Optical Implementation of Grover’s Algorithm: It’s all Done with Mirrors

Kwiat, Paul G.; Mitchell, Jay; Schwindt, Peter D. D.; White, Andrew G.

doi:10.1007/0-306-47097-7_41

Cited by 3 publications

(5 citation statements)

References 8 publications

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“…the simple projection operator given by Eq. 3, require a cascade of interferometers where the output of one interferometer is used as the input of the next [5,23,26]. Therefore, as the dimension of each state space increases, it becomes exceedingly hard to stabilize and is simply impractical beyond two qubits.…”

Section: Discussion: Advantages and Limitationsmentioning

confidence: 99%

“…After the unitary evolution the output needs to be projected onto the computational basis and irreversibly measured. One realization of the QCM has been linear optical quantum computing (LOQC) and one-way quantum computing (OWQC), which are also known as cluster-state quantum computing [2][3][4][5]. The essential feature of each of these approaches involves either a non-linear measuring process or a preparation of hyper-entangled input states (|IN ), or both.…”

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confidence: 99%

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Quantum computing in a piece of glass

Miller

Alsing

Kreymerman

et al. 2011

Quantum Information and Computation IX

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Quantum gates and simple quantum algorithms can be designed utilizing the diffraction phenomena of a photon within a multiplexed holographic element. The quantum eigenstates we use are the photon's linear momentum (LM) as measured by the number of waves of tilt across the aperture. Two properties of quantum computing within the circuit model make this approach attractive. First, any conditional measurement can be commuted in time with any unitary quantum gate - the timeless nature of quantum computing. Second, photon entanglement can be encoded as a superposition state of a single photon in a higher-dimensional state space afforded by LM. Our theoretical and numerical results indicate that OptiGrate's photo-thermal refractive (PTR) glass is an enabling technology. We will review our previous design of a quantum projection operator and give credence to this approach on a representative quantum gate grounded on coupled-mode theory and numerical simulations, all with parameters consistent with PTR glass. We discuss the strengths (high efficiencies, robustness to environment) and limitations (scalability, crosstalk) of this technology. While not scalable, the utility and robustness of such optical elements for broader quantum information processing applications can be substantial.Comment: 14 pages, 6 figure

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Section: Discussion: Advantages and Limitationsmentioning

confidence: 99%

mentioning

confidence: 99%

Quantum computing in a piece of glass

Miller

Alsing

Kreymerman

et al. 2011

Quantum Information and Computation IX

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show abstract

“…3, require a cascade of interferometers where the output of one interferometer is used as the input of the next. 7,26,30 Therefore, as the dimension of each state space increases, it becomes exceedingly hard to stabilize and is simply impractical beyond two qubits. Other approaches, such as crossed thin gratings lack the efficiency needed for QIP.…”

Section: Discussion: Advantages and Limitationsmentioning

confidence: 99%

“…One realization of the QCM has been linear optical quantum computing (LOQC) and one-way quantum computing (OWQC), which are also known as cluster-state quantum computing. [4][5][6][7] The essential feature of each of these approaches involves either a non-linear measuring process or a preparation of hyper-entangled input states (|IN ), or both. Here a sequence of measurements are made to project the output state (|OU T ) onto one or another of the computational basis states, i.e onto a mutually unbiased basis (MUB).…”

Section: Photonic Quantum Algorithms Within a Volume Hologrammentioning

confidence: 99%

A CNOT gate in a glass chip

2015

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In our earlier work we posited that simple quantum gates and quantum algorithms can be designed utilizing the diffraction phenomena of a photon within a multiplexed holographic element. The quantum eigenstates we use are the photons transverse linear momentum (LM) as measured by the number of waves of tilt across the aperture. Two properties of linear optical quantum computing (LOQC) within the circuit model make this approach attractive. First, any conditional measurement can be commuted in time with any unitary quantum gate; and second, photon entanglement can be encoded as a superposition state of a single photon in a higherdimensional state space afforded by LM. We describe here our experimental results for construction a controlled NOT (CNOT) gate logic within a holographic medium, and present the quantum state tomography for this device. Our theoretical and numerical results indicate that OptiGrates photo-thermal refractive (PTR) glass is an enabling technology. This work has been grounded on coupled-mode theory and numerical simulations, all with parameters consistent with PTR glass. We discuss the strengths (high efficiencies, robustness to environment) and limitations (scalability, crosstalk) of this technology. While not scalable, the utility and robustness of such optical elements for broader quantum information processing applications can be substantial.

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“…Optical systems that use photonic degrees of freedom play a key role in quantum information science and communication. During the ultimate decade scientists proposed optical implementations of all basic quantum computing operations, including Grover's search and Shor's quantum factoring algorithms [1,2]. Another actively studied direction in optical quantum computing is boson sampling [3].…”

Section: Introductionmentioning

confidence: 99%

Modeling two-qubit Grover’s algorithm implementation in a linear optical chip

et al. 2020

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This paper introduces a model of Grover’s algorithm suitable for implementation in a linear photonic chip. We compare two known realizations of its main components, two-qubit CZ gates, in order to define optimal chip architecture. The algorithm operation is simulated considering directional coupler imperfection influence on the scheme parameters. We also determined tolerance boundaries for distortions of the coupler dimensions.

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Optical Implementation of Grover’s Algorithm: It’s all Done with Mirrors

Cited by 3 publications

References 8 publications

Quantum computing in a piece of glass

Quantum computing in a piece of glass

A CNOT gate in a glass chip

Modeling two-qubit Grover’s algorithm implementation in a linear optical chip

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