  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.
