  Quantum computers have a potential for solving quantum chemistry problems
with higher accuracy than classical computers. Quantum computing quantum Monte
Carlo (QC-QMC) is a QMC with a trial state prepared in quantum circuit, which
is employed to obtain the ground state with higher accuracy than QMC alone. We
propose an algorithm combining QC-QMC with a hybrid tensor network to extend
the applicability of QC-QMC beyond a single quantum device size. In a two-layer
quantum-quantum tree tensor, our algorithm for the larger trial wave function
can be executed than preparable wave function in a device. Our algorithm is
evaluated on the Heisenberg chain model, graphite-based Hubbard model, hydrogen
plane model, and MonoArylBiImidazole using full configuration interaction QMC.
Our algorithm can achieve energy accuracy (specifically, variance) several
orders of magnitude higher than QMC, and the hybrid tensor version of QMC gives
the same energy accuracy as QC-QMC when the system is appropriately decomposed.
Moreover, we develop a pseudo-Hadamard test technique that enables efficient
overlap calculations between a trial wave function and an orthonormal basis
state. In a real device experiment by using the technique, we obtained almost
the same accuracy as the statevector simulator, indicating the noise robustness
of our algorithm. These results suggests that the present approach will pave
the way to electronic structure calculation for large systems with high
accuracy on current quantum devices.
