  The wave function Ansatze are crucial in the context of the Variational
Quantum Eigensolver (VQE). In the Noisy Intermediate-Scale Quantum era, the
design of low-depth wave function Ansatze is of great importance for executing
quantum simulations of electronic structure on noisy quantum devices. In this
work, we present a circuit-efficient implementation of two-body
Qubit-Excitation-Based (QEB) operator for building shallow-circuit wave
function Ansatze within the framework of Adaptive Derivative-Assembled
Pseudo-Trotter (ADAPT) VQE. This new algorithm is applied to study ground- and
excited-sate problems for small molecules, demonstrating significant reduction
of circuit depths compared to fermionic excitation-based and QEB ADAPT-VQE
algorithms. This circuit-efficient algorithm shows great promise for quantum
simulations of electronic structures, leading to improved performance on
current quantum hardware.
