Quantum algorithms for electronic structure and continuum models in electrochemistry

Abstract

Classical algorithms that simulate the electronic and vibrational structure of atoms and molecules are severely restricted by the exponential growth in computational resources that are required to accommodate large chemical problems. In contrast, the quantum mechanical foundations of quantum processors provide a novel framework by which the correspondence between chemical orbitals and physical qubits can be exploited to develop quantum algorithms that may surpass their classical counterparts and tackle demanding problems that would be otherwise impossible to solve [1]. In our quest towards a multi-scale simulation toolbox of quantum algorithms for the simulation of fundamental processes in Electrochemistry and physics, we present and discuss electronic structure calculations of simple molecules performed on the IBM System One quantum computer and introduce a new quantum algorithm to solve Partial Differential Equations (PDEs) with non-linearities. The simulation of quantum systems constitutes today one of the most fruitful applications of quantum computing in the era of Noisy Intermediate-Scale Quantum (NISQ) computers. Nonetheless, other dynamical systems that are not necessarily governed by the laws of quantum mechanics remain a fundamental challenge. Several approaches have emerged regarding the integration of arbitrary Partial Differential Equations (PDEs) on quantum computers [2]. A method based on the Feynmann-Kitaev formalism of quantum dynamics, where the full evolution of the system can be retrieved after a single optimization routine of an appropriate cost function has been recently put forth [3]. This spacetime formulation alleviates the accumulation of errors, but its application is restricted to quantum systems only. In this work, we introduce an extension of the Feynman-Kitaev formalism that is tailored to the integration of arbitrary PDEs with non-linearities and provide proof-of-principle calculations that demonstrate that fundamental processes such as diffusion and turbulence can be well-reproduced within this framework.

[1] Cao, Y., Romero, J., Olson, J. P., Degroote, M., Johnson, P. D., Kieferová, M., Kivlichan, I. D., Menke, T., Peropadre, B., Sawaya, N. P. D., Sim, S., Veis, L., & Aspuru-Guzik, A. (2019). Quantum Chemistry in the Age of Quantum Computing. Chemical Reviews, 119, 10856-10915. [2] Lubasch, M., Joo, J., Moinier, P., Kiffner, M., & Jaksch, D., Variational quantum algorithms for nonlinear problems. Physical Review A, 101, 010301(R) (2020). [3] S. Barison, F. Vicentini, I. Cirac, and G. Carleo, “Variational dynamics as a ground-state problem on a quantum computer,” arXiv preprint arXiv:2204.03454, 2022.