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Berry curvature is a fundamental element to characterize topological quantum physics, while a full measurement of Berry curvature in momentum space was not reported for topological states. Here we achieve two-dimensional Berry curvature reconstruction in a photonic quantum anomalous Hall system via Hall transport measurement of a momentum-resolved wave packet. Integrating measured Berry curvature over the two-dimensional Brillouin zone, we obtain Chern numbers corresponding to -1 and 0. Further, we identify bulk-boundary correspondence by measuring topology-linked chiral edge states at the boundary. The full topological characterization of photonic Chern bands from Berry curvature, Chern number, and edge transport measurements enables our photonic system to serve as a versatile platform for further in-depth study of novel topological physics.

The robust generation and manipulation of entangled multiphoton states on-chip has an essential role in quantum computation and communication. Lattice topology has emerged as a means of protecting photonic states from disorder but entanglement across different topologies remained unexplored. We report biphoton entanglement between topologically distinct spatial modes in a bipartite array of silicon waveguides. The results highlight topology as an additional degree of freedom for entanglement and open avenues for investigating information teleportation between trivial and topological modes.

Discord, originally notable as a signature of bipartite quantum correlation,in fact can be nonzero classically, i.e., arising from noisy measurements by one of the two parties. Here we redefine classical discord to quantify channel distortion,in contrast to the previous restriction of classical discord to a state,and we then show a monotonic relationship between classical (channel) discord and channel distortion. We show that classical discord is equivalent to (doubly stochastic) channel distortion by numerically discovering a monotonic relation between discord and total-variation distance for a bipartite protocol with one party having a noiseless channel and the other party having a noisy channel. Our numerical method includes randomly generating doubly stochastic matrices for noisy channels and averaging over a uniform measure of input messages. Connecting discord with distortion establishes discord as a signature of classical, not quantum, channel distortion., Comment: 24 pages, 2 figures

Inspired by recent breakthroughs with topological quantum materials, which pave the way to novel, high-efficiency, low-energy magnetoelectric devices and fault-tolerant quantum information processing, inter alia, topological quantum walks have emerged as an exciting topic in its own right, especially due to the theoretical and experimental simplifications this approach offers. Motivated by impressive progress in topological quantum walks, we provide a perspective on theoretical studies and experimental investigations of topological quantum walks focusing on current explorations of topological properties arising for single-walker quantum walks.

Topologically ordered materials may serve as a platform for new quantum technologies such as fault-tolerant quantum computers. To fulfil this promise, efficient and general methods are needed to discover and classify new topological phases of matter. We demonstrate that deep neural networks augmented with external memory can use the density profiles formed in quantum walks to efficiently identify properties of a topological phase as well as phase transitions. On a trial topological ordered model, our method's accuracy of topological phase identification reaches 97.4%, and is shown to be robust to noise on the data. Furthermore, we demonstrate that our trained DNN is able to identify topological phases of a perturbed model and predict the corresponding shift of topological phase transitions without learning any information about the perturbations in advance. These results demonstrate that our approach is generally applicable and may be used to identify a variety of quantum topological materials., Comment: 13 pages, 5 figures and 4 tables

Topological quantum states are characterized by nonlocal invariants, and their detection is intrinsically challenging. Various strategies have been developed to study topological Hamiltonians through their equilibrium states. We present a fundamentally new, high-precision dynamical approach, revealing topology through the unitary evolution after a quench from a topological trivial initial state with a two-dimensional Chern band realized in an ultracold $^{87}$Rb atom gas. The emerging ring structure in the spin dynamics uniquely determines the Chern number for the post-quench band and enables probing the full phase diagram of the band topology with high precision. Besides, we also measure the topological band gap and the domain wall structure dynamically formed in the momentum space during the long-term evolution. Our dynamical approach provides a way towards observing a universal bulk-ring correspondence, and has broad applications in exploring topological quantum matter., Comment: 9 pages, 5 figures for main text and 12 pages for supplementary material

We show that the evolution of two-component particles governed by a two-dimensional spin-orbit lattice Hamiltonian can reveal transitions between topological phases. A kink in the mean width of the particle distribution signals the closing of the band gap, a prerequisite for a quantum phase transition between topological phases. Furthermore, for realistic and experimentally motivated Hamiltonians the density profile in topologically non-trivial phases displays characteristic rings in the vicinity of the origin that are absent in trivial phases. The results are expected to have immediate application to systems of ultracold atoms and photonic lattices., Comment: Ref. [12] fixed; updates in response to referee comments

We analyze a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum-walk features such as localization that starkly distinguishes classical from quantum behavior. Motivated by technological thrusts, we study continuous-time quantum walks on enhanced variants of the chimera graph and on a diminished chimera graph with a random removal of sites. We explain the quantum walk by constructing a generating set for a suitable subgroup of graph isomorphisms and corresponding symmetry operators that commute with the quantum-walk Hamiltonian; the Hamiltonian and these symmetry operators provide a complete set of labels for the spectrum and the stationary states. Our quantum-walk characterization of the chimera graph and its variants yields valuable insights into graphs used for designing quantum-annealers.

We construct a decomposition procedure for converting split-step quantum walks into ordinary quantum walks with alternating coins, and we show that this decomposition enables a feasible linear optical realization of split-step quantum walks by eliminating quantum-control requirements. As salient applications, we show how our scheme will simulate Majorana modes and edge states.