Differentiable matrix product states for simulating variational quantum computational chemistry

TL;DR

This paper introduces a highly parallelizable classical simulator for variational quantum eigensolvers (VQE) using differentiable matrix product states, enabling efficient simulation of larger molecules and aiding near-term quantum algorithm development.

Contribution

It presents a novel differentiable matrix product state-based classical simulator for VQE that scales efficiently with qubits and parameters, improving simulation range and gradient computation.

Findings

Simulates molecules up to 40 qubits.

Efficient gradient computation similar to deep learning.

Extends the simulation range of VQE for quantum chemistry.

Abstract

Quantum Computing is believed to be the ultimate solution for quantum chemistry problems. Before the advent of large-scale, fully fault-tolerant quantum computers, the variational quantum eigensolver~(VQE) is a promising heuristic quantum algorithm to solve real world quantum chemistry problems on near-term noisy quantum computers. Here we propose a highly parallelizable classical simulator for VQE based on the matrix product state representation of quantum state, which significantly extend the simulation range of the existing simulators. Our simulator seamlessly integrates the quantum circuit evolution into the classical auto-differentiation framework, thus the gradients could be computed efficiently similar to the classical deep neural network, with a scaling that is independent of the number of variational parameters. As applications, we use our simulator to study commonly used small molecules such as HF, HCl, LiH and H$_2$O, as well as larger molecules CO$_2$, BeH$_2$ and H$_4$ with up to $40$ qubits. The favorable scaling of our simulator against the number of qubits and the number of parameters could make it an ideal testing ground for near-term quantum algorithms and a perfect benchmarking baseline for oncoming large scale VQE experiments on noisy quantum computers.