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

Abstract

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.

32 pages, 24 figures, 3 tables

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• Fault-tolerant quantum algorithms for quantum molecular systems: A survey
• Evaluating a quantum-classical quantum Monte Carlo algorithm with Matchgate shadows
• Unbiasing Fermionic Auxiliary-Field Quantum Monte Carlo with Matrix Product State Trial Wavefunctions
• Hybrid Tree Tensor Networks for quantum simulation
• Tensor-based quantum phase difference estimation for large-scale demonstration
• A quantum computing approach to fixed-node Monte Carlo using classical shadows
• Density matrix representation of hybrid tensor networks for noisy quantum devices
• Enhancing quantum computations with the synergy of auxiliary field quantum Monte Carlo and computational basis tomography
• A penalty-free quantum algorithm to find energy eigenstates