Digital Quantum Simulation of the Holstein-Primakoff Transformation on Noisy Qubits

TL;DR

This paper demonstrates the digital quantum simulation of bosonic systems using the Holstein-Primakoff transformation on noisy superconducting qubits, exploring error sources and optimizing parameters for current quantum hardware.

Contribution

It introduces a method for simulating bosonic modes via the Holstein-Primakoff transformation on cloud quantum processors, addressing hardware and algorithmic errors.

Findings

Successful simulation of driven harmonic oscillator and Jaynes-Cummings model

Identification of dominant errors from finite qubits and Trotter steps

Framework for extending to complex spin-boson and multimode models

Abstract

Quantum simulation of many-body systems offers a powerful approach to exploring collective quantum dynamics beyond classical computational reach. Although spin and fermionic models have been extensively simulated on digital quantum computers, the simulation of bosonic systems on programmable quantum processors is often hindered by the intrinsically large Hilbert space of bosonic modes. In this work, we study the digital quantum simulation of bosonic modes using the Holstein-Primakoff (HP) transformation and implement this protocol on a cloud-based superconducting quantum processor. Two representative models are realized on quantum hardware: (i) the driven harmonic oscillator and (ii) the Jaynes-Cummings model. Using data obtained from the quantum simulations, we systematically examine the interplay between algorithmic and hardware-induced errors to identify optimal simulation parameters. The dominant algorithmic errors arise from the finite number of qubits used in the HP mapping and the finite number of Trotter steps in the time evolution, while hardware errors mainly originate from gate infidelity, decoherence, and readout errors. This study advances the digital quantum simulation of many-body systems involving bosonic degrees of freedom on currently available cloud quantum processors and provides a framework that can be extended to more complex spin-boson and multimode cavity models.