Adapting the Harrow-Hassidim-Lloyd algorithm to quantum many-body theory

Abstract

Rapid progress in developing near- and long-term quantum algorithms for quantum chemistry has provided us with an impetus to move beyond traditional approaches and explore new ways to apply quantum computing to electronic structure calculations. In this work, we identify the connection between quantum many-body theory and a quantum linear solver, and implement the Harrow-Hassidim-Lloyd (HHL) algorithm to make precise predictions of correlation energies for light molecular systems via the (nonunitary) linearized coupled cluster theory, where the term “light molecular systems” refers to those molecules whose constituent atoms have low atomic number. For the purposes of practical computations, we make suitable changes to the HHL framework. This entails two aspects: (1) Adapt, prescribing a novel scaling approach that allows one to scale any arbitrary Hermitian matrix, A, that in turn dictates the controlled-rotation angles without having to precompute the eigenvalues of A, and yet achieve a reasonably high precision in |x〉, and (2) Lite, for which we devise techniques that reduce the depth of the relevant quantum circuit. In this context, we introduce the following variants of HHL for different eras of quantum computing: AdaptHHLite in its appropriate forms for noisy intermediate-scale quantum (NISQ), late-NISQ, and the early fault-tolerant eras, as well as AdaptHHL for the fault-tolerant quantum computing era. We demonstrate the ability of the NISQ variant of AdaptHHLite to capture correlation energy precisely, while simultaneously being resource lean, using simulation as well as the 11-qubit IonQ quantum hardware.