Digitization of scalar fields for quantum computing

Journal Article · 22 May 2019 · Physical Review A

DOI: https://doi.org/10.1103/physreva.99.052335 · OSTI ID:1609315

Klco, Natalie ^[1]; Savage, Martin J. ^[2]

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1. Univ. of Washington, Seattle, WA (United States); DOE/OSTI
2. 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 | ε_dig| | | ~ 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 | ε_latt| | ~ N_Q (total number of qubits in the simulation). For localized (delocalized) field-space wave functions, it is found that n_Q ~ 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; USDOE Office of Science (SC)
• Grant/Contract Number: FG02-00ER41132
• OSTI ID: 1609315
• Journal Information: Physical Review A, Journal Name: Physical Review A Journal Issue: 5 Vol. 99; ISSN PLRAAN; ISSN 2469-9926
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English