Size‐consistency and orbital‐invariance issues revealed by VQE‐UCCSD calculations with the FMO scheme

• Published in: Journal of computational chemistry 2024-10, Vol.45 (26), p.2204-2213
• Main Authors: Sugisaki, Kenji, Nakano, Tatsuya, Mochizuki, Yuji
• Format: Article
• Language: English
• Subjects: fragment molecular orbital; GPU; Invariance; Molecular orbitals; Quantum chemistry; Quantum computers; Qubits (quantum computing); Trotter error; UCC; variational quantum eigensolver
• ISSN: 0192-8651; 1096-987X; 1096-987X
• DOI: 10.1002/jcc.27438

The fragment molecular orbital (FMO) scheme is one of the popular fragmentation‐based methods and has the potential advantage of making the circuit shallow for quantum chemical calculations on quantum computers. In this study, we used a GPU‐accelerated quantum simulator (cuQuantum) to perform the electron correlation part of the FMO calculation as unitary coupled‐cluster singles and doubles (UCCSD) with the variational quantum eigensolver (VQE) for hydrogen‐bonded (FH) 3 and (FH) 2‐H 2O systems with the STO‐3G basis set. VQE‐UCCSD calculations were performed using both canonical and localized MO sets, and the results were examined from the point of view of size‐consistency and orbital‐invariance affected by the Trotter error. It was found that the use of localized MO leads to better results, especially for (FH) 2‐H 2O. The GPU acceleration was substantial for the simulations with larger numbers of qubits, and was about a factor of 6.7–7.7 for 18 qubit systems. Hydrogen‐bonded (FH) 3 and (FH) 2‐H 2O systems were used for the FMO‐based VQ‐UCCSD calculations with the STO‐3G basis set. The correlation energies obtained with canonical and localized MO sets were examined from the view point of size‐consistency and orbital‐invariance affected by Trotter error. It was found that the use of localized MO leads to better results, especially for (FH) 2‐H 2O.