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IEEE International Conference on Quantum Computing and Engineering (QCE)

Shallow Circuits for Quantum Simulation of Molecular Vibrations

M R Nirmal, Ankit Khandelwal, Manoj Karunakaran Nambiar

Published Aug 30, 2025• 0 citations
Publisher

Abstract

We present a method for constructing shallow quantum circuits to simulate molecular vibrations on near-term quantum devices. Derived from Givens rotation unitaries, we achieved more than 50 % reduction in the circuit depth compared to the unitary vibrational coupled cluster approach.
DOI
10.1109/qce65121.2025.10395

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Quantum computers hold great promise for molecular simulation, but noise remains a fundamental obstacle. We introduce a Quantum Monte Carlo (QMC) pre-screening procedure that constructs compact, physically motivated Givens rotation ansätze tailored to realistic quantum hardware. By identifying the most important wavefunction contributions early in a QMC simulation, we build circuits that are shallower that conventional alternatives while preserving number symmetry. Benchmarked on Quantinuum System Model H1, QMC-prescreened circuits outperform more complex ansätze under realistic noise conditions. The method offers a practical path toward chemical accuracy on quantum devices, by providing an adjustable trade-off between expressivity and circuit depth to generate shallow circuits suited to current high-noise devices, as well as deeper, more expressive circuits that can be deployed on future lower-noise devices.
Molecular vibrations underpin important phenomena such as spectral properties, energy transfer, and molecular bonding. However, obtaining a detailed understanding of the vibrational structure of even small molecules is computationally expensive. While several algorithms exist for efficiently solving the electronic structure problem on a quantum computer, there has been comparatively little attention devoted to solving the vibrational structure problem with quantum hardware. In this work, we discuss the use of quantum algorithms for investigating both the static and dynamic vibrational properties of molecules. We introduce a physically motivated unitary vibrational coupled cluster ansatz, which also makes our method accessible to noisy, near-term quantum hardware. We numerically test our proposals for the water and sulfur dioxide molecules.
Molecular vibrations underpin important phenomena such as spectral properties, energy transfer, and molecular bonding. However, obtaining a detailed understanding of the vibrational structure of even small molecules is computationally expensive. While numerous algorithms exist for solving the electronic structure problem on a quantum computer, there has been comparatively little attention devoted to solving the vibrational structure problem with quantum hardware. In this work, we discuss the use of quantum algorithms for investigating both the static and dynamic vibrational properties of molecules. We introduce a physically motivated unitary vibrational coupled cluster ansatz, which also makes our method accessible to noisy, near-term quantum hardware. We numerically test our proposals for the water and sulfur dioxide molecules.
In this work, we present a comprehensive comparative study between two different Ansatz quantum circuits , specifically the Unitary Vibrational Coupled Cluster (UVCC) and the Compact Heuristic Circuit (CHC) with use in computational chemistry . By incorporating these circuits into the Variational Quantum Eigensolver (VQE), we aim to find the vibrational ground state energy of small molecules. Our results, obtained using both the UVCC and CHC ansatzes with and without quantum hardware noise, are benchmarked against classical computational methods for energy state determination. We emphasize the efficiency and accuracy of the CHC Ansatz , which significantly reduces circuit complexity without sacrificing the fidelity of the results. This characteristic demonstrates the potential of the CHC Ansatz for scalable quantum chemistry applications, particularly in the Noisy Intermediate-Scale Quantum (NISQ) era. Furthermore, we employ the CHC Ansatz in conjunction with the Variational Quantum Deflation (VQD) algorithm to determine the excited vibrational state energies, which is compared against the reliable method of quantum Equation of Motion(qEOM). Through this comparative study, we aim to provide valuable insights into the practical applications of these Ansatz in quantum simulations of molecular systems, highlighting their respective advantages and potential for future quantum chemistry research.
Shallow, CNOT-efficient quantum circuits are crucial for performing accurate computational chemistry simulations on current noisy quantum hardware. Here, we explore the usefulness of noniterative energy corrections, based on the method of moments of coupled-cluster theory, for accelerating convergence toward full configuration interaction. Our preliminary numerical results relying on iteratively constructed ansätze suggest that chemically accurate energies can be obtained with substantially more compact circuits, implying enhanced resilience to gate and decoherence noise.