Quantum walks: a comprehensive review

Venegas-Andraca, Salvador E.

doi:10.1007/s11128-012-0432-5

Cited by 874 publications

(667 citation statements)

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

Large scale quantum walks by means of optical fiber cavities

Boutari

Feizpour

Barz

et al. 2016

J. Opt.

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“…As there are few real-life materials that are topological insulators, 3 there is an intense search for model systems that simulate topological insulators in the laboratory. [4][5][6] Discrete-time quantum walks (DTQW) 7 are quantum generalizations of the random walk, with a quantum speedup that could be employed for fast quantum search 8 or even for general quantum computation. 9 They have been realized in many experimental setups, including atoms in optical lattices, 10,11 trapped ions, 12,13 and light in optical setups.…”

Section: Introductionmentioning

confidence: 99%

Scattering theory of topological phases in discrete-time quantum walks

2014

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One-dimensional discrete-time quantum walks show a rich spectrum of topological phases that have so far been exclusively analysed based on the Floquet operator in momentum space. In this work we introduce an alternative approach to topology which is based on the scattering matrix of a quantum walk, adapting concepts from time-independent systems. For quantum walks with gaps in the quasienergy spectrum at 0 and π, we find three different types of topological invariants, which apply dependent on the symmetries of the system. These determine the number of protected boundary states at an interface between two quantum walk regions. Unbalanced quantum walks on the other hand are characterised by the number of perfectly transmitting unidirectional modes they support, which is equal to their non-trivial quasienergy winding. Our classification provides a unified framework that includes all known types of topology in one dimensional discrete-time quantum walks and is very well suited for the analysis of finite size and disorder effects. We provide a simple scheme to directly measure the topological invariants in an optical quantum walk experiment.

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“…: [3][4][5][6][7]). It was originally proposed with the aim of finding quantum algorithms that are faster than classical algorithms for the same problem, because in general quantum walks diffuse faster than its classical counter parts.…”

Section: Introductionmentioning

confidence: 99%

“…For a recent review on various aspects of localisation in quantum walks, see e.g., Ref. [4] and [39].…”

Section: Introductionmentioning

confidence: 99%