Analog Circuit-QED Simulator of Quantum Spin Dynamics Through the Extended Bose-Hubbard Model

TL;DR

This paper introduces a circuit-QED based analog simulator for quantum spin dynamics using an extended Bose-Hubbard model, validated through numerical simulations and designed for experimental realization.

Contribution

It develops a novel framework employing Dyson-Maleev transformation to simulate spin models with circuit-QED, overcoming non-Hermiticity issues and establishing equivalence with Holstein-Primakoff encoding.

Findings

Numerical simulations confirm accurate reproduction of spin dynamics

Designed a scalable circuit-QED architecture with Josephson junctions

Validated the approach as experimentally feasible

Abstract

We propose and validate a framework for analog simulation of the Heisenberg spin model using a circuit quantum electrodynamics (circuit-QED) platform. Our method involves the Dyson-Maleev transformation, for which we develop a procedure to circumvent its inherent non-Hermiticity, yielding the extended Bose-Hubbard (EBH) Hamiltonian. We demonstrate the equivalence of this approach to the Holstein-Primakoff encoding for spin-1/2 systems. For the experimental realization of this EBH model, we design a scalable circuit-QED architecture based on an engineered Josephson junction array. Numerical simulations confirm that the microwave photon dynamics in this simulator accurately reproduces the original spin dynamics. Our work establishes an experimentally accessible method for investigating complex quantum spin dynamics in a highly controllable bosonic setting.