Free-fermionic states, also known as matchgates or Gaussian states, are a fundamental class of quantum states due to their efficient classical simulability and their crucial role across various domains of Physics. With the advent of quantum devices, experiments now yield data from quantum states, including estimates of expectation values. We establish that deciding whether a given dataset, formed by a few Majorana correlation functions estimates, can be consistent with a free-fermionic state is an NP-complete problem. Our result also extends to datasets formed by estimates of Pauli expectation values. This is in stark contrast to the case of stabilizer states, where the analogous problem can be efficiently solved. Moreover, our results directly imply that free-fermionic states are computationally hard to properly PAC-learn, where PAC-learning of quantum states is a learning framework introduced by Aaronson. Remarkably, this is the first class of classically simulable quantum states shown to have this property.
Stabilizer-based quantum simulation of fermion dynamics with local qubit encodings
IBM Quantum, IBM Research Europe - Zurich（IBM量子，IBM欧洲苏黎世研究中心）；Institute for Theoretical Physics, ETH Zürich（苏黎世联邦理工学院理论物理研究所）；Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院物理研究所）
The University of Hong Kong（香港大学）；HK Institute of Quantum Science & Technology（香港量子科学研究所）；Freie Universität Berlin（柏林自由大学）；Dahlem Center for Complex Quantum Systems, Freie Universität Berlin（柏林自由大学达勒姆复杂量子系统中心）；Helmholtz-Zentrum Berlin für Materialien und Energie（柏林亥姆霍兹材料与能源中心）
Practical Tests and Witnesses of Fermionic non-Gaussianity
Quantum Research Center, Technology Innovation Institute（技术革新研究所量子研究中心）；Institut für Theoretische Physik, Universität zu Köln（科隆大学理论物理研究所）；Barcelona Supercomputing Center（巴塞罗那超级计算中心）
Fermionic transport through a driven quantum point contact: breakdown of Floquet thermalization beyond a critical driving frequency
Russian Quantum Center（俄罗斯量子中心）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究所）；Steklov Mathematical Institute of Russian Academy of Sciences（俄罗斯科学院斯捷克洛夫数学研究所）
HierarchicalEOM.jl: An efficient Julia framework for hierarchical equations of motion in open quantum systems
National Cheng Kung University（国立成功大学）；Center for Quantum Frontiers of Research and Technology, NCKU（国立成功大学量子前沿研究与技术中心）；RIKEN（理化学研究所）；China Academy of Engineering Physics（中国工程物理研究院）；The University of Michigan（密歇根大学）
本文介绍开源 Julia 框架 HierarchicalEOM.jl，用统一接口实现 HEOM 的谱、稳态及 ADOs 动力学计算，并在典型开放量子系统中验证其相对 QuTiP 的显著加速。
