Recent quantum algorithms pertaining to electronic structure theory primarily focus on threshold-based dynamic construction of ansatz by selectively including important many-body operators. These methods can be made systematically more accurate by tuning the threshold to include more number of operators into the ansatz. However, such improvements come at the cost of rapid proliferation of the circuit depth, especially for highly correlated molecular systems. In this work, we address this issue by the development of a novel theoretical framework that relies on the segregation of an ansatz into a dynamically selected core principal component, which is, by construction adiabatically decoupled from the remaining operators. This enables us to perform computations involving the principal component using extremely shallow-depth circuits whereas, the effect of the remaining auxiliary component is folded into the energy function via a cost-efficient non-iterative correction, ensuring the requisite accuracy. We propose a formalism that analytically predicts the auxiliary parameters from the principal ones, followed by a suite of non-iterative auxiliary subspace correction techniques with different levels of sophistication. The auxiliary subspace corrections incur no additional quantum resources, yet complement an inadequately expressive core of the ansatz to recover significant amount of electronic correlations. We have numerically validated the resource efficiency and accuracy of our formalism with a number of strongly correlated molecular systems.
Energy Landscape Plummeting in Variational Quantum Eigensolver: Subspace Optimization, Non-iterative Corrections and Generator-informed Initialization for Improved Quantum Efficiency
Auxiliary-qubit-free quantum approximate optimization algorithm for the minimum dominating set problem
State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications（北京邮电大学网络与交换技术国家重点实验室）；National Key Laboratory of Security Communication, Institute of Southwestern Communication（西南通信研究所信息安全通信国家级重点实验室）
Emergent Kinetic Constraints and Subspace Fragmentation in Rydberg Arrays
University of Science and Technology of China（中国科学技术大学）；Laboratory of Quantum Information, University of Science and Technology of China（中国科学技术大学量子信息实验室）；Anhui Province Key Laboratory of Quantum Network, University of Science and Technology of China（中国科学技术大学安徽省量子网络重点实验室）；CAS Center for Excellence in Quantum Information and Quantum Physics（中国科学院量子信息与量子物理卓越创新中心）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）
Subspace Variational Quantum Simulation: Fidelity Lower Bounds as Measures of Training Success
Institute for Convergence Research and Education in Advanced Technology, Yonsei University（延世大学先进技术与教育融合研究院）；Department of Quantum Information, Graduate School, Yonsei University（延世大学研究生院量子信息系）；School of Computer Engineering, Kumoh National Institute of Technology（庆北国立科技大学生物计算机工程学院）
Transducer leakage error suppression using invariant-based shortcut
School of Physics, Anhui University（安徽大学物理学院）；Laboratory for Advanced Computing and Intelligence Engineering（先进计算与智能工程实验室）；School of Physics, Zhengzhou University（郑州大学物理学院）；Institute of Quantum Materials and Physics, Henan Academy of Science（河南省科学院量子材料与物理研究所）
在最近的工作[D. K. Burgarth等人，国家通信5，5173（2014）]表明，一系列频繁的测量可以将量子系统的动力学投影到动力学可能更复杂的子空间上。在这个子空间中，甚至可以实现完全的可控性，尽管在投影之前系统的可控性非常差，因为控制哈密顿量彼此交换。我们也可以考虑相反的情况：量子系统的任何哈密顿算符，一般来说彼此之间是不可交换的，可以通过将它们嵌入到扩展的希尔伯特空间中而使它们成为可交换的，因此扩展空间中的动力学变得平凡而简单。这种使非对易的哈密尔顿算子成为对易的思想叫做“哈密尔顿纯化"。“通过频繁的测量将系统投影回原始希尔伯特空间，恢复了原始的非对易哈密顿算子。在这里，我们将这个想法推广到开放系统动力学，提出了一个简单的结构，使Lindbladian，以及哈密顿，交换的一个更大的空间与辅助系统。我们表明，原来的动态可以恢复通过经常测量辅助系统在一个非选择性的方式。此外，我们还提供了一个通用的Lindbladian对，它描述了一个“可访问的”开放量子系统的通用系统大小。这使我们能够得出结论，通过一系列频繁的非选择性测量，一个不可访问的开放量子系统通常变得可访问。这进一步阐明了测量反作用对量子系统控制的作用。
Reducing multi-qubit interactions in adiabatic quantum computation without adding auxiliary qubits. Part 1: The "deduc-reduc" method and its application to quantum factorization of numbers
