Quantum simulation of ${\varphi }^4$ theories in qudit systems

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.

6 pages, 3 figures