The quantum sine-Gordon model with quantum circuits

TL;DR

This paper demonstrates that superconducting quantum circuits can effectively simulate the quantum sine-Gordon model, with numerical and analytical results supporting their viability for studying complex quantum field theories.

Contribution

It introduces a quantum circuit implementation of the qSG model, benchmarks it against Bethe ansatz results, and shows its advantages over traditional lattice models like the XYZ chain.

Findings

Numerical results agree with Bethe ansatz calculations.

Analytical form-factor calculations match numerical data.

Quantum circuits are feasible with current superconducting technology.

Abstract

Analog quantum simulation has the potential to be an indispensable technique in the investigation of complex quantum systems. In this work, we numerically investigate a one-dimensional, faithful, analog, quantum electronic circuit simulator built out of Josephson junctions for one of the paradigmatic models of an integrable quantum field theory: the quantum sine-Gordon (qSG) model in 1+1 space-time dimensions. We analyze the lattice model using the density matrix renormalization group technique and benchmark our numerical results with existing Bethe ansatz computations. Furthermore, we perform analytical form-factor calculations for the two-point correlation function of vertex operators, which closely agree with our numerical computations. Finally, we compute the entanglement spectrum of the qSG model. We compare our results with those obtained using the integrable lattice-regularization based on the quantum XYZ chain and show that the quantum circuit model is less susceptible to corrections to scaling compared to the XYZ chain. We provide numerical evidence that the parameters required to realize the qSG model are accessible with modern-day superconducting circuit technology, thus providing additional credence towards the viability of the latter platform for simulating strongly interacting quantum field theories.