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arXiv:2212.11921

Quantum Car-Parrinello Molecular Dynamics: A Cost-Efficient Molecular Simulation Method on Near-Term Quantum Computers

Kohdai Kuroiwa, Takahiro Ohkuma, Hirokazu Sato, Imai, Ryosuke

Published Dec 22, 2022• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2212.11921

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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.
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.
Quantum mechanics has introduced a new theoretical framework for the study of molecules, enabling the prediction of properties and dynamics through the solution of the Schrödinger equation applied to these systems. However, solving this equation is computationally expensive, which has led to the development of various mathematical frameworks and computational methods designed to balance the available resources with the desired level of accuracy. In particular, quantum computers have emerged as a promising technology with the potential to address these problems more efficiently in the coming decades, whether through reductions in memory, time, and energy consumption, i. e.\textit{i. e.}i. e., reductions in computational complexity or by enhancing precision. This research field is known as Quantum Simulation. Given the current technological limitations of quantum computers, Variational Quantum Algorithms (VQAs), especially the Variational Quantum Eigensolver (VQE), stand out as a feasible approach to demonstrating advantages over classical methods in the near term. This feasibility arises from their lower demand for quantum gates and the reduced depth of the circuits required for their implementation. In this work, we present the application of quantum mechanics to the study of molecules, provide an introduction to the fundamentals of quantum computing, and explore the integration of these fields by employing the VQE in molecular simulations. Finally, we discuss the spatial and temporal complexity associated with the algorithm, highlighting its implications and challenges.
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.
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.
Determining the properties of molecules and materials is one of the premier applications of quantum computing. A major question in the field is how to use imperfect near-term quantum computers to solve problems of practical value. Inspired by the recently developed variants of the quantum counterpart of the equation-of-motion (qEOM) approach and the orbital-optimized variational quantum eigensolver (oo-VQE), we present a quantum algorithm (oo-VQE-qEOM) for the calculation of molecular properties by computing expectation values on a quantum computer. We perform noise-free quantum simulations of BeH 2 in the series of STO-3G/6-31G/6-31G* basis sets and of H 4 and H 2 O in 6-31G using an active space of four electrons and four spatial orbitals (8 qubits) to evaluate excitation energies, electronic absorption, and, for twisted H 4, circular dichroism spectra. We demonstrate that the proposed algorithm can reproduce the results of conventional classical CASSCF calculations for these molecular systems.
Quantum simulation is one of the brightest near term quantum computing applications and it promises the possibility to simulate complex quantum systems that cannot be simulated by classic computers. The current paper introduces a detailed discussion of quantum simulation methods that are being run with the Cirq framework by Google, along with a detailed discussion in terms of their application in various fields. We explore the principles of quantum simulation theory and create reproducible codes of molecular modeling, materials science, financial analysis. We use variational quantum algorithms, specifically Variational Quantum Eigensolver (VQE) to simulate molecular structures and quantum chemistry. We also consider quantum solution to materials science problems and illustrate quantum Monte Carlo solution of financial problems. The results of the experiment, which are achieved by means of simulation, indicate that our Cirq implementations can simulate target systems with high accuracy, but the practical quantum advantage depends on the developments in hardware. Our results point out the existing capacities and limitations of quantum simulation on near term quantum devices, as well as point out future directions of research in this emerging field.