Digital quantum simulation of the BCS model with a central-spin-like quantum processor

TL;DR

This paper introduces a quantum algorithm for simulating the BCS model on star-connected quantum hardware, demonstrating its implementation and analyzing its complexity through classical simulation.

Contribution

It presents a novel digital quantum simulation algorithm tailored for star-shaped quantum processors, specifically applied to the BCS model.

Findings

Successfully mapped the BCS model onto star-shaped quantum hardware.

Demonstrated the algorithm's effectiveness through classical simulation of dynamics.

Analyzed the circuit complexity for practical implementation.

Abstract

The simulation of quantum systems is one of the most promising applications of quantum computers. In this paper we present a quantum algorithm to perform digital quantum simulations of the BCS model on a quantum register with a star shaped connectivity map, as it is, e.g., featured by color centers in diamond. We show how to effectively translate the problem onto the quantum hardware and implement the algorithm using only the native interactions between the qubits. Furthermore we discuss the complexity of the circuit. We use the algorithm to simulate the dynamics of the BCS model by subjecting its mean-field ground state to a time-dependent perturbation. The quantum simulation algorithm is studied using a classical simulation.