Implementation of Quantum Search Algorithm using Classical Fourier Optics

Bhattacharya, Nandini; Heuvell, H.B. van Linden van den; Spreeuw, R. J. C.

doi:10.1103/physrevlett.88.137901

Cited by 158 publications

(114 citation statements)

References 29 publications

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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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Section: Introductionmentioning

confidence: 99%

Scattering theory of topological phases in discrete-time quantum walks

2014

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“…[6,5,4]-where it differs from them is in the actual physical implementation. All these wave implementations require exponentially more spatial resources compared to their digital counterparts, O(N) vs. O(log 2 N).…”

Section: Possible Applicationsmentioning

confidence: 99%

“…The wave version of the algorithm requires N distinct wave modes, instead of n qubits, but does not involve quantum entanglement at any stage [4]. Such a wave search has been experimentally implemented using classical Fourier optics, with a phase-shift plate providing the oracle [5]. An analogue version of the algorithm has been described using a classical coupled pendulum model, where one of the pendulums is slightly different than the rest and the uniform superposition state |s is identified with the center-of-mass mode [6].…”

Section: The Optimal Search Algorithmmentioning

confidence: 99%

Wave Algorithms: Optimal Database Search and Catalysis

Patel¹

2006

AIP Conference Proceedings

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Abstract. Grover's database search algorithm, although discovered in the context of quantum computation, can be implemented using any physical system that allows superposition of states. A physical realization of this algorithm is described using coupled simple harmonic oscillators, which can be exactly solved in both classical and quantum domains. Classical wave algorithms are far more stable against decoherence compared to their quantum counterparts. In addition to providing convenient demonstration models, they may have a role in practical situations, such as catalysis. COMPUTING WITH WAVESAny physical system-with some initial state, some final state, and some interaction in between-is a candidate for processing information. One only needs to construct a suitable map between physical properties of the system and abstract mathematical variables. Most of the development in computer algorithms has been in the framework of "particle-like" discrete digital languages. It is known that "wave-like" analogue computation can also be carried out (e.g. using RLC circuits), but that has not been explored as intensively. The obvious reason is that discrete variables allow a degree of precision, by implementation of error correction procedures, that continuous variables cannot provide. In addition, computational complexity is believed to be the same for digital and analogue algorithms, so the choice between the two is left to considerations of hardware stability.With the advent of quantum computation, several quantum algorithms have been discovered, which are superior to their counterparts based on Boolean logic. Naturally, with both "particle-like" and "wave-like" behaviour at their disposal, quantum algorithms cannot do any worse than their classical counterparts. It is routinely stated that the simple parallelism provided by superposition and interference of quantum states is the key ingredient for the superiority of quantum algorithms. Now both superposition and interference are generic features of wave dynamics, and it is worthwhile to investigate the advantages they bring to an algorithm by exploring implementations based on "wave-like" behaviour alone. Of course, the classical wave implementations will be less efficient than the fully quantum ones, but they are expected to be much more stable (in particular, they have no entanglement and much weaker decoherence) and so may turn 1

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“…Otherwise, the analogy between quantum mechanics and classical optics has been recently explored [1][2][3][4][5][6]. The key idea is to exploit the wave nature of the electromagnetic field in order to represent the quantum state of one or more particles.…”

Section: Introductionmentioning

confidence: 99%

Optically simulated universal quantum computation

Francisco¹,

Ledesma²,

Wetter³

et al. 2008

AIP Conference Proceedings

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Articles you may be interested inQuantum computer aided design simulation and optimization of semiconductor quantum dots J. Appl. Phys. 114, 164302 (2013) Abstract. Recently, classical optics based systems to emulate quantum information processing have been proposed. The analogy is based on the possibility of encoding a quantum state of a system with a 2^-dimensional Hilbert space as an image in the input of an optical system. The probability amplitude of each state of a certain basis is associated with the complex amplitude of the electromagnetic field in a given slice of the laser wavefront. Temporal evolution is represented as the change of the complex amplitude of the field when the wavefront pass through a certain optical arrangement. Different modules that represent universal gates for quantum computation have been implemented. For instance, unitary operations acting on the qbits space (or U(2) gates) are represented by means of two phase plates, two spherical lenses and a phase grating in a typical image processing set up. In this work, we present CNOT gates which are emulated by means of a cube prism that splits a pair of adjacent rays incoming from the input image. As an example of application, we present an optical module that can be used to simulate the quantum teleportation process. We also show experimental results that illustrate the validity of the analogy. Although the experimental results obtained are promising and show the capability of the system for simulate the real quantum process, we must take into account that any classical simulation of quantum phenomena, has as fundamental limitation the impossibility of representing non local entanglement. In this classical context, quantum teleportation has only an illustrative interpretation.

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Implementation of Quantum Search Algorithm using Classical Fourier Optics

Cited by 158 publications

References 29 publications

Scattering theory of topological phases in discrete-time quantum walks

Scattering theory of topological phases in discrete-time quantum walks

Wave Algorithms: Optimal Database Search and Catalysis

Optically simulated universal quantum computation

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