Determination of molecular energetics and properties is one of the core challenges in the near-term quantum computing. To this end, hybrid quantum-classical algorithms are preferred for Noisy Intermediate Scale Quantum (NISQ) architectures. The Projective Quantum Eigensolver (PQE) is one such algorithms that optimizes the parameters of the chemistry-inspired unitary coupled cluster (UCC) ansatz using a conventional coupled cluster-like residual minimization. Such a strategy involves the projection of the Schrodinger equation on to linearly independent basis towards the parameter optimization, restricting the ansatz is solely defined in terms of the excitation operators. This warrants the inclusion of high-rank operators for strongly correlated systems, leading to increased utilization of quantum resources. In this manuscript, we develop a methodology for determining the generalized operators in terms of a closed form residual equations in the PQE framework that can be efficiently implemented in a quantum computer with manageable quantum resources. Such a strategy requires the removal of the underlying redundancy in high-rank excited determinants, generated due to the presence of the generalized operators in the ansatz, by projecting them on to an internally contracted lower dimensional manifold. With the application on several molecular systems, we have demonstrated our ansatz achieves similar accuracy to the (disentangled) UCC with singles, doubles and triples (SDT) ansatz, while utilizing an order of magnitude fewer quantum gates. Furthermore, when simulated under stochastic Gaussian noise or depolarizing hardware noise, our method shows significantly improved noise resilience compared to the other members of PQE family and the state-of-the-art variational quantum eigensolver.
Projective Quantum Eigensolver via Adiabatically Decoupled Subsystem Evolution: a Resource Efficient Approach to Molecular Energetics in Noisy Quantum Computers
Optimizing Unitary Coupled Cluster Wave Functions on Quantum Hardware: Error Bound and Resource-Efficient Optimizer
Eviden Quantum Lab（Eviden量子实验室）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；École Polytechnique, I.P. Paris（巴黎理工学院高等师范学校）；MajuLab, CNRS–UCA-SU-NUS-NTU International Joint Research Laboratory（MajuLab，CNRS-南法大学-苏黎世联邦理工学院-新加坡国立大学-南洋理工大学国际联合研究实验室）
Bayesian Parameter Shift Rule in Variational Quantum Eigensolvers
BIFOLD；Technische Universität Berlin（柏林工业大学）；Università degli Studi di Padova（帕多瓦大学）；RIKEN Center for AIP（理化学研究所先进智能项目中心）；University of Bonn（波恩大学）；Helmholtz Institute for Radiation and Nuclear Physics（亥姆霍兹辐射与核物理研究所）；Deutsches Elektronen-Synchrotron（德国电子同步加速器研究所）；The Cyprus Institute（塞浦路斯研究所）；Oldendorff Carriers GmbH & Co. KG（奥滕多夫航运有限公司）
