Leveraging small scale quantum computers with unitarily downfolded Hamiltonians

TL;DR

This paper introduces a quantum unitary downfolding method called QDSRG, enabling the use of small quantum computers for complex chemical calculations by reducing problem size and avoiding exponential classical scaling.

Contribution

The paper presents a novel classical-quantum hybrid formalism, QDSRG, that simplifies quantum chemistry problems for near-term quantum devices, avoiding costly density matrix evaluations.

Findings

QDSRG accurately models challenging chemical systems.

Demonstrated quantum computations on IBM devices for H2 dissociation and isomerization.

Reduced problem complexity from hundreds of qubits to a single qubit.

Abstract

In this work, we propose a quantum unitary downfolding formalism based on the driven similarity renormalization group (QDSRG) that may be combined with quantum algorithms for both noisy and fault-tolerant hardware. The QDSRG is a classical polynomially-scaling downfolding method that avoids the evaluation of costly three- and higher-body reduced density matrices while retaining the accuracy of classical multireference many-body theories. We calibrate and test the QDSRG on several challenging chemical problems and propose a strategy for avoiding classical exponential-scaling steps in the QDSRG scheme. We report QDSRG computations of two chemical systems using the variational quantum eigensolver on IBM quantum devices: i) the dissociation curve of H$_2$ using a quintuple-$\zeta$ basis and ii) the bicyclobutane isomerization reaction to $trans$-butadiene, demonstrating the reduction of problems that require several hundred qubits to a single qubit. Our work shows that the QDSRG is a viable approach to leverage near-term quantum devices for the accurate estimation of molecular properties.