Qubit coupled-cluster method: A systematic approach to quantum chemistry on a quantum computer

TL;DR

This paper introduces the qubit coupled-cluster (QCC) method, a systematic approach for quantum chemistry on quantum computers that efficiently uses two-qubit gates to accurately compute molecular ground states.

Contribution

The paper presents a novel QCC method with a factorization technique that limits entanglement to two-qubit gates, improving efficiency and scalability in quantum chemistry calculations.

Findings

Achieved chemical accuracy in H₂ and LiH ground-state energies.

Provided an exact factorization of multi-qubit rotations into two-qubit operations.

Demonstrated efficient resource use in quantum simulations of molecules.

Abstract

A unitary coupled-cluster (UCC) form for the wavefunction in the variational quantum eigensolver has been suggested as a systematic way to go beyond the mean-field approximation and include electron correlation in solving quantum chemistry problems on a quantum computer. Although being exact in the limit of including all possible coupled-cluster excitations, practically, the accuracy of this approach depends on how many and what kind of terms are included in the wavefunction parametrization. Another difficulty of UCC is a growth of the number of simultaneously entangled qubits even at the fixed fermionic excitation rank. Not all quantum computing architectures can cope with this growth. To address both problems we introduce a qubit coupled-cluster (QCC) method that starts directly in the qubit space and uses energy response estimates for ranking the importance of individual entanglers for the variational energy minimization. Also, we provide an exact factorization of a unitary rotation of more than two qubits to a product of two-qubit unitary rotations. Thus, the QCC method with the factorization technique can be limited to only two-qubit entanglement gates and allows for very efficient use of quantum resources in terms of the number of coupled-cluster operators. The method performance is illustrated by calculating ground-state potential energy curves of H$_2$ and LiH molecules with chemical accuracy, $\le 1$ kcal/mol.