Quantum simulation of $\phi^4$ theories in qudit systems

TL;DR

This paper explores implementing quantum algorithms for lattice $\

Contribution

It introduces a method to simulate $\

Findings

Efficient encoding of $\

Use of variational methods for state preparation and gate synthesis.

Potential for scalable quantum simulation of quantum field theories.

Abstract

We discuss the implementation of quantum algorithms for lattice $\Phi^4$ theory on circuit quantum electrodynamics (cQED) system. The field is represented on qudits in a discretized field amplitude basis. The main advantage of qudit systems is that its multi-level characteristic allows the field interaction to be implemented only with diagonal single-qudit gates. Considering the set of universal gates formed by the single-qudit phase gate and the displacement gate, we address initial state preparation and single-qudit gate synthesis with variational methods.