# Quantum simulation scheme of two-dimensional xy-model Hamiltonian with controllable coupling

## TL;DR

This paper proposes a quantum simulation scheme for the 2D xy-model Hamiltonian using coupled cavity resonators with controllable coupling via an ancilla transmon qubit, enabling in situ tuning of interaction strength.

## Contribution

It introduces a novel method to realize a 2D xy-model Hamiltonian with adjustable coupling in a cavity array using an ancilla transmon qubit.

## Key findings

- Controllable xy-coupling strength achieved via ancilla transmon.
- Resonator hopping leads to a tight-binding Hamiltonian.
- Scheme enables in situ tuning of quantum interactions.

## Abstract

We study a scheme of quantum simulator for two-dimensional xy-model Hamiltonian. Previously the quantum simulator for a coupled cavity array spin model has been explored, but the coupling strength is fixed by the system parameters. In the present scheme several cavity resonators can be coupled with each other simultaneously via an ancilla qubit. In the two-dimensional Kagome lattice of the resonators the hopping of resonator photonic modes gives rise to the tight-binding Hamiltonian which in turn can be transformed to the quantum xy-model Hamiltonian. We employ the transmon as an ancilla qubit to achieve in situ controllable xy-coupling strength.