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

Abstract

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)${\hspace{0.17em}}_3$ and (FH)${\hspace{0.17em}}_2$-H${\hspace{0.17em}}_2$O 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)${\hspace{0.17em}}_2$-H${\hspace{0.17em}}_2$O. 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.