Digitization of scalar fields for quantum computing

Qubit, operator, and gate resources required for the digitization of lattice lambda phi(4) 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 lambda phi(4), 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 vertical bar log vertical bar log vertical bar epsilon(d)(ig) vertical bar parallel to similar to 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 vertical bar log vertical bar epsilon(latt) parallel to similar to N-Q (total number of qubits in the simulation). For localized (delocalized) field-space wave functions, it is found that n(Q) similar to 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.