Variational quantum eigenvalue solver algorithm utilizing bridge-inspired quantum circuits and a gradient filter module.

• The variational quantum eigensolver based on the bridge-inspired quantum circuits and gradient filter module (BG-VQE) is proposed to calculate the molecular ground state energy. • The bridge-inspired quantum circuits effectively reduces quantum gates and circuit depth overhead while preserving the representational capacity of the original quantum circuits. • The strategy of clustering and reordering the Pauli Hamiltonians to save quantum resources is transferable and versatile. • The gradient filter module is proposed to eliminate ineffective variational parameters to reduce the complexity of classical optimization. The complexity of theoretical simulation for drug molecule synthesis increases exponentially with the growth in system dimensions, posing a challenging task for precise solutions. Currently, the quantum algorithm capable of accurately simulating chemical molecule properties in the era of Noisy Intermediate-Scale Quantum (NISQ) devices is the Variational Quantum Eigensolver (VQE) algorithm. This paper introduces a variational quantum eigensolver based on the bridge-inspired quantum circuits and gradient filter module (BG), using Unitary Coupled Cluster Singles and Doubles (UCCSD) as the foundation (BG-VQE). The primary contributions are as follows: (1) The design of bridge rules among Hamiltonian quantum terms and rules for reordering Hamiltonian quantum terms based on similarity. By constructing a B-UCCSD ansatz according to the bridge rules and the new Hamiltonian pool, the quantum gate count and circuit depth are reduced without compromising the representative capacity of the original UCCSD ansatz; (2) The design of a variational parameter filtering module based on gradient values, which efficiently eliminates ineffective variational parameters based on their gradients. This reduction in the parameter counts of the B-UCCSD ansatz, at the cost of minimal precision loss, accelerates the calculation. Furthermore, we validate the transferability of the strategies proposed in this paper by empowering ADAPT-VQE with the BG strategy. Experimental calculations of ground state energies for H2, H3, H4, and H6 molecules were conducted using BG-VQE. By comparing the results with the UCCSD-VQE, ADAPT-VQE and BG-ADAPT-VQE, the effectiveness and superiority of BG-VQE are demonstrated. Furthermore, by performing BG-VQE calculations with different Trotter decomposition slice numbers, we demonstrate the feasibility of BG-VQE in computing the ground-state energies of HeH+, BeH 2 , and H 2 O molecules. The proposed approach won the championship in the Quantum Biochemical Engineering track of the 2nd CCF Origin Pilot Cup Quantum Computing Challenge in the professional group. [ABSTRACT FROM AUTHOR]