Hardware-efficient formulation of molecular cavity-QED Hamiltonians

TL;DR

This paper introduces a quantum computing approach to efficiently simulate molecular cavity-QED Hamiltonians, overcoming classical computational challenges by leveraging near-term quantum hardware and novel basis choices.

Contribution

It develops a localized photonic basis method that maps QED Hamiltonians onto a 1D qubit chain, reducing noise and improving simulation fidelity on quantum devices.

Findings

Using a localized basis improves fidelity compared to standing-waves basis.

Zero-noise extrapolation enhances the accuracy of quantum dynamics simulations.

The approach remains effective even when relaxing the 1D chain approximation.

Abstract

Light-matter coupled Hamiltonians are central to cavity materials engineering and polaritonic chemistry, but are challenging to simulate with classical hardware due to the scaling of the Hilbert space with the number of quantum photon modes and matter complexity. Leveraging the fact that quantum computers naturally represent photonic modes efficiently, we present a novel approach to simulate quantum-electrodynamical (QED) systems on near-term quantum hardware. After developing the bosonic and mixed operators in the Qiskit Nature framework, we employ them to simulate a first-order Trotterized Hamiltonian for a spontaneous-emission problem of a two-level system in an optical cavity. We find that using a standing-waves photonic basis approach leads to fidelity issues due to hardware connectivity constraints and two-qubits gates errors. Hence, we propose using a localized photonic basis approach that enforces nearest-neighbor couplings, thanks to which we can map the Hamiltonian as a 1D qubit chain. We significantly reduce the noise and, by applying the zero-noise extrapolation error mitigation technique, we recover the accurate quantum dynamics. Finally, we also show that this approach is resilient when relaxing the 1D qubit chain approximation.