Gaussian fermionic matrix product states (GfMPS) form a class of ansatz quantum states for 1d systems of noninteracting fermions. We show, for a simple critical model of free hopping fermions, that: (i) any GfMPS approximation to its ground state must have bond dimension scaling superpolynomially with the system size, whereas (ii) there exists a non-Gaussian fermionic MPS approximation to this state with polynomial bond dimension. This proves that, in general, imposing Gaussianity at the level of the tensor network may significantly alter its capability to efficiently approximate critical Gaussian states. We also provide numerical evidence that the required bond dimension is subexponential, and thus can still be simulated with moderate resources.
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）
On the infeasibility of entanglement generation in Gaussian quantum systems via classical control
Research School of Engineering, The Australian National University（澳大利亚国立大学工程研究学院）；School of Information Technology and Electrical Engineering, University of New South Wales at the Australian Defence Force Academy（新南威尔士大学澳大利亚国防军学院信息技术与电气工程学院）；ARC Centre for Quantum Computation and Communication Technology, Research School of Engineering, The Australian National University（澳大利亚国立大学工程研究学院量子计算与通信技术ARC中心）
Fermionic non-Gaussianity via Bell sampling: monotones and efficient quantum algorithms
Technical University of Munich（慕尼黑工业大学）；TUM School of Natural Sciences, Physics Department（自然科学与工程学院物理系）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
