitary quantum systems are well described by evolution via a non-Hermitian effective Hamiltonian, as in the Wigner-Weisskopf theory for spontaneous decay. Conversely, any non-Hermitian Hamiltonian evolution can be accommodated in a corresponding unitary system $+$ environment model via a generalization of Wigner-Weisskopf theory. This demonstrates the physical relevance of novel features such as exceptional points in quantum dynamics, and opens up avenues for studying many-body systems in the complex plane of coupling constants. In the case of lattice field theory, sparsity lends these channels the promise of efficient simulation on standardized quantum hardware. We thus consider quantum operations that correspond to Suzuki-Lie-Trotter approximation of lattice field theories undergoing nonunitary time evolution, with potential applicability to studies of spin or gauge models at finite chemical potential, with topological terms, to quantum phase transitions—a range of models with sign problems. Furthermore, we develop non-Hermitian quantum circuits and explore their promise on a benchmark, the quantum one-dimensional Ising model with complex longitudinal magnetic field, showing that observables can probe the Lee-Yang edge singularity. The development of attractors past critical points in the space of complex couplings indicates a potential for study on near-term noisy hardware.

Authors:

Hubisz, Jay ^[1]; Sambasivam, Bharath  ^[1];

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• Search DOE PAGES for ORCID "0000-0002-5765-9469"

Unmuth-Yockey, Judah ^[2]

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+ Show Author Affiliations

1. Syracuse Univ., NY (United States)
2. Syracuse Univ., NY (United States); Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

Publication Date:

Thu Nov 18 00:00:00 EST 2021

Research Org.:

Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)

Sponsoring Org.:

USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:

1834172

Alternate Identifier(s):

OSTI ID: 1905122

Report Number(s):

FERMILAB-PUB-20-660-T; arXiv:2012.05257
Journal ID: ISSN 2469-9926; oai:inspirehep.net:1835721; TRN: US2300138

Grant/Contract Number:  

AC02-07CH11359; SC0009998; SC0019139

Resource Type:

Accepted Manuscript

Journal Name:

Physical Review A

Additional Journal Information:

Journal Volume: 104; Journal Issue: 5; Journal ID: ISSN 2469-9926

Publisher:

American Physical Society (APS)

Country of Publication:

United States

Language:

English

Subject:

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Effective field theory; Lattice field theory; Open quantum systems; Quantum algorithms; Quantum criticality; Quantum master equation; Spin lattice models; effective field theory; lattice field theory; open quantum systems; quantum algorithms; quantum criticality; quantum master equation; spin lattice models