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arXiv:2008.08144 · Physical Review Research

Microcanonical and finite-temperature ab initio molecular dynamics simulations on quantum computers

Igor O. Sokolov, Panagiotis Kl. Barkoutsos, Lukas Moeller, Philippe Suchsland, Guglielmo Mazzola, Ivano Tavernelli

Published Feb 10, 2021• 44 citations
arXivHTMLPDF

Abstract

Ab initio molecular dynamics (AIMD) is a powerful tool to predict properties of molecular and condensed matter systems.However, the quality of this procedure relies on the availability of rigorous electronic structure calculations.The development of quantum processors has shown great potential for the efficient evaluation of accurate ground and excited state energies of molecular systems, opening up new avenues for molecular dynamics simulations.In this work, we address the use of variational quantum algorithms for the calculation of accurate atomic forces to be used in AIMD.In particular, we provide solutions for the alleviation of the statistical noise associated with the measurements of the expectation values of energies and forces, as well as schemes for the mitigation of the hardware noise sources (in particular, gate infidelities, qubit decoherence, and readout errors).Despite the relative large error in the calculation of the potential energy, our results show that the proposed algorithms can provide accurate MD trajectories in the microcanonical (constant energy) ensemble.Furthermore, exploiting the intrinsic noise associated to the quantum measurement process, we also propose a Langevin dynamics algorithm for the simulation of canonical, i.e., constant temperature, dynamics.Both algorithms (microcanonical and canonical) are applied to the simulation of simple molecular systems such as H 2 and H + 3 .Finally, we also provide results for the dynamics of H 2 obtained with IBM quantum computer ibmq_athens.

