The Applications Of Photonic Quantum Walks In Quantum Simulations

Quantum walks,the counterpart of classical random walks,have many particular properties under the existence of quantum coherence.It is not only considered as a universal tool to realize quantum information processing,but also is widely applied in quantum simulations,quantum computation,quantum measurement and so on.In recent years,quantum walk was not only widely reported in fundamental physics,such as capturing the essence of quantum sources,the implementation of generalized quantum measurements,the verification of fundamental problems in quantum mechanics,but also in practical fields,such as practical quantum communication network,information recovery process,the search algorithms.These studies enable people to have a deeper understanding of the nature of the quantum world.In the future,these researches can also make a contribution to applicable quantum communication and universal quantum computers.However,for the application of quantum walk in quantum simulation,most of the current researches are still at the theoretical level.The crucial question is therefore how to present the complex quantum model in quantum walk,and how to design and realize the large-scale,universal and flexible quantum walk platform.Solving these problems can not only help us to understand the physical nature behind the complex physical phenomena,but also can lay a foundation for the final applications.In this paper,quantum walk is realised experimentally by linear optical elements.Then quantum walk can be used to simulate various complex quantum system.such as periodic quantum systems and non-hermitian quantum systems.The experimental implementation of these systems is not only accompanied various symmetry,such as PT symmetry,time reversal symmetry,pseudo Hermitian,etc.,but also by topological properties,such as topological edge state,topology invariants,bulk boundary correspondence and so on.We prepare single photon resource by spontaneous parametric down conversion and then realize the non-unitary quantum walk.Through the design and realization of partial measurement and quantum state reconstruction and other unique measurement methods,we can directly observe topological edge states,measure topological invariants,and verify non-hermitian bulk boundary correspondence.The details are as follows:1,The introduction of basic elements of linear optical system and the process of spontaneous parametric down conversion,which is used to prepare single photon and entanglement photon pairs.Based on the control of the various degree of freedoms of photons,such as polarization,path and arrival time,the experimental realization of quantum walks in free space and loop fiber structure are described in detail.Finally,combining the projection measurement and quantum state tomography,a universal quantum simulation platform is provided to study the application of optical quantum walk.2,Observation of topological edge state in PT symmetric quantum walk.we report the experimental realization of passive PT-symmetric quantum dynamics for single photons by temporally alternating photon losses in the quantum walks interferometers.The ability to impose PT symmetry allows us to realize and investigate Floquet topological phases driven by PT symmetric quantum walks.We observe topological edge states between regions with different bulk topological properties and confirm the robustness of these edge states with respect to PT symmetry-preserving perturbations and PT symmetry-breaking static disorder.3,Detecting topological invariants in non-unitary discrete-time quantum walks.We report the experimental detection of bulk topological invariants in non-unitary discrete-time quantum walks with single photons.The non-unitarity of the quantum dynamics is enforced by periodically performing partial measurements on the polarization of the walker photon,which effectively introduces loss to the dynamics.The topological invariant of the non-unitary quantum walk is manifested in the quantized average displacement of the walker,which is probed by monitoring the photon loss.We also observe the transition by measuring the second moment and the average chiral displacement of the walking distribution probability.4,Observation of critical phenomena in parity-time-symmetric quantum dynamics.We experimentally simulate non-unitary quantum dynamics using a single-photon interferometric network and study the information flow between a PT symmetric non-Hermitian system and its environment.We observe oscillations of quantum-state distinguishability and complete information retrieval in the PT symmetry-unbroken regime.We then characterize in detail critical phenomena of the information flow near the exceptional point separating the PT-unbroken and-broken regimes,and demonstrate power-law behavior in key quantities such as the distinguishability and the recurrence time.Finally,by introducing an ancilla as an environment and probing quantum entanglement between the system and the environment,we confirm that the observed information retrieval is induced by a finite-dimensional entanglement partner in the environment.5,Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics.Bulk-boundary correspondence,a central principle in topological matter relating bulk topological invariants to edge states,breaks down in a generic class of non-Hermitian systems.We experimentally observe non-Hermitian bulk-boundary correspondence in discrete-time non-unitary quantum-walk dynamics of single photons.We experimentally demonstrate photon localizations near boundaries even in the absence of topological edge states,thus confirm the non-Hermitian skin effect.Facilitated by our experimental scheme of edge-state reconstruction,we directly measure topological edge states,which match excellently with nonBloch topological invariants calculated from localized bulk-state wave functions.