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Title: Digitization of scalar fields for quantum computing

Journal Article · · Physical Review A
 [1];  [1]
  1. Univ. of Washington, Seattle, WA (United States)

Qubit, operator, and gate resources required for the digitization of lattice λΦ4 scalar field theories onto quantum computers are considered, building upon the foundational work by Jordan et al. [Quantum Inf. Comput. 14, 1014 (2014); Science 336, 1130 (2012)], with a focus towards noisy intermediate-scale quantum devices. The Nyquist-Shannon sampling theorem, introduced in this context by Macridin et al. [Phys. Rev. A 98, 042312 (2018)] building on the work of Somma [Quantum Inf. Comput. 16, 1125 (2016)], provides a guide with which to evaluate the efficacy of two field-space bases, the eigenstates of the field operator, as used by Jordan et al., and eigenstates of a harmonic oscillator, to describe ( 0 + 1 )- and ( d + 1 )-dimensional scalar field theory. We show how techniques associated with improved actions, which are heavily utilized in lattice QCD calculations to systematically reduce lattice-spacing artifacts, can be used to reduce the impact of the field digitization in λΦ4, but are found to be inferior to a complete digitization improvement of the Hamiltonian using a quantum Fourier transform. When the Nyquist-Shannon sampling theorem is satisfied, digitization errors scale as | log | log | εdig| | | ~ n Q (number of qubits describing the field at a given spatial site) for the low-lying states, leaving the familiar power-law lattice-spacing and finite-volume effects that scale as | log | εlatt| | ~ NQ (total number of qubits in the simulation). For localized (delocalized) field-space wave functions, it is found that nQ ~ 4 ( 7 ) qubits per spatial lattice site are sufficient to reduce theoretical digitization errors below error contributions associated with approximation of the time-evolution operator and noisy implementation on near-term quantum devices. Only classical computing resources have been used to obtain the results presented in this work.

Research Organization:
Univ. of Washington, Seattle, WA (United States)
Sponsoring Organization:
USDOE Office of Science (SC); USDOE
Grant/Contract Number:
FG02-00ER41132; ERKJ335; ERKJ333
OSTI ID:
1609315
Alternate ID(s):
OSTI ID: 1515572
Journal Information:
Physical Review A, Vol. 99, Issue 5; ISSN 2469-9926
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 91 works
Citation information provided by
Web of Science

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Cited By (8)

Phase structure of the ( 1 + 1 )-dimensional massive Thirring model from matrix product states journal November 2019
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General Methods for Digital Quantum Simulation of Gauge Theories text January 2019
Quantum Chemistry as a Benchmark for Near-Term Quantum Computers preprint January 2019
Gluon Field Digitization for Quantum Computers text January 2019
Review on novel methods for lattice gauge theories text January 2019
Selected topics of quantum computing for nuclear physics* journal February 2021