The experimental realization of increasingly complex quantum states underscores the pressing need for new methods of state learning and verification. In one such framework, quantum state tomography, the aim is to learn the full quantum state from data obtained by measurements. Without prior assumptions on the state, this task is prohibitively hard. Here, we present an efficient algorithm for learning states on $n$ fermion modes prepared by any number of Gaussian and at most $t$ non-Gaussian gates. By Jordan-Wigner mapping, this also includes $n$-qubit states prepared by nearest-neighbour matchgate circuits with at most $t$ SWAP-gates. Our algorithm is based exclusively on single-copy measurements and produces a classical representation of a state, guaranteed to be close in trace distance to the target state. The sample and time complexity of our algorithm is $\mathrm{poly}(n,2^t)$; thus if $t=O(\log(n))$, it is efficient. We also show that, if $t$ scales slightly more than logarithmically, any learning algorithm to solve the same task must be inefficient, under common cryptographic assumptions. We also provide an efficient property testing algorithm that, given access to copies of a state, determines whether such a state is far or close to the set of states for which our learning algorithm works. In addition to the outputs of quantum circuits, our tomography algorithm is efficient for some physical target states, such as those arising in time dynamics and low-energy physics of impurity models. Beyond tomography, our work sheds light on the structure of states prepared with few non-Gaussian gates and offers an improved upper bound on their circuit complexity, enabling an efficient circuit compilation method.
Quantum statistics of Schrödinger cat states prepared by logical gate with non-Gaussian resource state
测量诱导连续变量逻辑门能够制备薛定谔猫态，如果门使用非高斯资源态，例如立方相位态[I]。V. Sokolov，Phys. Lett. A 384，126762（2020）]。我们的方案提供了一种替代的混合电路，使用光子减法和（或）Fock资源状态和光子数探测器。我们揭示的条件下，门有条件地准备量子叠加的两个未失真的“副本”的任意输入状态，占据相空间中的有限区域。详细分析了门输出态与高质量薛定谔猫态之间的保真度。对于一组具有代表性的输入Fock态，给出了输出态量子统计的Wigner函数随门参数和测量结果的变化的解释.
Schrödinger cat states prepared by logical gate with non-Gaussian resource state: effect of finite squeezing and efficiency versus monotones
利用量子测量诱导门，以理想立方相态为非高斯源，在相平面上产生两个高保真度的薛定谔猫态[N.I. Masalaeva，I.V. Sokolov，Phys. Lett. A 424，127846（2022）]。在这项工作中，我们研究了有限的初始压缩的资源状态上的门性能的影响。我们给出了门输出态的精确解，并证明了存在一定程度的压缩，使得输出猫态的质量几乎不随压缩的进一步增加而改善。另一方面，预期的辅助测量结果的概率随着压缩而减小。由于有条件方案的整体效率应占成功的概率，我们认为，这种措施的非高斯的资源状态的维格纳对数负性和非高斯性可能不直接适用于评估的效率的非高斯门的基础上量子纠缠和随后的投影测量。
Optimal and improved gate decompositions for accelerated classical simulation of near-Gaussian fermionic circuits
Phasecraft Ltd（Phasecraft有限公司）；Department of Mathematics, School of Computation, Information and Technology, Technical University of Munich（慕尼黑工业大学计算、信息与技术学院数学系）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与技术中心）
Efficient Learning of Quantum States Prepared With Few Non-Clifford Gates
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Simons Institute for the Theory of Computing, UC Berkeley（伯克利大学理论计算研究所）；Rice University（里士满大学）；Portland State University（波特兰州立大学）
High-fidelity collisional quantum gates with fermionic atoms
Max-Planck-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与技术中心）；Department of Physics and SUPA, University of Strathclyde（斯特拉斯克莱德大学物理系和SUPA）；Laboratoire Charles Fabry, Institut d’Optique Graduate School, CNRS, Université Paris-Saclay（夏尔·法布里实验室，高等光学学院，法国国家科学研究中心，巴黎萨克雷大学）
Optimal Particle-Conserved Linear Encoding for Practical Fermionic Simulation
Imperial College London（帝国理工学院）；Fraunhofer Institute for Industrial Mathematics（弗劳恩霍夫工业数学研究所）；City University of Hong Kong（香港城市大学）；Hon Hai (Foxconn) Research Institute（鸿海（富士康）研究院）；Fraunhofer Center for Maritime Logistics（弗劳恩霍夫海事物流中心）
Fermionic entropy: an efficiently measurable strong monotone for non-Gaussianity
Università degli Studi di Salerno（萨莱诺大学）；INFN, Sezione di Napoli, Gruppo Collegato di Salerno（意大利国家核物理研究所，那不勒斯分部，萨莱诺协作组）；Freie Universität Berlin（柏林自由大学）
