The simulation of many-body open quantum systems is key to solving numerous outstanding problems in physics, chemistry, material science, and in the development of quantum technologies. Near-term quantum computers may bring considerable advantage for the efficient simulation of their static and dynamical properties, thanks to hybrid quantum-classical variational algorithms to approximate the dynamics of the density matrix describing the quantum state in terms of an ensemble average. Here, a variational quantum algorithm is developed to simulate the real-time evolution of the density matrix governed by the Lindblad master equation, under the assumption that the quantum state has a bounded entropy along the dynamics, entailing a low-rank representation of its density matrix. The algorithm encodes each pure state of the statistical mixture as a parametrized quantum circuit, and the associated probabilities as additional variational parameters stored classically, thereby requiring a significantly lower number of qubits than algorithms where the full density matrix is encoded in the quantum memory. Two variational Ansätze are proposed, and their effectiveness is assessed in the simulation of the dynamics of a 2D dissipative transverse field Ising model. The results underscore the algorithm's efficiency in simulating the dynamics of open quantum systems in the low-rank regime with limited quantum resources on a near-term quantum device.
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。
Neural Network Backflow with Low-Rank Multi-Determinant Updates
Yale University（耶鲁大学）；Energy Sciences Institute, Yale University（耶鲁大学能源科学研究所）；Department of Applied Physics, Yale University（耶鲁大学应用物理系）；Department of Physics, Yale University（耶鲁大学物理系）
Pre-training Tensor-Train Networks Facilitates Machine Learning with Variational Quantum Circuits
Georgia Institute of Technology（佐治亚理工学院）；NVIDIA Research（NVIDIA研究）；IBM Research（IBM研究）；Hon Hai (Foxconn) Quantum Computing Research Center（鸿海（富士康）量子计算研究中心）
Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open quantum dynamics in structured thermal environments
A Longitudinal Analysis of the CEC Single-Objective Competitions (2010-2024) and Implications for Variational Quantum Optimization
VSB - Technical University of Ostrava（俄斯特拉发理工大学）；IT4Innovations National Supercomputing Center, VSB - Technical University of Ostrava（俄斯特拉发理工大学 IT4创新国家超级计算中心）；Klaipeda University（克莱佩达大学）；Technical University of Munich（慕尼黑工业大学）；Indian Statistical Institute（印度统计研究所）；Università dell’Aquila（阿奎拉大学）
Numerical Optimization Strategies for the Variational Hamiltonian Ansatz in Noisy Quantum Environments
Gran Sasso Science Institute（格兰萨索科学研究所）；VSB-Technical University of Ostrava（俄斯特拉发理工大学）；IT4Innovations National Supercomputing Center, VSB–Technical University of Ostrava（俄斯特拉发理工大学 IT4创新国家超算中心）；Technical University of Munich（慕尼黑工业大学）；Fraunhofer Institute for Chemical Technology ICT（弗劳恩霍夫化学技术研究所）；Saarland University（萨尔兰大学）；University of L’Aquila（拉奎拉大学）