DOI
10.1103/physrevresearch.3.013125

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Ab initio molecular dynamics (AIMD) is a powerful tool to predict properties of molecular and condensed matter systems.However, the quality of this procedure relies on the availability of rigorous electronic structure calculations.The development of quantum processors has shown great potential for the efficient evaluation of accurate ground and excited state energies of molecular systems, opening up new avenues for molecular dynamics simulations.In this work, we address the use of variational quantum algorithms for the calculation of accurate atomic forces to be used in AIMD.In particular, we provide solutions for the alleviation of the statistical noise associated with the measurements of the expectation values of energies and forces, as well as schemes for the mitigation of the hardware noise sources (in particular, gate infidelities, qubit decoherence, and readout errors).Despite the relative large error in the calculation of the potential energy, our results show that the proposed algorithms can provide accurate MD trajectories in the microcanonical (constant energy) ensemble.Furthermore, exploiting the intrinsic noise associated to the quantum measurement process, we also propose a Langevin dynamics algorithm for the simulation of canonical, i.e., constant temperature, dynamics.Both algorithms (microcanonical and canonical) are applied to the simulation of simple molecular systems such as H 2 and H + 3 .Finally, we also provide results for the dynamics of H 2 obtained with IBM quantum computer ibmq_athens.
Ab initio molecular dynamics (AIMD) is a valuable technique for studying molecules and materials at finite temperatures where the nuclei evolve on potential energy surfaces obtained from accurate electronic structure calculations. In this work, we present an approach to running AIMD simulations on noisy intermediate-scale quantum (NISQ)-era quantum computers. The electronic energies are calculated on a quantum computer using the variational quantum eigensolver (VQE) method. Algorithms for computation of analytical gradients entirely on a quantum computer require quantum fault-tolerant hardware, which is beyond NISQ-era. Therefore, we compute the energy gradients numerically using finite differences, the Hellmann–Feynman theorem, and a correlated sampling technique. This method only requires additional classical calculations of electron integrals for each degree of freedom without any additional computations on a quantum computer beyond the initial VQE run. As a proof of concept, AIMD simulations are demonstrated for the H2 molecule on IBM quantum devices. In addition, we demonstrate the validity of the method for larger molecules using full configuration interaction wave functions. As quantum hardware and noise mitigation techniques continue to improve, the method can be utilized for studying larger molecular systems.
Quantum computers offer the potential to simulate chemical systems beyond the capabilities of classical computers. However, current quantum computing approaches to ab initio molecular dynamics (AIMD) and vibrational analysis largely rely on the Variational Quantum Eigensolver (VQE), whose circuit depth, iterative optimization, and measurement overhead hinder the practical simulation of molecular systems. Here, we extend Sample-based Quantum Diagonalization (SQD), a quantum sampling-based electronic-structure method, to AIMD and vibrational analysis on noisy quantum hardware. The resulting framework enables nuclear forces and Hessians to be derived from quantum-computed electronic energies, facilitating molecular dynamics and characterization of potential energy surfaces. We demonstrate the approach using diverse molecular processes, including H2 bond vibration, the proton-exchange reaction (H+ + H2), the bimolecular nucleophilic substitution (SN2) reaction (Cl- + CH3Cl), and proton-transfer dynamics between two water molecules involving transient formation of the Zundel cation (H2O···H+···OH2). Across these systems, SQD-AIMD trajectories and vibrational frequencies obtained with noisy quantum hardware/noise-models show excellent agreement with classical reference calculations and substantially improved accuracy relative to previously reported VQE-based simulations. Importantly, the SQD-based approach eliminates costly variational optimization and significantly reduces measurement requirements relative to VQE, enabling AIMD simulations spanning approximately 500 timesteps (∼200 fs), substantially longer than previously reported AIMD simulations on quantum hardware. These results establish SQD-AIMD and SQD-vibrational analysis as practical and scalable frameworks for simulating chemical reaction dynamics and elucidating reaction mechanisms on near-term quantum hardware, extending quantum computing applications beyond static electronic structure calculations.
Nuclear quantum effects are critical for describing proton transfer and hydrogen bonding, but their incorporation into quantum chemistry calculations is often computationally prohibitive on classical hardware. A promising alternative are quantum computers due to their linear scaling in the space requirements with system size. We introduce a novel hybrid quantum-classical algorithm for ab-initio molecular dynamics that incorporates nuclear quantum effects via the nuclear-electronic orbital method. The proposed algorithm evaluates ground state energies and forces on the quantum computer using a variational quantum eigensolver, while the molecular geometries are updated classically. We validate our approach through simulations of H2\text{H}_2H2​, H2O\text{H}_2\text{O}H2​O and the Zundel ion H5O2+\text{H}_5\text{O}_2^+H5​O2+​, comparing the simulated vibrational spectra with experimental data. Upon inclusion of nuclear quantum effects, the proton shuttling movement in the Zundel ion becomes effectively barrierless, and errors in the simulated frequencies improve significantly. Employing compact hardware-efficient ansatz circuits we achieve results comparable to the more accurate UCCSD ansatzes, which hints towards the feasibility of executing our algorithm on near-term quantum devices.
Ab-initio molecular dynamics (AIMD) is a powerful tool to simulate physical movements of molecules for investigating properties of materials. While AIMD is successful in some applications, circumventing its high computational costs is imperative to perform large-scale and long-time simulations. In recent days, near-term quantum computers have attracted much attentions as a possible solution to alleviate the challenge. Specifically, Kuroiwa et al. proposed a new AIMD method called quantum Car-Parrinello molecular dynamics (QCPMD), which exploits the Car-Parrinello method and Langevin formulation to realize cost-efficient simulations at the equilibrium state, using near-term quantum devices. In this work, we build on the proposed QCPMD method and introduce the classical shadow technique to further improve resource efficiency of the simulations. More precisely, classical shadows are used to estimate the forces of all nuclei simultaneously, implying this approach is more effective as the number of molecules increases. We numerically study the performance of our scheme on the H2\text{H}_2H2​ molecule and show that QCPMD with classical shadows can simulate the equilibrium state. Our results will give some insights into efficient AIMD simulations on currently-available quantum computers.
We demonstrate a quantum-classical workflow for ab initio molecular dynamics (AIMD) in which quantum measurements from a chemistry-inspired LUCJ ansatz are post-processed using Sample-based Quantum Diagonalization (SQD) to recover determinant subspaces and deliver energies and analytical nuclear gradients for dynamics. As an exact benchmark, we use full configuration interaction (FCI) in the STO-3G basis, enabling a direct assessment of the accuracy of SQD. In gas-phase benchmarks, SQD reproduces FCI energies and gradients to within 1 kcal mol−1^{-1}−1 of the FCI reference and yields stable AIMD trajectories. In explicit-solvent QM/MM simulations, SQD retains this agreement, matching FCI energy fluctuations and RMS gradient profiles and reproducing solute-solvent structure as quantified by radial distribution functions. Overall, these benchmarks establish LUCJ+SQD as a practical route for integrating current quantum hardware into QM/MM molecular dynamics and provide an early demonstration of condensed-phase QM/MM dynamics driven by a quantum electronic-structure engine.
In this paper, we propose a cost-reduced method for finite-temperature molecular dynamics on a near-term quantum computer, Quantum Car-Parrinello molecular dynamics (QCPMD). One of the most promising applications of near-term quantum computers is quantum chemistry. It has been expected that simulations of molecules via molecular dynamics can be also efficiently performed on near-term quantum computers by applying a promising near-term quantum algorithm of the variational quantum eigensolver (VQE). However, this method may demand considerable computational costs to achieve a sufficient accuracy, and otherwise, statistical noise can significantly affect the results. To resolve these problems, we invent an efficient method for molecular time evolution inspired by Car-Parrinello method. In our method, parameters characterizing the quantum state evolve based on equations of motion instead of being optimized. Furthermore, by considering Langevin dynamics, we can make use of the intrinsic statistical noise. As an application of QCPMD, we propose an efficient method for vibrational frequency analysis of molecules in which we can use the results of the molecular dynamics calculated by QCPMD. Numerical experiments show that our method can precisely simulate the Langevin dynamics at the equilibrium state, and we can successfully predict a given molecule's eigen frequencies. Furthermore, in the numerical simulation, our method achieves a substantial cost reduction compared with molecular dynamics using the VQE. Our method achieves an efficient computation without using widely employed method of the VQE. In this sense, we open up a new possibility of molecular dynamics on near-term quantum computers. We expect our results inspire further invention of efficient near-term quantum algorithms for simulation of molecules.