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arXiv:2208.12487 · Journal of Chemical Theory and Computation

Solvent Distribution Effects on Quantum Chemical Calculations with Quantum Computers

Yuichiro Yoshida, Wataru Mizukami, Norio Yoshida

Published Feb 20, 2024• 4 citations
arXivHTMLPDF

Abstract

We present a combination of three-dimensional reference interaction site model self-consistent field (3D-RISM-SCF) theory and the variational quantum eigensolver (VQE) to consider the solvent distribution effects within the framework of quantum-classical hybrid computing. The present method, 3D-RISM-VQE, does not include any statistical errors from the solvent configuration sampling owing to the analytical treatment of the statistical solvent distribution. We apply 3D-RISM-VQE to compute the spatial distribution functions of solvent water around a water molecule, the potential and Helmholtz energy curves of NaCl, and to analyze the Helmholtz energy component and related properties of H 2 O and NH 4 + . Moreover, we utilize 3D-RISM-VQE to analyze the extent to which solvent effects alter the efficiency of quantum calculations compared with calculations in the gas phase using the L 1 -norms of molecular electronic Hamiltonians. Our results demonstrate that the efficiency of quantum chemical calculations on a quantum computer in solution is virtually the same as that in the gas phase.

DOI
10.1021/acs.jctc.3c01189

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We present a combination of three-dimensional reference interaction site model self-consistent field (3D-RISM-SCF) theory and the variational quantum eigensolver (VQE) to consider the solvent distribution effects within the framework of quantum-classical hybrid computing. The present method, 3D-RISM-VQE, does not include any statistical errors from the solvent configuration sampling owing to the analytical treatment of the statistical solvent distribution. We apply 3D-RISM-VQE to compute the spatial distribution functions of solvent water around a water molecule, the potential and Helmholtz energy curves of NaCl, and to analyze the Helmholtz energy component and related properties of H 2 O and NH 4 + . Moreover, we utilize 3D-RISM-VQE to analyze the extent to which solvent effects alter the efficiency of quantum calculations compared with calculations in the gas phase using the L 1 -norms of molecular electronic Hamiltonians. Our results demonstrate that the efficiency of quantum chemical calculations on a quantum computer in solution is virtually the same as that in the gas phase.
Quantum chemical calculations on quantum computers have been focused mostly on simulating molecules in the gas phase. Molecules in liquid solution are, however, most relevant for chemistry. Continuum solvation models represent a good compromise between computational affordability and accuracy in describing solvation effects within a quantum chemical description of solute molecules. In this work, we extend the variational quantum eigensolver to simulate solvated systems using the polarizable continuum model. To account for the state dependent solute-solvent interaction we generalize the variational quantum eigensolver algorithm to treat non-linear molecular Hamiltonians. We show that including solvation effects does not impact the algorithmic efficiency. Numerical results of noiseless simulations for molecular systems with up to 12 spin-orbitals (qubits) are presented. Furthermore, calculations performed on a simulated noisy quantum hardware (IBM Q, Mumbai) yield computed solvation free energies in fair agreement with the classical calculations.
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Quantum chemistry applications on quantum computers currently rely heavily on the variational quantum eigensolver (VQE) algorithm. This hybrid quantum-classical algorithm aims at finding ground-state solutions of molecular systems based on the variational principle. VQE calculations can be systematically implemented for perturbations to each molecular degree of freedom, generating a Born-Oppenheimer potential-energy surface (PES) for the molecule. The PES can then be used to derive thermodynamic properties, which are often desirable for applications in chemical engineering and materials design. It is clear from this process that quantum chemistry applications contain a substantial classical computing component in addition to steps that can be performed using a quantum computer. In order to design efficient work flows that take full advantage of each hardware type, it is critical to consider the entire process so that the high-accuracy electronic energies possible from quantum computing are not squandered in the process of calculating thermodynamic properties. We present a summary of the hybrid quantum-classical work flow to compute thermodynamic properties. This work flow contains many options that can significantly affect the efficiency and the accuracy of the results, including classical optimizer attributes, number of ansatz repetitions, and how the vibrational Schr\"odinger equation is solved to determine vibrational modes. We also analyze the effects of these options by employing robust statistics along with simulations and experiments on actual quantum hardware. We show that, through careful selection of work flow options, nearly order-of-magnitude increases in accuracy are possible at equivalent computing time.
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Variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm designed for noisy intermediate-scale quantum (NISQ) computers. It is promising for quantum chemical calculations (QCC) because it can calculate the ground-state energy of a target molecule. Although VQE has a potential to achieve a higher accuracy than classical approximation methods in QCC, it is challenging to achieve it on current NISQ computers due to the significant impact of noises. Density matrix embedding theory (DMET) is a well-known technique to divide a molecule into multiple fragments, which is available to mitigate the noise impact on VQE. However, our preliminary evaluation shows that the naive combination of DMET and VQE does not outperform a gold standard classical method. In this work, we present three approaches to mitigate the noise impact for the DMET+VQE combination. (1) The size of quantum circuits used by VQE is decreased by reducing the number of bath orbitals which represent interactions between multiple fragments in DMET. (2) Reduced density matrices (RDMs), which are used to calculate a molecular energy in DMET, are calculated accurately based on expectation values obtained by executing quantum circuits using a noise-less quantum computer simulator. (3) The parameters of a quantum circuit optimized by VQE are refined with mathematical post-processing. The evaluation using a noisy quantum computer simulator shows that our approaches significantly improve the accuracy of the DMET+VQE combination. Moreover, we demonstrate that on a real NISQ device, the DMET+VQE combination applying our three approaches achieves a higher accuracy than the gold standard classical method.
Abstract Quantum computing leverages the quantum resources of superposition and entanglement to efficiently solve computational problems considered intractable for classical computers. Examples include calculating molecular and nuclear structure, simulating strongly interacting electron systems, and modeling aspects of material function. While substantial theoretical advances have been made in mapping these problems to quantum algorithms, there remains a large gap between the resource requirements for solving such problems and the capabilities of currently available quantum hardware. Bridging this gap will require a co-design approach, where the expression of algorithms is developed in conjunction with the hardware itself to optimize execution. Here we describe an extensible co-design framework for solving chemistry problems on a trapped-ion quantum computer and apply it to estimating the ground-state energy of the water molecule using the variational quantum eigensolver (VQE) method. The controllability of the trapped-ion quantum computer enables robust energy estimates using the prepared VQE ansatz states. The systematic and statistical errors are comparable to the chemical accuracy, which is the target threshold necessary for predicting the rates of chemical reaction dynamics, without resorting to any error mitigation techniques based on Richardson extrapolation.