Photonic quantum walks with four-dimensional coins

Lorz, Lennart; Meyer-Scott, Evan; Nitsche, Thomas; Potoček, Václav; Gábris, Aurél; Barkhofen, Sonja; Jex, Igor; Silberhorn, Christine

doi:10.1103/physrevresearch.1.033036

Cited by 24 publications

(13 citation statements)

References 76 publications

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“…While implementing a time-domain reconfigurable loop architecture as described above is not a straightforward task, several groups have performed experiments with tens of modes interfering in time-domain multiplexed configurations. These include time-bin ( 35 ) and temporal-to-spatial–encoded ( 36 ) boson sampling experiments ( 35 ) and controllable photonic random walk over multiple time-bins ( 37 , 38 ). Moreover, recent experiments have shown that it is possible to operate with very high phase stability ( 39 ), high quantum-efficiency photon-number detection ( 40 ), and very low loss reconfigurable interferometric elements ( 41 ).…”

Section: Resultsmentioning

confidence: 99%

Quantum computational advantage via high-dimensional Gaussian boson sampling

et al. 2022

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Photonics is a promising platform for demonstrating a quantum computational advantage (QCA) by outperforming the most powerful classical supercomputers on a well-defined computational task. Despite this promise, existing proposals and demonstrations face challenges. Experimentally, current implementations of Gaussian boson sampling (GBS) lack programmability or have prohibitive loss rates. Theoretically, there is a comparative lack of rigorous evidence for the classical hardness of GBS. In this work, we make progress in improving both the theoretical evidence and experimental prospects. We provide evidence for the hardness of GBS, comparable to the strongest theoretical proposals for QCA. We also propose a QCA architecture we call high-dimensional GBS, which is programmable and can be implemented with low loss using few optical components. We show that particular algorithms for simulating GBS are outperformed by high-dimensional GBS experiments at modest system sizes. This work thus opens the path to demonstrating QCA with programmable photonic processors.

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Section: Resultsmentioning

confidence: 99%

Quantum computational advantage via high-dimensional Gaussian boson sampling

et al. 2022

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“…This result alone could play an important role e.g. in experimental scenarios like [8] which are by construction limited to a one-dimensional walking space but have a higher than two-dimensional coin space. Equation (27) shows that the various phases ϕ could be accessed by varying a phase parameter in the step operator, which could perhaps be achieved directly by means of sub-wavelength optical pulse dilations.…”

Section: Applicationsmentioning

confidence: 96%

“…With a special case of k = 1, we obtain a walk on a line with doubled edges. This is an interesting scenario because it is one the dynamics of which are explored experimentally in [8].…”

Section: Projection Theorymentioning

confidence: 99%

Projection Theorem for Discrete-Time Quantum Walks

Potoček

2020

Electron. Proc. Theor. Comput. Sci.

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We make and generalize the observation that summing of probability amplitudes of a discrete-time quantum walk over partitions of the walking graph consistent with the step operator results in a unitary evolution on the reduced graph which is also a quantum walk. Since the effective walking graph of the projected walk is not necessarily simpler than the original, this may bring new insights into the dynamics of some kinds of quantum walks using known results from thoroughly studied cases like Euclidean lattices. We use abstract treatment of the walking space and walker displacements in aim for a generality of the presented statements. Using this approach we also identify some pathological cases in which the projection mapping breaks down.For walks on lattices, the operation typically results in quantum walks with hyper-dimensional coin spaces. Such walks can, conversely, be viewed as projections of walks on inaccessible, larger spaces, and their properties can be inferred from the parental walk. We show that this is is the case for a lazy quantum walk, a walk with large coherent jumps and a walk on a circle with a twisted boundary condition. We also discuss the relation of this theory to the time-multiplexing optical implementations of quantum walks. Moreover, this manifestly irreversible operation can, in some cases and with a minor adjustment, be undone, and a quantum walk can be reconstructed from a set of its projections.

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“…universal quantum simulator [72][73][74][75][76]. We devised a looped Michelson interferometer as a platform for time-multiplexed quantum walks, which overcomes some of the restrictions of previous implementations [77]. The main advantage of this architecture is a higher dimensional internal state for walkers (i.e., the photons), arising from the additionally available traveling direction in the loop, clockwise and counter-clockwise.…”

Section: A Motivation and Setup Descriptionmentioning

confidence: 99%

“…In addition, we successfully implemented three electro-optic modulators (EOMs) in our setup to manipulate the polarization of the travelling photons. This increased configurability allowed us to study the walker's evolution on complex graph structures, such as realizing quantum walks on a circle with periodic boundary conditions and other scenarios which are only accessible with higher dimensional internal states [77].…”

Section: A Motivation and Setup Descriptionmentioning

confidence: 99%

Quantum photonics with active feedback loops

Engelkemeier,

Lorz,

et al. 2020

Preprint

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We develop a unified theoretical framework for the efficient description of multi-photon states generated and propagating in loop-based optical networks which contain nonlinear elements. These active optical components are modeled as nonlinear media, resembling a two-mode squeezer. First, such nonlinear components can be seeded to manipulate quantum states of light, as such enabling photon addition protocols. And, second, they can function as an amplifying medium. To prove the practical importance of our approach, the impact of multiple round trips is analyzed for states propagating in experimentally relevant loop configurations of networks, such as time-multiplexed driven quantum walks and iterative photon-number state generation protocols. Our method not only enables us to model such complex systems but also allows us to propose alternative setups that overcome previous limitations. To characterize the systems under study, we provide exact expressions for fidelities with target states, success probabilities of heralding-type measurements, and correlations between optical modes, including many realistic imperfections. Moreover, we provide an easily implementable numerical approach by devising a vector-type representation of photonic states, measurement operators, and passive and active processes.

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Photonic quantum walks with four-dimensional coins

Cited by 24 publications

References 76 publications

Quantum computational advantage via high-dimensional Gaussian boson sampling

Quantum computational advantage via high-dimensional Gaussian boson sampling

Projection Theorem for Discrete-Time Quantum Walks

Quantum photonics with active feedback loops

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