Implementing time-evolution operators in shallow quantum circuits is important for quantum simulations. The standard method of Trotterization requires a large number of gates to achieve practical accuracy. Variational Quantum Simulation (VQS) is an algorithm that calculates the time evolution of a quantum state and can be executed with shallower circuits than Trotterization. However, the operator obtained by VQS evolves only a fixed initial state and is not the time evolution operator itself. In this paper, we propose Variational Quantum Operator Simulation (VQOS), a method to realize time evolution operators in shallow quantum circuits. This method is based on the variational principle for operators and does not require the implementation of the desired Trotter decomposition of the time evolution operator. We performed numerical simulations of the VQOS algorithm and successfully implemented the time evolution operator for closed systems in a quantum circuit that is up to 5 times shallower than the Trotterization. By providing a more practical way to implement time evolution operators, VQOS increases the applicability of near-term quantum computers.
Efficient Operator Selection and Warm-Start Strategy for Excitations in Variational Quantum Eigensolvers
ICAMS, Ruhr University Bochum（鲁尔大学波鸿校区计算物理与材料科学研究所）；German Aerospace Center (DLR), Institute for Frontier Materials on Earth and in Space（德国航空航天中心前沿地球与空间材料研究所）
A Variational Framework for Time-Dependent Quantum Systems with Applications to Floquet Hamiltonians
Memorial University of Newfoundland and Labrador（纽芬兰与拉布拉多纪念大学）；National Research Council Canada（加拿大国家研究委员会）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；University of Waterloo（滑铁卢大学）；Compute Everything Technologies Ltd.（Compute Everything科技有限公司）
Efficient application of the factorized form of the unitary coupled-cluster ansatz for the variational quantum eigensolver algorithm by using linear combination of unitaries
针对变分量子本征求解器中分解 UCC 算符实现复杂度高的问题，本文利用隐藏 SU(2) 对称性和酉线性组合，将秩 n 算符的整体复杂度降至 n³。
Quantum machine learning for the quantum lattice Boltzmann method: Trainability of variational quantum circuits for the nonlinear collision operator across multiple time steps
Aix-Marseille University（艾克斯-马赛大学）；Quanscient Oy（Quanscient公司）；Faculty of Technical Sciences, University of Novi Sad（诺维萨德大学技术科学学院）；CNRS（法国国家科学研究中心）；M2P2 Laboratory（M2P2实验室）；Lappeenranta–Lahti University of Technology（拉彭兰塔-拉赫蒂理工大学）
Variational Real-Time Dynamics on Reduced Operator Manifolds
IQM Quantum Computers（IQM量子计算机）；Technical University of Munich, CIT, Department of Computer Science（慕尼黑工业大学计算与工程学院计算机科学系）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；CNRS, Laboratoire de Physique Théorique de la Matière Condensée, Sorbonne Université（法国国家科学研究中心凝聚态物质理论物理实验室索邦大学）
State Specific Measurement Protocols for the Variational Quantum Eigensolver
Institute for Computer Science, University of Augsburg（奥格斯堡大学计算机科学研究所）；Center for Advanced Analytics and Predictive Sciences, University of Augsburg（奥格斯堡大学高级分析与预测科学中心）
