Non-iterative disentangled unitary coupled-cluster based on lie-algebraic structure

Abstract

Due to their non-iterative nature, fixed unitary coupled cluster (UCC) ansätze are attractive for performing quantum chemistry variational quantum eigensolver (VQE) computations as they avoid pre-circuit measurements on a quantum computer. However, achieving chemical accuracy for strongly correlated systems with UCC requires further inclusion of higher-order fermionic excitations beyond triples increasing circuit depth. We introduce k-non-iterative disentangled unitary coupled cluster (NI-DUCC), a fixed and non-iterative disentangled UCC compact ansatz, based on specific ‘k’ sets of ‘qubit’ excitations, eliminating the needs for fermionic-type excitations. These elements scale linearly ( O(n)) by leveraging Lie algebraic structures, with n being the number of qubits. The key excitations are screened through specific selection criteria, including the enforcement of all symmetries, to ensure the construction of a robust set of generators. NI-DUCC employs ‘k’ products of the exponential of O(n)- anti-Hermitian Pauli operators, where each single Pauli string has a length p. This results in a fewer two-qubit CNOT gates circuit scaling, O(knp), suitable for hardware implementations. Tested on LiH, H6 and BeH2, NI-DUCC-VQE achieves both chemical accuracy and rapid convergence even for molecules deviating significantly from equilibrium. It is hardware-efficient, reaching the exact full configuration interaction energy solution at specific layers, while reducing significantly the VQE optimization steps. NI-DUCC-VQE effectively addresses the gradient measurement bottleneck of ADAPT-VQE-like iterative algorithms, yet the classical computational cost of constructing the O(n) set of excitations increases exponentially with the number of qubits. We provide a first implementation for constructing the generators’ set, able to handle up to 20 qubits and discuss the efficiency perspectives.