Continuous and deterministic all-photonic cluster state of indistinguishable photons.

Cluster states are key resources for measurement-based quantum information processing. Photonic cluster and graph states, in particular, play indispensable roles in quantum network and quantum metrology. We demonstrate a semiconductor quantum dot based device in which the confined hole spin acts as a needle in a quantum knitting machine producing continuously and deterministically at sub-Gigahertz repetition rate single indistinguishable photons which are all polarization entangled to each other and to the spin in a one dimensional cluster state. By projecting two nonadjacent photons onto circular polarization bases we disentangle the spin from the photons emitted in between. This way we demonstrate a novel way for producing deterministic and continuous all-photonic cluster states. We use polarization tomography on four sequentially detected photons to demonstrate and to directly quantify the robustness of the cluster's entanglement and the determinism in its photon generation.

Photonic topological Anderson insulators.

The hallmark property of two-dimensional topological insulators is robustness of quantized electronic transport of charge and energy against disorder in the underlying lattice1. That robustness arises from the fact that, in the topological bandgap, such transport can occur only along the edge states, which are immune to backscattering owing to topological protection. However, for sufficiently strong disorder, this bandgap closes and the system as a whole becomes topologically trivial: all states are localized and all transport vanishes in accordance with Anderson localization2,3. The recent suggestion4 that the reverse transition can occur was therefore surprising. In so-called topological Anderson insulators, it has been predicted4 that the emergence of protected edge states and quantized transport can be induced, rather than inhibited, by the addition of sufficient disorder to a topologically trivial insulator. Here we report the experimental demonstration of a photonic topological Anderson insulator. Our experiments are carried out in an array of helical evanescently coupled waveguides in a honeycomb geometry with detuned sublattices. Adding on-site disorder in the form of random variations in the refractive index of the waveguides drives the system from a trivial phase into a topological one. This manifestation of topological Anderson insulator physics shows experimentally that disorder can enhance transport rather than arrest it.

Learning a Local Hamiltonian from Local Measurements.

Recovering an unknown Hamiltonian from measurements is an increasingly important task for certification of noisy quantum devices and simulators. Recent works have succeeded in recovering the Hamiltonian of an isolated quantum system with local interactions from long-ranged correlators of a single eigenstate. Here, we show that such Hamiltonians can be recovered from local observables alone, using computational and measurement resources scaling linearly with the system size. In fact, to recover the Hamiltonian acting on each finite spatial domain, only observables within that domain are required. The observables can be measured in a Gibbs state as well as a single eigenstate; furthermore, they can be measured in a state evolved by the Hamiltonian for a long time, allowing us to recover a large family of time-dependent Hamiltonians. We derive an estimate for the statistical recovery error due to approximation of expectation values using a finite number of samples, which agrees well with numerical simulations.

Quantized Magnetization Density in Periodically Driven Systems.

We study micromotion in two-dimensional periodically driven systems in which all bulk Floquet eigenstates are localized by disorder. We show that this micromotion gives rise to a quantized time-averaged orbital magnetization density in any region completely filled with fermions. The quantization of magnetization density has a topological origin, and reveals the physical nature of the new phase identified in P. Titum, E. Berg, M. S. Rudner, G. Refael, and N. H. Lindner [Phys. Rev. X 6, 021013 (2016)PRXHAE2160-330810.1103/PhysRevX.6.021013]. We thus establish that the topological index of this phase can be accessed directly in bulk measurements, and propose an experimental protocol to do so using interferometry in cold-atom-based realizations.

Disorder-induced Floquet topological insulators.

We investigate the possibility of realizing a disorder-induced topological Floquet spectrum in two-dimensional periodically driven systems. Such a state would be a dynamical realization of the topological Anderson insulator. We establish that a disorder-induced trivial-to-topological transition indeed occurs, and characterize it by computing the disorder averaged Bott index, suitably defined for the time-dependent system. The presence of edge states in the topological state is confirmed by exact numerical time evolution of wave packets on the edge of the system. We consider the optimal driving regime for experimentally observing the Floquet topological Anderson insulator, and discuss its possible realization in photonic lattices.

Error distributions on large entangled states with non-Markovian dynamics.

We investigate the distribution of errors on a computationally useful entangled state generated via the repeated emission from an emitter undergoing strongly non-Markovian evolution. For emitter-environment coupling of pure-dephasing form, we show that the probability that a particular patten of errors occurs has a bound of Markovian form, and thus, accuracy threshold theorems based on Markovian models should be just as effective. Beyond the pure-dephasing assumption, though complicated error structures can arise, they can still be qualitatively bounded by a Markovian error model.

