TY - JOUR

T1 - Quantum algorithms for open lattice field theory

AU - Hubisz, Jay

AU - Sambasivam, Bharath

AU - Unmuth-Yockey, Judah

N1 - Funding Information:
We would like to thank Erik Gustafson and Mike Hite for stimulating discussion while developing this work. We especially thank Hari Krovi for extensive discussion throughout the development of this project. We thank Yannick Meurice, Erik Gustafson, Roni Harnik, and Simon Catterall for useful comments on the manuscript. J.H. and B.S. are supported in part by the U.S. Department of Energy (DOE), Office of Science, Office of High Energy Physics, under Award No. DE-SC0009998. J.U.-Y. was supported by the U.S. Department of Energy Grant No. DE-SC0019139, and by Fermi Research Alliance, LLC, under Contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics.
Publisher Copyright:
© 2021 American Physical Society.

PY - 2021/11

Y1 - 2021/11

N2 - 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. 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.

AB - 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. 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.

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U2 - 10.1103/PhysRevA.104.052420

DO - 10.1103/PhysRevA.104.052420

M3 - Article

AN - SCOPUS:85119953977

SN - 2469-9926

VL - 104

JO - Physical Review A

JF - Physical Review A

IS - 5

M1 - A15

ER -