Dong-Ling Deng

Quantum Entanglement in Neural Network States

Machine learning, one of todays 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 is recently becoming highly desirable in the applications of machine learning techniques to quantum many-body physics. Here, we study the quantum entanglement properties of neural-network states, with a focus on the restricted-Boltzmann-machine (RBM) architecture. We prove that the entanglement 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 efficiently quantum states with massive entanglement. We further examine generic RBM states with random weight parameters. We find that their averaged entanglement entropy obeys volume-law scaling and 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 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, which paves a novel way to bridge computer science based machine learning techniques to outstanding quantum condensed matter physics problems.

Machine learning topological states

Machine learning, the core of artificial intelligence and data science, is a very active field, with vast applications throughout science and technology. Recently, machine learning techniques have been adopted to tackle intricate quantum many-body problems and phase transitions. In this work, the authors construct exact mappings from exotic quantum states to machine learning network models. This work shows for the first time that the restricted Boltzmann machine can be used to study both symmetry-protected topological phases and intrinsic topological order. The exact results are expected to provide a substantial boost to the field of machine learning of phases of matter.

State-Independent Experimental Test of Quantum Contextuality with a Single Trapped Ion

Using a single trapped ion, we have experimentally demonstrated state-independent violation of a recent version of the Kochen-Specker inequality in a three-level system (qutrit) that is intrinsically indivisible. Three ground states of the (171)Yb(+) ion representing a qutrit are manipulated with high fidelity through microwaves and detected with high efficiency through a two-step quantum jump technique. Qutrits constitute the most fundamental system to show quantum contextuality and our experiment represents the first one that closes the detection efficiency loophole for experimental tests of quantum contextuality in such a system.

State-Independent Experimental Test of Quantum Contextuality in an Indivisible System

We report the first state-independent experimental test of quantum contextuality on a single photonic qutrit (three-dimensional system), based on a recent theoretical proposal [Phys. Rev. Lett. 108, 030402 (2012)]. Our experiment spotlights quantum contextuality in its most basic form, in a way that is independent of either the state or the tensor product structure of the system.

Experimental Certification of Random Numbers via Quantum Contextuality

The intrinsic unpredictability of measurements in quantum mechanics can be used to produce genuine randomness. Here, we demonstrate a random number generator where the randomness is certified by quantum contextuality in connection with the Kochen-Specker theorem. In particular, we generate random numbers from measurements on a single trapped ion with three internal levels, and certify the generated randomness by showing a bound on the minimum entropy through observation of violation of the Klyachko-Can-Binicioglu-Shumovsky (KCBS) inequality. Concerning the test of the KCBS inequality, we close the detection efficiency loophole for the first time and make it relatively immune to the compatibility loophole. In our experiment, we generate 1 × 105 random numbers that are guaranteed to have 5.2 × 104 bits of minimum entropy with a 99% confidence level.

Probe of three-dimensional chiral topological insulators in an optical lattice.

We propose a feasible experimental scheme to realize a three-dimensional chiral topological insulator with cold fermionic atoms in an optical lattice, which is characterized by an integer topological invariant distinct from the conventional Z(2) topological insulators and has a remarkable macroscopic zero-energy flat band. To probe its property, we show that its characteristic surface states--the Dirac cones--can be probed through time-of-flight imaging or Bragg spectroscopy and the flat band can be detected via measurement of the atomic density profile in a weak global trap. The realization of this novel topological phase with a flat band in an optical lattice will provide a unique experimental platform to study the interplay between interaction and topology and open new avenues for application of topological states.

Hamiltonian tomography for quantum many-body systems with arbitrary couplings

Characterization of qubit couplings in many-body quantum systems is essential for benchmarking quantum computation and simulation. We propose a tomographic measurement scheme to determine all the coupling terms in a general many-body Hamiltonian with arbitrary long-range interactions, provided the energy density of the Hamiltonian remains finite. Different from quantum process tomography, our scheme is fully scalable with the number of qubits as the required rounds of measurements increase only linearly with the number of coupling terms in the Hamiltonian. The scheme makes use of synchronized dynamical decoupling pulses to simplify the many-body dynamics so that the unknown parameters in the Hamiltonian can be retrieved one by one. We simulate the performance of the scheme under the influence of various pulse errors and show that it is robust to typical noise and experimental imperfections.

Quantum nonergodicity and fermion localization in a system with a single-particle mobility edge

Quantum thermalization of isolated systems undergoing unitary time evolution is a fundamental problem in quantum statistical mechanics. Its study has been revived recently in the context of many-body Anderson localization. Previous works have focused on localization of many-body systems with all the single-particle states being localized. As a significant step forward, this work studies localization aspects of noninteracting many-particle systems in the presence of a single-particle mobility edge. By systemically investigating entanglement entropy scaling and nonthermal fluctuations in various lattice models, the authors establish a nonergodic extended phase as a generic intermediate phase (between purely ergodic extended and nonergodic localized phases) for the many-body localization transition of noninteracting fermions. This work also sheds light on the interacting transition scenario as well.

Systematic Construction of tight-binding Hamiltonians for Topological Insulators and Superconductors

A remarkable discovery in recent years is that there exist various kinds of topological insulators and superconductors characterized by a periodic table according to the system symmetry and dimensionality. To physically realize these peculiar phases and study their properties, a critical step is to construct experimentally relevant Hamiltonians which support these topological phases. We propose a general and systematic method based on the quaternion algebra to construct the tight binding Hamiltonians for all the three-dimensional topological phases in the periodic table characterized by arbitrary integer topological invariants, which include the spin-singlet and the spin-triplet topological superconductors, the Hopf and the chiral topological insulators as particular examples. For each class, we calculate the corresponding topological invariants through both geometric analysis and numerical simulation.

Hopf insulators and their topologically protected surface states

Three-dimensional (3D) topological insulators in general need to be protected by certain kinds of symmetries other than the presumed