Topological transitions for lattice bosons in a magnetic field.

The Hall response provides an important characterization of strongly correlated phases of matter. We study the Hall conductivity of interacting bosons on a lattice subjected to a magnetic field. We show that for any density or interaction strength, the Hall conductivity is characterized by an integer. We find that the phase diagram is intersected by topological transitions between different values of this integer. These transitions lead to surprising effects, including sign reversal of the Hall conductivity and extensive regions in the phase diagram where it acquires a negative sign, which implies that flux flow is reversed in these regions--vortices there flow upstream. Our findings have immediate applications to a wide range of phenomena in condensed matter physics, which are effectively described in terms of lattice bosons.

Electronic Floquet gyro-liquid crystal.

Floquet engineering uses coherent time-periodic drives to realize designer band structures on-demand, thus yielding a versatile approach for inducing a wide range of exotic quantum many-body phenomena. Here we show how this approach can be used to induce non-equilibrium correlated states with spontaneously broken symmetry in lightly doped semiconductors. In the presence of a resonant driving field, the system spontaneously develops quantum liquid crystalline order featuring strong anisotropy whose directionality rotates as a function of time. The phase transition occurs in the steady state of the system achieved due to the interplay between the coherent external drive, electron-electron interactions, and dissipative processes arising from the coupling to phonons and the electromagnetic environment. We obtain the phase diagram of the system using numerical calculations that match predictions obtained from a phenomenological treatment and discuss the conditions on the system and the external drive under which spontaneous symmetry breaking occurs. Our results demonstrate that coherent driving can be used to induce non-equilibrium quantum phases of matter with dynamical broken symmetry.

Floquet metal-to-insulator phase transitions in semiconductor nanowires.

We study steady states of semiconductor nanowires subjected to strong resonant time-periodic drives. The steady states arise from the balance between electron-phonon scattering, electron-hole recombination via photoemission, and Auger scattering processes. We show that tuning the strength of the driving field drives a transition between an electron-hole metal (EHM) phase and a Floquet insulator (FI) phase. We study the critical point controlling this transition. The EHM-to-FI transition can be observed by monitoring the presence of peaks in the density-density response function, which are associated with the Fermi momentum of the EHM phase and are absent in the FI phase. Our results may help guide future studies toward inducing exotic nonequilibrium phases of matter by periodic driving.

Topological quantum computation--from basic concepts to first experiments.

Quantum computation requires controlled engineering of quantum states to perform tasks that go beyond those possible with classical computers. Topological quantum computation aims to achieve this goal by using non-Abelian quantum phases of matter. Such phases allow for quantum information to be stored and manipulated in a nonlocal manner, which protects it from imperfections in the implemented protocols and from interactions with the environment. Recently, substantial progress in this field has been made on both theoretical and experimental fronts. We review the basic concepts of non-Abelian phases and their topologically protected use in quantum information processing tasks. We discuss different possible realizations of these concepts in experimentally available solid-state systems, including systems hosting Majorana fermions, their recently proposed fractional counterparts, and non-Abelian quantum Hall states.

Proposal for pulsed on-demand sources of photonic cluster state strings.

We present a method to convert certain single photon sources into devices capable of emitting large strings of photonic cluster state in a controlled and pulsed "on-demand" manner. Such sources would greatly reduce the resources required to achieve linear optical quantum computation. Standard spin errors, such as dephasing, are shown to affect only 1 or 2 of the emitted photons at a time. This allows for the use of standard fault tolerance techniques, and shows that the photonic machine gun can be fired for arbitrarily long times. Using realistic parameters for current quantum dot sources, we conclude high entangled-photon emission rates are achievable, with Pauli-error rates per photon of less than 0.2%. For quantum dot sources, the method has the added advantage of alleviating the problematic issues of obtaining identical photons from independent, nonidentical quantum dots, and of exciton dephasing.

Vortex quantum dynamics of two dimensional lattice bosons.

We study hard-core lattice bosons in a magnetic field near half filling. The bare vortex hopping rate is extracted from exact diagonalizations of square clusters. We deduce a quantum melting of the vortex lattice above vortex density of 6.5x10(-3) per lattice site. The Hall conductivity reverses sign abruptly as the density crosses half filling, where its characteristic temperature scale vanishes. We prove that at precisely half filling, each vortex carries a spin-1/2 quantum number ("v spin"). Experimental implications of these results are discussed.