Authors: Mohammad Haidar | Olivier Adjoua | Siwar Baddredine | Alberto Peruzzo | Jean‐Philip Piquemal
Source: Quantum Science and Technology (preprint, 2025-02-07)
Field: Chemistry — Spectroscopy

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 ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">O</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> ) 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">O</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> - anti-Hermitian Pauli operators, where each single Pauli string has a length p . This results in a fewer two-qubit CNOT gates circuit scaling, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">O</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>k</mml:mi> <mml:mi>n</mml:mi> <mml:mi>p</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> , suitable for hardware implementations. Tested on LiH, H 6 and BeH 2 , 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">O</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> 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. Coupled cluster ; Quantum computer ; Controlled NOT gate ; Quantum circuit ; Qubit ; Bethe ansatz ; Quantum ; Mathematics ; Chemistry ; Quantum mechanics ; Quantum gate ; Topology (electrical circuits) ; Discrete mathematics ; Physics ; Quantum network ; Combinatorics ; Molecule Molecular spectroscopy and chirality ; Quantum Information and Cryptography ; Atomic and Subatomic Physics Research