2020/12/13 by Jie Liu, Zhenyu Li, Jinlong Yang
Computer Science · Physics and Astronomy · #Benchmark (surveying) #Density matrix #Mechanical and Optical Resonators #Operator (biology) #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum algorithm #Quantum computer #Scheme (mathematics) #Solver #quant-ph
paper · pdf · doi:10.1063/5.0054822
27 pages and 5 figures
arxiv created 2020/12/13 · openalex created_date 2020/12/21 · openalex publication_date 2021/06/28 · arxiv updated 2021/07/28 · openalex updated_date 2026/08/05
Recently, adaptive variational quantum algorithms, e.g., Adaptive Derivative-Assembled Pseudo-Trotter-Variational Quantum Eigensolver (ADAPT-VQE) and Iterative Qubit-Excitation Based-Variational Quantum Eigensolver (IQEB-VQE), have been proposed to optimize the circuit depth, while a huge number of additional measurements make these algorithms highly inefficient. In this work, we reformulate the ADAPT-VQE with reduced density matrices (RDMs) to avoid additional measurement overhead. With Valdemoro's reconstruction of the three-electron RDM, we present a revised ADAPT-VQE algorithm, termed ADAPT-V, without any additional measurements but at the cost of increasing variational parameters compared to the ADAPT-VQE. Furthermore, we present an ADAPT-Vx algorithm by prescreening the anti-Hermitian operator pool with this RDM-based scheme. ADAPT-Vx requires almost the same variational parameters as ADAPT-VQE but a significantly reduced number of gradient evaluations. Numerical benchmark calculations for small molecules demonstrate that ADAPT-V and ADAPT-Vx provide an accurate description of the ground- and excited-state potential energy curves. In addition, to minimize the quantum resource demand, we generalize this RDM-based scheme to circuit-efficient IQEB-VQE algorithm and achieve significant measurement reduction.