Bootstrap Embedding on a Quantum Computer

Abstract

We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian governing fragments of the total system, in such a way that fragment solutions can harness the capabilities of quantum computers. By employing state-of-art quantum subroutines including the quantum SWAP test and quantum amplitude amplification, we show how a quadratic speedup can be obtained over the classical algorithm, in principle. Utilization of quantum computation also allows the algorithm to match�at little additional computational cost�full density matrices at fragment boundaries, instead of being limited to 1-RDMs. Current quantum computers are small, but quantum bootstrap embedding provides a potentially generalizable strategy for harnessing such small machines through quantum fragment matching.

Tailored and Externally Corrected Coupled Cluster with Quantum Inputs

“…To date, there exist several approaches to include dynamic correlation effects in quantum simulations of chemistry, e.g., virtual quantum subspace expansion (VQSE), second-order perturbation theory using the variational quantum eigensolver (VQE) ,, together with quantum subspace expansion (QSE), named NEVPT2­(VQE,QSE), nonorthogonal configuration interaction approaches, and NEVPT2 based on qubit reduced density matrices (RDMs), named QRDM-NEVPT2 . We note that a plethora of other methods for studies of chemical systems exists, e.g., based on embedding techniques. − The QRDM-NEVPT2 method, in addition to VQE state preparation and optimization, requires quantum evaluation of the three-particle reduced density matrix (3RDM) and four-particle RDM-like terms, exploiting a cumulant approximation. For quantum active space (AS) methods, it is already quite resource-intense with respect to the required number of measurement repetitions, so-called shots, to accurately determine the 2RDM for energy evaluation.…”