Noise-Mitigated Variational Quantum Eigensolver with Pre-training and Zero-Noise Extrapolation

TL;DR

This paper introduces a noise-mitigating variational quantum eigensolver that combines pre-training, zero-noise extrapolation, and efficient measurement strategies to accurately compute molecular ground states on noisy quantum hardware.

Contribution

It presents a novel hybrid quantum-classical algorithm that integrates matrix product state-based pre-training, zero-noise extrapolation with neural networks, and an intelligent measurement grouping strategy.

Findings

Successfully constrained noise errors within 10^{-2} to 10^{-1} range.

Outperformed mainstream variational quantum eigensolvers in simulations.

Demonstrated effectiveness on the H_4 molecule using MindSpore Quantum framework.

Abstract

As a hybrid quantum-classical algorithm, the variational quantum eigensolver is widely applied in quantum chemistry simulations, especially in computing the electronic structure of complex molecular systems. However, on existing noisy intermediate-scale quantum devices, some factors such as quantum decoherence, measurement errors, and gate operation imprecisions are unavoidable. To overcome these challenges, this study proposes an efficient noise-mitigating variational quantum eigensolver for accurate computation of molecular ground state energies in noisy environments. We design the quantum circuit with reference to the structure of matrix product states and utilize it to pre-train the circuit parameters, which ensures circuit stability and mitigates fluctuations caused by initialization. We also employ zero-noise extrapolation to mitigate quantum noise and combine it with neural networks to improve the accuracy of the noise-fitting function, which significantly eliminates noise interference. Furthermore, we implement an intelligent grouping strategy for measuring Hamiltonian Pauli strings, which not only reduces measurement errors but also improves sampling efficiency. We perform numerical simulations to solve the ground state energy of the $H_4$ molecule by using MindSpore Quantum framework, and the results demonstrate that our algorithm can constrain noise errors within the range of $\mathcal{O}(10^{-2}) \sim \mathcal{O}(10^{-1})$, outperforming mainstream variational quantum eigensolvers. This work provides a new strategy for high-precision quantum chemistry calculations on near-term noisy quantum hardware. The updated code is available at https://gitee.com/mindspore/mindquantum/tree/research/paper_with_code/eigensolver_with_mps_and_ZNE or https://github.com/mindspore-lab/models/tree/master/research/arxiv_papers/MPS_eigensolver_with_ZNE.