@article {ISI:000485187000003,
title = {Quantum information scrambling through a high-complexity operator mapping},
journal = {Phys. Rev. A},
volume = {100},
number = {3},
year = {2019},
month = {SEP 6},
pages = {032309},
publisher = {AMER PHYSICAL SOC},
type = {Article},
abstract = {Quantum information scrambling has attracted much attention amid the effort to reconcile the conflict between quantum-mechanical unitarity and the thermalization irreversibility in many-body systems. Here we propose an unconventional mechanism to generate quantum information scrambling through a high-complexity mapping from logical to physical degrees-of-freedom that hides the logical information into nonseparable many-body correlations. Corresponding to this mapping, we develop an algorithm to efficiently sample a Slater-determinant wave function and compute all physical observables in dynamics with a polynomial cost in system size. The system shows information scrambling in the quantum many-body Hilbert space characterized by the spreading of Hamming distance. At late time we find emergence of classical diffusion dynamics in this quantum many-body system. We establish that the operator mapping enabled growth in an out-of-time-order correlator exhibits exponential-scrambling behavior. The quantum information-hiding mapping approach may shed light on the understanding of fundamental connections among computational complexity, information scrambling, and quantum thermalization.},
issn = {2469-9926},
doi = {10.1103/PhysRevA.100.032309},
author = {Li, Xiaopeng and Zhu, Guanyu and Han, Muxin and Wang, Xin}
}
@article {ISI:000401235900001,
title = {Quantum Entanglement in Neural Network States},
journal = {PHYSICAL REVIEW X},
volume = {7},
number = {2},
year = {2017},
month = {MAY 11},
abstract = {Machine learning, one of today{\textquoteright}s most rapidly growing interdisciplinary fields, promises an unprecedented perspective for solving intricate quantum many-body problems. Understanding the physical aspects of the representative artificial neural-network states has recently become highly desirable in the applications of machine-learning techniques to quantum many-body physics. In this paper, we explore the data structures that encode the physical features in the network states by studying the quantum entanglement properties, with a focus on the restricted-Boltzmann-machine (RBM) architecture. We prove that the entanglement entropy of all short-range RBM states satisfies an area law for arbitrary dimensions and bipartition geometry. For long-range RBM states, we show by using an exact construction that such states could exhibit volume-law entanglement, implying a notable capability of RBM in representing quantum states with massive entanglement. Strikingly, the neural-network representation for these states is remarkably efficient, in the sense that the number of nonzero parameters scales only linearly with the system size. We further examine the entanglement properties of generic RBM states by randomly sampling the weight parameters of the RBM. We find that their averaged entanglement entropy obeys volume-law scaling, and the meantime strongly deviates from the Page entropy of the completely random pure states. We show that their entanglement spectrum has no universal part associated with random matrix theory and bears a Poisson-type level statistics. Using reinforcement learning, we demonstrate that RBM is capable of finding the ground state (with power-law entanglement) of a model Hamiltonian with a long-range interaction. In addition, we show, through a concrete example of the one-dimensional symmetry-protected topological cluster states, that the RBM representation may also be used as a tool to analytically compute the entanglement spectrum. Our results uncover the unparalleled power of artificial neural networks in representing quantum many-body states regardless of how much entanglement they possess, which paves a novel way to bridge computer-science-based machine-learning techniques to outstanding quantum condensed-matter physics problems.},
issn = {2160-3308},
doi = {10.1103/PhysRevX.7.021021},
author = {Deng, Dong-Ling and Li, Xiaopeng and S. Das Sarma}
}
@article { ISI:000376908700003,
title = {Quantum nonergodicity and fermion localization in a system with a single-particle mobility edge},
journal = {PHYSICAL REVIEW B},
volume = {93},
number = {18},
year = {2016},
month = {MAY 31},
pages = {184204},
issn = {2469-9950},
doi = {10.1103/PhysRevB.93.184204},
author = {Li, Xiaopeng and Pixley, J. H. and Deng, Dong-Ling and Ganeshan, Sriram and S. Das Sarma}
}