Digital Quantum Simulation of Scalar Yukawa Coupling

TL;DR

This paper demonstrates digital quantum simulation of scalar Yukawa interactions on IBM Q, designing low-depth circuits for up to three bosons, and validates results with error mitigation against classical benchmarks.

Contribution

It introduces low-depth quantum circuits for simulating Yukawa dynamics with up to three bosons and applies error mitigation to validate quantum results.

Findings

Successful circuit compression for one boson

Efficient circuit design for three bosons with 8 CNOTs per Trotter step

Good agreement with classical benchmarks after error mitigation

Abstract

Motivated by the revitalized interest in the digital simulation of medium- and high-energy physics phenomena, we investigate the dynamics following a Yukawa-interaction quench on IBM Q. Adopting the zero-dimensional version of the scalar Yukawa-coupling model as our point of departure, we design low-depth quantum circuits emulating its dynamics with up to three bosons. In the one-boson case we demonstrate circuit compression, i.e., a constant-depth circuit containing only two controlled-NOT (CNOT) gates. In the more complex three-boson case, we design a circuit in which one Trotter step entails $8$ CNOTs. Using an analogy with the traveling-salesman problem, we also provide a CNOT-cost estimate for higher boson-number truncations. Based on these circuits, we quantify the system dynamics by evaluating the expected boson number at an arbitrary time after the quench and the survival probability of the initial vacuum state (the Loschmidt echo). We also utilize these circuits to drive adiabatic transitions and compute the energies of the ground- and first-excited states of the considered model. Finally, through error mitigation -- i.e, zero-noise extrapolation -- we demonstrate a good agreement of our results with a numerically-exact classical benchmark.