2018/08/31 by Natalie Klco, Martin J. Savage · 1 citation
Physics and Astronomy · #quant-ph #hep-lat #hep-ph #nucl-th
paper · pdf · doi:10.1103/physreva.99.052335
published as Phys. Rev. A 99, 052335 (2019) · 48 pages, 19 figures, 4 tables
arxiv created 2019/05/24 · arxiv updated 2019/05/28
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, Lee and Preskill, with a focus towards noisy intermediate-scale quantum (NISQ) devices. The Nyquist-Shannon sampling theorem, introduced in this context by Macridin, Spentzouris, Amundson and Harnik building on the work of Somma, provides a guide with which to evaluate the efficacy of two field-space bases, the eigenstates of the field operator, as used by Jordan, Lee and Preskill, 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\rm dig|||∼ nQ (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\rm latt||∼ NQ (total number of qubits in the simulation). For localized(delocalized) field-space wavefunctions, 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.