Parallel Quantum Chemistry on Noisy Intermediate-Scale Quantum Computers

TL;DR

This paper introduces a parallel hybrid quantum-classical algorithm leveraging reduced density-matrix functional theory to efficiently solve quantum-chemical ground-state energies on noisy intermediate-scale quantum computers, enabling larger molecule simulations.

Contribution

It presents a novel parallel algorithm based on RDMFT and adaptive cluster approximation, improving scalability and resource efficiency for quantum chemistry calculations on NISQ devices.

Findings

Successfully demonstrated on IBM quantum computers

Reduces qubit count and circuit depth

Enables treatment of larger molecules

Abstract

A novel parallel hybrid quantum-classical algorithm for the solution of the quantum-chemical ground-state energy problem on gate-based quantum computers is presented. This approach is based on the reduced density-matrix functional theory (RDMFT) formulation of the electronic structure problem. For that purpose, the density-matrix functional of the full system is decomposed into an indirectly coupled sum of density-matrix functionals for all its subsystems using the adaptive cluster approximation to RDMFT. The approximations involved in the decomposition and the adaptive cluster approximation itself can be systematically converged to the exact result. The solutions for the density-matrix functionals of the effective subsystems involves a constrained minimization over many-particle states that are approximated by parametrized trial states on the quantum computer similarly to the variational quantum eigensolver. The independence of the density-matrix functionals of the effective subsystems introduces a new level of parallelization and allows for the computational treatment of much larger molecules on a quantum computer with a given qubit count. In addition, for the proposed algorithm techniques are presented to reduce the qubit count, the number of quantum programs, as well as its depth. The new approach is demonstrated for Hubbard-like systems on IBM quantum computers based on superconducting transmon qubits.