Variational quantum imaginary time evolution for matrix product state Ansatz with tests on transcorrelated...

Area of Science:

• Quantum chemistry
• Computational physics
• Quantum computing algorithms

Background:

• Matrix Product State (MPS) Ansatz is a powerful tool for molecular Hamiltonian ground state calculations.
• Quantum Circuit MPS (QCMPS) offers a method for simulating chemical systems with reduced qubit requirements.

Purpose of the Study:

• To improve the optimization performance and robustness of the QCMPS Ansatz.
• To explore the application of VarQITE for enhancing QCMPS in quantum chemistry.
• To assess the effectiveness of QCMPS with VarQITE for non-Hermitian and transcorrelated Hamiltonians.

Main Methods:

• Employed variational quantum imaginary time evolution (VarQITE) to optimize the QCMPS Ansatz.
• Utilized McLachlan's variational principle to derive analytical metrics and gradients for VarQITE.
• Performed numerical simulations for H2, H4, and LiH molecules.
• Evaluated VarQITE's effectiveness on transcorrelated Hamiltonians for ground state preparation.

Main Results:

• VarQITE significantly improved the convergence efficiency and robustness of QCMPS.
• Simulations of H2, H4, and LiH molecules validated the enhanced QCMPS performance.
• Ground state energy estimates for transcorrelated Hamiltonians achieved accuracy comparable to the Complete Basis Set (CBS) limit.
• Demonstrated high-fidelity ground state energy calculations for beryllium atom and LiH molecule using only three qubits.

Conclusions:

• The combination of QCMPS and VarQITE offers a practical quantum chemistry algorithm for near-term quantum devices.
• Significant qubit reduction is achievable through QCMPS and transcorrelation, maintaining high accuracy.
• The VarQITE approach enhances the feasibility of quantum simulations for complex chemical systems.