Scalable Quantum Simulations of Scattering in Scalar Field Theory on 120 Qubits

TL;DR

This paper demonstrates scalable quantum simulations of scalar field theory scattering using 120 qubits, employing variational circuits and error mitigation to observe interaction effects consistent with classical simulations.

Contribution

It introduces a scalable variational quantum algorithm for simulating scattering in scalar field theory on large quantum hardware, with error mitigation enabling meaningful results.

Findings

Interaction effects observed match classical simulations.

Circuits with up to 4924 two-qubit gates successfully executed.

Error mitigation strategies enabled extraction of meaningful data.

Abstract

Simulations of collisions of fundamental particles on a quantum computer are expected to have an exponential advantage over classical methods and promise to enhance searches for new physics. Furthermore, scattering in scalar field theory has been shown to be BQP-complete, making it a representative problem for which quantum computation is efficient. As a step toward large-scale quantum simulations of collision processes, scattering of wavepackets in one-dimensional scalar field theory is simulated using 120 qubits of IBM's Heron superconducting quantum computer ibm_fez. Variational circuits compressing vacuum preparation, wavepacket initialization, and time evolution are determined using classical resources. By leveraging physical properties of states in the theory, such as symmetries and locality, the variational quantum algorithm constructs scalable circuits that can be used to simulate arbitrarily-large system sizes. A new strategy is introduced to mitigate errors in quantum simulations, which enables the extraction of meaningful results from circuits with up to 4924 two-qubit gates and two-qubit gate depths of 103. The effect of interactions is clearly seen, and is found to be in agreement with classical Matrix Product State simulations. The developments that will be necessary to simulate high-energy inelastic collisions on a quantum computer are discussed.