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Quantum Computing is believed to be the ultimate solution for quantumchemistry problems. Before the advent of large-scale, fully fault-tolerantquantum computers, the variational quantum eigensolver~(VQE) is a promisingheuristic quantum algorithm to solve real world quantum chemistry problems onnear-term noisy quantum computers. Here we propose a highly parallelizableclassical simulator for VQE based on the matrix product state representation ofquantum state, which significantly extend the simulation range of the existingsimulators. Our simulator seamlessly integrates the quantum circuit evolutioninto the classical auto-differentiation framework, thus the gradients could becomputed efficiently similar to the classical deep neural network, with ascaling that is independent of the number of variational parameters. Asapplications, we use our simulator to study commonly used small molecules suchas HF, HCl, LiH and H$_2$O, as well as larger molecules CO$_2$, BeH$_2$ andH$_4$ with up to $40$ qubits. The favorable scaling of our simulator againstthe number of qubits and the number of parameters could make it an idealtesting ground for near-term quantum algorithms and a perfect benchmarkingbaseline for oncoming large scale VQE experiments on noisy quantum computers.

Differentiable matrix product states for simulating variational quantum computational chemistry