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arXiv:2602.17806 · Physical Review A

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

Kelvin Yip, Alessandro Monteros, Sahel Ashhab, Lin Tian

quant-phSubmitted Feb 19, 2026• Announced Feb 23, 2026• 0 citations
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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.

Comments
12 pages, 8 figures

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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.
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Abstract We explore the potential for hybrid development of quantum hardware where currently available quantum computers simulate open cavity quantum electrodynamical (CQED) systems for applications in optical quantum communication, simulation and computing. Our simulations make use of a recent quantum algorithm that maps the dynamics of a singly excited open Tavis–Cummings model containing N atoms coupled to a lossy cavity. We report the results of executing this algorithm on two noisy intermediate-scale quantum computers: a superconducting processor and a trapped ion processor, to simulate the population dynamics of an open CQED system featuring N = 3 atoms. By applying technology-specific transpilation and error mitigation techniques, we minimize the impact of gate errors, noise, and decoherence in each hardware platform, obtaining results which agree closely with the exact solution of the system. These results can be used as a recipe for efficient and platform-specific quantum simulation of cavity–emitter systems on contemporary and future quantum computers.