Variational Quantum Imaginary Time Evolution for Matrix Product State Ansatz with Tests on Transcorrelated Hamiltonians

TL;DR

This paper introduces an improved variational quantum imaginary time evolution method for matrix product state ansatz, enabling efficient ground state simulations of molecular systems and transcorrelated Hamiltonians with fewer qubits on near-term quantum devices.

Contribution

It enhances the QCMPS approach with VarQITE, improving convergence and robustness, and demonstrates its effectiveness on small molecules and transcorrelated Hamiltonians with minimal qubits.

Findings

Improved convergence and robustness of QCMPS with VarQITE.

Successful simulation of molecules using only three qubits.

Energy estimates close to CBS limit with fewer qubits.

Abstract

The matrix product state (MPS) ansatz offers a promising approach for finding the ground state of molecular Hamiltonians and solving quantum chemistry problems. Building on this concept, the proposed technique of quantum circuit MPS (QCMPS) enables the simulation of chemical systems using a relatively small number of qubits. In this study, we enhance the optimization performance of the QCMPS ansatz by employing the variational quantum imaginary time evolution (VarQITE) approach. Guided by McLachlan's variational principle, the VarQITE method provides analytical metrics and gradients, resulting in improved convergence efficiency and robustness of the QCMPS. We validate these improvements numerically through simulations of $\rm H_2$, $\rm H_4$, and $\rm LiH$ molecules. Additionally, given that VarQITE is applicable to non-Hermitian Hamiltonians, we evaluate its effectiveness in preparing the ground state of transcorrelated (TC) Hamiltonians. This approach yields energy estimates comparable to the complete basis set (CBS) limit while using even fewer qubits. Specifically, we perform simulations of the beryllium atom and $\rm LiH$ molecule using only three qubits, maintaining high fidelity with the CBS ground state energy of these systems. This qubit reduction is achieved through the combined advantages of both the QCMPS ansatz and transcorrelation. Our findings demonstrate the potential practicality of this quantum chemistry algorithm on near-term quantum devices.