Journal Article

Efficient Application of the Factorized form of the Unitary Coupled-Cluster Ansatz for the Variational Quantum Eigensolver Algorithm by Using Linear Combination of Unitaries

Xu, Luogen, Freericks, James K.

2023

Overview

The variational quantum eigensolver is one of the most promising algorithms for near-term quantum computers. It has the potential to solve quantum chemistry problems involving strongly correlated electrons with relatively low-depth circuits, which are otherwise difficult to solve on classical computers. The variational eigenstate is constructed from a number of factorized unitary coupled-cluster terms applied onto an initial (single-reference) state. Current algorithms for applying one of these operators to a quantum state require a number of operations that scale exponentially with the rank of the operator. We exploit a hidden SU(2) symmetry to allow us to employ the linear combination of unitaries approach, Our Prepare subroutine uses n+2 ancilla qubits for a rank-n operator. Our Select(U^) scheme uses O(n)Cnot gates. This results in a full algorithm that scales like the cube of the rank of the operator n3, a significant reduction in complexity for rank five or higher operators. This approach, when combined with other algorithms for lower-rank operators (when compared to the standard implementation), will make the factorized form of the unitary coupled-cluster approach much more efficient to implement on all types of quantum computers.

• Publisher: MDPI AG,MDPI
• Subject: Algorithms / Approximation / Circuits / Clusters / Computational chemistry / Eigenvectors / Energy / factorized unitary coupled-cluster ansatz / Hilbert space / linear combination of unitaries / MATHEMATICS AND COMPUTING / Operators / Quantum chemistry / Quantum computers / Quantum computing / Qubits (quantum computing) / Science & Technology - Other Topics