Article Dans Une Revue Quantum Science and Technology Année : 2025

Non-Iterative Disentangled Unitary Coupled-Cluster based on Lie-algebraic structure

Résumé

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-NI-DUCC, a fixed and Non-iterative Disentangled Unitary Coupled-Cluster 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 operator has a length p. This results in a fewer two-qubit CNOT gates circuit, 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. While NI-DUCC-VQE effectively addresses the gradient measurement bottleneck of ADAPT-VQE-like iterative algorithms, 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.

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Dates et versions

hal-04678082 , version 1 (20-07-2025)

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Mohammad Haidar, Olivier Adjoua, Siwar Badreddine, Alberto Peruzzo, Jean-Philip Piquemal. Non-Iterative Disentangled Unitary Coupled-Cluster based on Lie-algebraic structure. Quantum Science and Technology, 2025, 10, pp.025031. ⟨10.1088/2058-9565/adb3c5⟩. ⟨hal-04678082⟩
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