Quantum computing quantum Monte Carlo with hybrid tensor network for electronic structure calculations

Quantum computers are expected to solve quantum chemistry problems with higher accuracy than classical computers. Quantum computing quantum Monte Carlo (QC-QMC) is an algorithm that can be combined with quantum algorithms such as variational quantum eigenvalue solver (VQE) to obtain ground states with higher accuracy than VQE or QMC alone. In this presentation, we propose an algorithm that combines QC-QMC with a hybrid tensor network (HTN) to extend the applicability of QC-QMC to systems beyond the size of a single quantum device, which is called HTN+QMC. In the case of HTN with a two-layer quantum-quantum tree tensor, HTN+QMC for O(n²) qubit trial wave functions is executable only for n-qubit devices excluding an ancilla qubit. The algorithm was evaluated in the Heisenberg chain model, graphite-based Hubbard model, hydrogen plane model, and MonoArylBiImidazole. The full configuration interaction QMC was employed as the QMC method. The results show that this algorithm can achieve several orders of magnitude higher energy accuracy than VQE and QMC, and HTN+QMC gives the same energy accuracy as QC-QMC if the system is appropriately decomposed. Furthermore, we developed a pseudo-Hadamard test technique that can efficiently perform overlap calculations between the trial wavefunction and the standard basis state. Real device experiments using this technique show that the accuracy is almost the same as that of the statevector simulator, demonstrating the noise robustness of HTN+QMC. These results pave the way to highly accurate electronic state calculations of large systems using current quantum devices.