Single-particle digitization strategy for quantum computation of a ${\varphi }^4$ scalar field theory

Abstract

Motivated by the parton picture of high energy quantum chromodynamics, we develop a single-particle digitization strategy for the efficient quantum simulation of relativistic scattering processes in a $d+1$ dimensional scalar ${\varphi }^4$ field theory. We work out quantum algorithms for initial state preparation, time evolution and final state measurements. We outline a non-perturbative renormalization strategy in this single-particle framework.

Comments: 31 pages, 13 figures; journal version published in Phys. Rev. A 103, 042410 (2021); Table I modified to to include more precise estimate for cost of initial state preparation; Appendix B (discussion of state preparation) significantly extended & figures 10 and 11 added