Trigonometric continuous-variable gates and hybrid quantum simulations of the sine-Gordon model

TL;DR

This paper introduces trigonometric continuous-variable gates for hybrid quantum computing, enabling efficient simulation of the sine-Gordon model and other interacting field theories on near-term hardware.

Contribution

It presents a novel universality paradigm based on trigonometric gates, expanding beyond polynomial functions for simulating bosonic quantum field theories.

Findings

Successfully simulated the sine-Gordon model dynamics

Prepared ground states via quantum imaginary-time evolution

Demonstrated potential for broader applications in physics and chemistry

Abstract

Hybrid qubit-qumode quantum computing platforms provide a natural setting for simulating interacting bosonic quantum field theories. However, existing continuous-variable gate constructions rely predominantly on polynomial functions of canonical quadratures. In this work, we introduce a complementary universality paradigm based on trigonometric continuous-variable gates, which enable a Fourier-like representation of bosonic operators and are particularly well suited for periodic and non-perturbative interactions. We present a deterministic ancilla-based method for implementing unitary and non-unitary trigonometric gates whose arguments are arbitrary Hermitian functions of qumode quadratures. As a concrete application, we develop a hybrid qubit-qumode quantum simulation of the lattice sine-Gordon model. Using these gates, we prepare ground states via quantum imaginary-time evolution, simulate real-time dynamics, compute time-dependent vertex two-point correlation functions, and extract quantum kink profiles under topological boundary conditions. Our results demonstrate that trigonometric continuous-variable gates provide a physically natural framework for simulating interacting field theories on near-term hybrid quantum hardware, while establishing a parallel route to universality beyond polynomial gate constructions. We expect that the trigonometric gates introduced here to find broader applications, including quantum simulations of condensed matter systems, quantum chemistry, and biological models.