Ab Initio Polaritonic Chemistry on Diverse Quantum Computing Platforms: Qubit, Qudit, and Hybrid Qubit-Qumode Architectures

TL;DR

This study compares qubit, qudit, and hybrid qubit-qumode quantum computing architectures for simulating polaritonic chemistry, demonstrating that hybrid approaches offer better resource efficiency and accuracy on near-term hardware.

Contribution

The paper introduces and benchmarks three quantum simulation strategies for polaritonic chemistry, highlighting the advantages of hybrid qubit-qumode platforms over traditional qubit-based methods.

Findings

All three platforms accurately predict polaritonic eigenstates.

Hybrid qubit-qumode approach is most resource-efficient.

Qudit-based approach closely follows hybrid in performance.

Abstract

Trying to export ab initio polaritonic chemistry onto emerging quantum computers raises fundamental questions. A central one is how to efficiently represent both fermionic and bosonic degrees of freedom on the same platform, in order to develop computational strategies that can accurately capture strong electron-photon correlations at a reasonable cost for implementation on near-term hardware. Given the hybrid fermion-boson nature of polaritonic problem, one may legitimately ask: should we rely exclusively on conventional qubit-based platforms, or consider alternative computational paradigms? To explore this, we investigate in this work three strategies: qubit-based, qudit-based, and hybrid qubit-qumode approaches. For each platform, we design compact, physically motivated quantum circuit ans\"{a}tze and integrate them within the state-averaged variational quantum eigensolver to compute multiple polaritonic eigenstates simultaneously. A key element of our approach is the development of compact electron-photon entangling circuits, tailored to the native capabilities and limitations of each hardware architecture. We benchmark all three strategies on a cavity-embedded H$_{2}$ molecule, reproducing characteristic phenomena such as light-induced avoided crossings. Our results show that each platform achieves comparable accuracy in predicting polaritonic eigen-energies and eigenstates. However, with respect to quantum resources required the hybrid qubit-qumode approach offers the most favorable tradeoff between resource efficiency and accuracy, followed closely by the qudit-based method. Both of which outperform the conventional qubit-based strategy. Our work presents a hardware-conscious comparison of quantum encoding strategies for polaritonic systems and highlights the potential of higher-dimensional quantum platforms to simulate complex light-matter systems.