Advanced Quantum Algorithms for Many-body systems (AQAM-2025)

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

Nov 18, 2025, 3:25 PM

25m

Contributed Talk (25 min including questions)

Speaker

Even Chiari;Chiari (Université de Strasbourg)

Description

Describing polaritonic systems at the ab initio level is computationally demanding, as it requires a high-level representation of the interaction between confined electromagnetic fields and the electronic structure of a molecule. Capturing these effects accurately necessitates efficient encoding schemes that can handle both electronic and photonic degrees of freedom within a quantum computational framework [1, 2].

In this work [3], we address this challenge using a quantum algorithm, specifically, the ensemble-VQE [4–6], which enables the calculation of both ground and excited states. This algorithm is initially formulated on a qubit-based architecture. While fermionic degrees of freedom are naturally well-suited to qubit encoding, the same does not hold for bosonic modes. Although the number of qubits required scales linearly with the number of fermionic modes, it typically scales with the product of the number of bosons and bosonic modes. Furthermore, standard boson-to-qubit mappings often introduce unphysical states, artificially increasing the size of the Hamiltonian and making quantum computations significantly more difficult.

These limitations motivated us to ask a broader question:

• Should hybrid fermionic-bosonic quantum simulations remain confined to a qubit-only framework?
• Or could we leverage the intrinsic properties of alternative quantum devices/platforms to better encode bosonic degrees of freedom?

To explore these questions, we go beyond the conventional qubit-based architecture and investigate two other approaches for modeling cavity quantum electrodynamics systems: a qudit-based [7–11] architecture and a hybrid qubit–qumode framework [12–15].

Qudit-based approach

A qudit is a generalization of a qubit with a dimension $d > 2$, meaning that the possible states are:

$$ \{|0\rangle, |1\rangle, |2\rangle, \ldots, |d-1\rangle\} $$ and any linear combination of them. Quantum computing with qudits is a young field, and the availability of standard gate sets remains limited. However, the motivation for using them is to take advantage of the $d$ discrete levels to encode a bosonic Fock space directly, up to a given truncation. ### Qumode-based approach Qumodes refer to genuine quantum harmonic oscillators, either mechanical or electromagnetic, that naturally behave as bosonic modes. They are described using continuous-variable representations, which are inherently better suited to bosonic systems than the discrete-variable representations used by qubits and qudits. As with qudits, qumodes aim to encode the bosonic Fock space, with the added benefit that hardware implementations are often more direct. # Benchmark and results We benchmark all three strategies on a cavity-embedded H₂ molecule, resolving the three lowest-energy polaritonic states using noiseless quantum circuit simulations [16, 17]. All platforms yield comparable accuracy in predicting polaritonic eigenenergies and eigenstates, with energy errors below $10^{-4}$ Ha and eigenstate fidelities exceeding $99.99\%$ overlap with the QED-FCI reference solutions. In terms of quantum resource requirements (e.g., number of entangling gates and quantum information units), the hybrid qubit–qumode approach offers the best trade-off between efficiency and accuracy, followed closely by the qudit-based method — both outperform the standard qubit-only architecture.

References

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3. E. Chiari et al., arXiv:2506.12504 (2025)
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17. T. J. Stavenger et al., IEEE HPEC, pp. 1–8 (2022)