  Recently, an adaptive variational algorithm termed Adaptive
Derivative-Assembled Pseudo-Trotter ansatz Variational Quantum Eigensolver
(ADAPT-VQE) has been proposed by Grimsley et al. (Nat. Commun. 10, 3007) while
the number of measurements required to perform this algorithm scales O(N^8). In
this work, we present an efficient adaptive variational quantum solver of the
Schrodinger equation based on ADAPT-VQE together with the reduced density
matrix reconstruction approach, which reduces the number of measurements from
O(N^8) to O(N^4). This new algorithm is quite suitable for quantum simulations
of chemical systems on near-term noisy intermediate-scale hardware due to low
circuit complexity and reduced measurement. Numerical benchmark calculations
for small molecules demonstrate that this new algorithm provides an accurate
description of the ground-state potential energy curves. In addition, we
generalize this new algorithm for excited states with the variational quantum
deflation approach and achieve the same accuracy as ground-state simulations.
