Quantum walk coherences on a dynamical percolation graph

Elster, Fabian; Barkhofen, Sonja; Nitsche, Thomas; Novotný, Jaroslav; Gábris, Aurél; Jex, Igor; Silberhorn, Christine

doi:10.1038/srep13495

Cited by 34 publications

(53 citation statements)

References 56 publications

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“…Additionally, polarization control can be included in walk design to access an additional degree of freedom. We also note that the relatively slow dynamics possible with long fiber lengths makes it possible to create a walk structure that depends on the step number and lattice position, as has been demonstrated in hybrid bulk-fiber setups [37,38]. A promising route for control within our all-fiber apparatus is strainoptic modulation [39].…”

Section: Discussionmentioning

confidence: 80%

Large scale quantum walks by means of optical fiber cavities

Boutari

Feizpour

Barz

et al. 2016

J. Opt.

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We demonstrate a platform for implementing quantum walks that overcomes many of the barriers associated with photonic implementations. We use coupled fiber-optic cavities to implement time-bin encoded walks in an integrated system. We show that this platform can achieve very low losses combined with high-fidelity operation, enabling an unprecedented large number of steps in a passive system, as required for scenarios with multiple walkers. Furthermore the platform is reconfigurable, enabling variation of the coin, and readily extends to multidimensional lattices. We demonstrate variation of the coin bias experimentally for three different values. INTRODUCTIONQuantum walks are the quantum counterparts to random walks. A quantum walker moves by superpositions of possible paths, resulting in a probability amplitude for being observed at a particular position [1][2][3]. Optical multiport interferometers provide an attractive implementation for quantum walks, since optical fields naturally exhibit coherence between pathways and allow multi-walker scenarios using multiple single photons. However, this approach is susceptible to losses, which limit the achievable scale before being overtaken by noise, and which abrogate many of the advantages implied for applications in quantum information processing [4][5][6][7][8][9][10][11][12]. This challenge motivates the development of low-loss, modular, guided-wave interferometer networks for quantum walks.Quantum walks with multiple interacting walkers have been shown to realize universal quantum computation [13]. For the case of multiple non-interacting walkers, quantum walks are also thought to have quantum computational power, as shown by the boson sampling problem [14]. Quantum walks with a single walker can implement quantum computation, though this requires an exponentially large graph [15,16]. A key feature of quantum walks as information processors is that they do not require time-dependent feedforward control. Quantum walks, both discrete and continuous, have been realised using cold atoms [17,18], single optically trapped atoms [19], trapped ions [20][21][22], and photons. Optical systems have been used to implement quantum walks using bulk optics [23,24], photonic chips [25][26][27][28], fiber optics [29], and hybrid bulkfiber optic approaches [30][31][32].In most experimental implementations, the quantum walk takes place over spatial locations arranged in a lattice. The physical size of the lattice then determines the maximum size of the walk. This limitation can be avoided by use of optical cavities, in which case the number of physical elements required is independent of the size of the walk. This approach was first formulated for frequency-encoded quantum walks [33]. From an experimental perspective, a further key advance was the development of optical cavities that implement time-encoded walks [29,30]. In this case, the walker's location is represented by the time at which a pulse completes a round trip of a cavity [29,30]. In practice, the achievable scale of t...

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Section: Discussionmentioning

confidence: 80%

Large scale quantum walks by means of optical fiber cavities

Boutari

Feizpour

Barz

et al. 2016

J. Opt.

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“…Introducing a dynamical coin dramatically increases the versatility of a quantum walk as a model system: it offers new possibilities, e.g. in altering the structure of the underlying graph [37] (see also section 4.1) as well as in 'in situ' preparation of the initial state of the quantum walk (see section 4.2).…”

Section: Dynamical Coin and Dynamical Graphmentioning

confidence: 99%

“…Still, all of these implementations have been realised on a static underlying graph and the principle of time-multiplexing appeared to be incompatible with reconfigurations of the lattice structure. In order to overcome this restriction, a sophisticated double-step scheme was invented, which allowed the demonstration of a quantum walk on a dynamical percolation graph [37]. Such a graph is defined as having its edges probabilistically added or removed in time to imitate porous or fluctuating media.…”

Section: Introductionmentioning

confidence: 99%

Quantum walks with dynamical control: graph engineering, initial state preparation and state transfer

et al. 2016

Self Cite

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Quantum walks are a well-established model for the study of coherent transport phenomena and provide a universal platform in quantum information theory. Dynamically influencing the walker's evolution gives a high degree of flexibility for studying various applications. Here, we present timemultiplexed finite quantum walks of variable size, the preparation of non-localised input states and their dynamical evolution. As a further application, we implement a state transfer scheme for an arbitrary input state to two different output modes. The presented experiments rely on the full dynamical control of a time-multiplexed quantum walk, which includes adjustable coin operation as well as the possibility to flexibly configure the underlying graph structures.

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“…Although for certainty we consider ultracold atoms trapped in optical lattices, the idea can be applied to other arrays of quantum emitters, e.g. superconducting qubits as used in circuit cavity QED [4][5][6][7][8][9], matter waves scattering [10], Rydberg [11,12] and other polaritonic and spin excitations [13], optomechanical arrays [14,15], multimode cavities [16,17], and even purely photonic systems with multiple path interference (where, similarly to optical lattices, the quantum walks and boson sampling were discussed [18][19][20][21]).…”

Section: Introductionmentioning

confidence: 99%

Collective dynamics of multimode bosonic systems induced by weak quantum measurement

et al. 2016

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In contrast to the fully projective limit of strong quantum measurement, where the evolution is locked to a small subspace (quantum Zeno dynamics), or even frozen completely (quantum Zeno effect), the weak non-projective measurement can effectively compete with standard unitary dynamics leading to nontrivial effects. Here we consider global weak measurement addressing collective variables, thus preserving quantum superpositions due to the lack of which path information. While for certainty we focus on ultracold atoms, the idea can be generalized to other multimode quantum systems, including various quantum emitters, optomechanical arrays, and purely photonic systems with multiple-path interferometers (photonic circuits). We show that light scattering from ultracold bosons in optical lattices can be used for defining macroscopically occupied spatial modes that exhibit long-range coherent dynamics. Even if the measurement strength remains constant, the quantum measurement backaction acts on the atomic ensemble quasi-periodically and induces collective oscillatory dynamics of all the atoms. We introduce an effective model for the evolution of the spatial modes and present an analytic solution showing that the quantum jumps drive the system away from its stable point. We confirm our finding describing the atomic observables in terms of stochastic differential equations.

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Quantum walk coherences on a dynamical percolation graph

Cited by 34 publications

References 56 publications

Large scale quantum walks by means of optical fiber cavities

Large scale quantum walks by means of optical fiber cavities

Quantum walks with dynamical control: graph engineering, initial state preparation and state transfer

Collective dynamics of multimode bosonic systems induced by weak quantum measurement

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