Excited-State Quantum Chemistry on Qumode-Based Processors via Variational Quantum Deflation

TL;DR

This paper introduces a bosonic quantum algorithm framework (QumVQD) for efficiently computing electronic and vibrational excited states in quantum chemistry, demonstrating high accuracy and reduced error sensitivity.

Contribution

The authors develop a symmetry-enforced variational quantum deflation method tailored for bosonic processors, reducing computational overhead and improving error resilience in excited state calculations.

Findings

Achieved chemical accuracy in H2 electronic excited states with reduced Hilbert space.

Computed vibrational eigenstates of CO2 and H2S with significantly fewer entangling gates.

Demonstrated enhanced noise robustness due to shallower circuit depths.

Abstract

Variational quantum algorithms on bosonic quantum processors are an emerging paradigm for quantum chemistry calculations, exploiting the natural alignment between molecular structure and harmonic oscillator-based hardware. We introduce the qumode-based variational quantum deflation framework (QumVQD) for finding both electronic and vibrational excited state energies on qumode-based architectures. For electronic structure, we incorporated particle number conservation constraints via Fock basis Hamming weight filtering. This symmetry enforcement achieves a significant reduction in computational overhead, scaling the Hilbert space dimension as O$M \choose n_e$ rather than O$(2^M)$ for $M$ spin orbitals and $n_e$ electrons. We validate the approach through electronic structure calculations on H$_{\text{2}}$, achieving agreement with full configuration interaction (FCI) using the STO-3G basis within chemical accuracy across potential energy surfaces. Extending to vibrational structure, we combine QumVQD with Hamiltonian fragmentation based on Bogoliubov transforms, computing CO$_{\text{2}}$ and H$_{\text{2}}$S vibrational eigenstates to spectroscopic accuracy with entangling gate counts 1-2 orders of magnitude lower than analogous qubit-based algorithms. We performed noise characterization using amplitude-damping models and gate-fidelity analysis, which demonstrates enhanced error resilience due to reduced circuit depth compared to qubit-based algorithms. Together, these results highlight the potential of bosonic quantum devices for advancing computational chemistry, particularly in areas where qubit-based devices struggle.