Rapid solution of problems by quantum computation

Deutsch, David; Jozsa, Richard

doi:10.1098/rspa.1992.0167

Cited by 1,825 publications

(691 citation statements)

References 2 publications

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“…Deutsch-Jozsa (DJ) algorithm provides a demonstration of the advantage of quantum superpositions over classical computing [20]. The DJ algorithm determines the type of an unknown function when it is either constant or balanced.…”

Section: Deutsch-jozsa Algorithmmentioning

confidence: 99%

“…However the DJ algorithm would require only a single function call [20]. The Cleve version of DJ algorithm implemented by using a unitary transformation by the propagator U f while adding an extra qubit, is given by [35],…”

Section: Deutsch-jozsa Algorithmmentioning

confidence: 99%

“…The scheme is easily scalable to higher qubit systems. The geometric controlled phase gates were used to implement Deutsch-Jozsa (DJ) algorithm [20] and Grover's search algorithm [21] in the two-qubit system. To the best of our knowledge, this is the first implementation of quantum algorithms using geometric phase.…”

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confidence: 99%

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Use of non-adiabatic geometric phase for quantum computing by NMR

Das

Kumar

2005

Journal of Magnetic Resonance

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Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled logic gates by controlled dynamics of qubits. In controlled dynamics, one qubit undergoes coherent evolution and acquires appropriate phase, depending on the state of other qubits. If the evolution is geometric, then the phase acquired depend only on the geometry of the path executed, and is robust against certain types of errors. This phenomenon leads to an inherently fault-tolerant quantum computation. Here we suggest a technique of using non-adiabatic geometric phase for quantum computation, using selective excitation. In a two-qubit system, we selectively evolve a suitable subsystem where the control qubit is in state |1 , through a closed circuit. By this evolution, the target qubit gains a phase controlled by the state of the control qubit. Using these geometric phase gates we demonstrate implementation of Deutsch-Jozsa algorithm and Grover's search algorithm in a two-qubit system.

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Section: Deutsch-jozsa Algorithmmentioning

confidence: 99%

Section: Deutsch-jozsa Algorithmmentioning

confidence: 99%

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Use of non-adiabatic geometric phase for quantum computing by NMR

Das

Kumar

2005

Journal of Magnetic Resonance

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“…σ (2) 0 is the polarization operator of the second qubit corresponding to the state |0 . The polarization operators of j th qubit when it is in state |0 or |1 are σ (j) 0 = |0 0| = 1 0 0 0…”

Section: The Conditional Phase Shift Gatementioning

confidence: 99%

“…Theoretical possibility of quantum information processing (QIP) has generated a lot of enthusiasm for its experimental realization [1][2][3][4][5][6][7][8]. Nuclear magnetic resonance (NMR) has played a leading role for practical demonstration of quantum algorithms and quantum gates .…”

Section: Introductionmentioning

confidence: 99%

Implementation of conditional phase-shift gate for quantum information processing by NMR, using transition-selective pulses

Das

Mahesh

Kumar

2002

Journal of Magnetic Resonance

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Experimental realization of quantum information processing in the field of nuclear magnetic resonance (NMR) has been well established. Implementation of conditional phase shift gate has been a significant step, which has lead to realization of important algorithms such as Grover's search algorithm and quantum Fourier transform. This gate has so far been implemented in NMR by using coupling evolution method. We demonstrate here the implementation of the conditional phase shift gate using transition selective pulses. As an application of the gate, we demonstrate Grover's search algorithm and quantum Fourier transform by simulations and experiments using transition selective pulses.

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Toward a charge-transfer model of neuromolecular computing

Wallace

Price

Breitbeil

1998

Int. J. Quant. Chem.

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A computational model of charge transfer through an associated polyenic system is presented. This model is based on proposed transient alignment of adjacent ethylenes of phospholipid diacyls in the neural membrane. Influx of anions and cations into the cytosol at ; 10 8 ionsrs at ligand-gated channels hypothetically establishes the conditions for charge transfer through adjacent diacyl ethylenes. It is suggested that this process produces interactions between phospholipid potential energy hypersurfaces.Ž . These interactions operating in many-dimensional Hilbert space represent a form of massively parallel computation. Basic theoretical principles of quantum computing relevant to the present model are briefly discussed. A preliminary computational model of charge transfer through stacked ethylenes is then presented. In this model molecules were aligned with planes parallel and perpendicular. Singly charged counterions were positioned at the ends of the stacks and ab initio Hartree᎐Fock calculations at the Ž . 6-31 q G d, p level were carried out. Degree of charge transfer between counterions was monitored by Mulliken population analysis from which atomic charges and dipole moments were calculated. The results of these calculations are interpreted in a larger neurobiological context. Models are proposed which relate the charge-transfer process to Ž . ion channel dynamics openrclosed , changes in membrane potential, and macroscopic memory systems. A hypothetical feedback circuitry which could regulate membrane potential and prevent recurrent excitation or hyperpolarization is described. Potential tests of the model utilizing photoinduced charge transfer through a polyenic molecular wire are proposed. It is concluded that this research could lead to a better understanding of computational processes in neurophysiology and cognition.

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Rapid solution of problems by quantum computation

Abstract: A class of problems is described which can be solved more efficiently by quantum computation than by any classical or stochastic method. The quantum computation solves the problem with certainty in exponentially less time than any classical deterministic computation.

Cited by 1,825 publications

References 2 publications

Use of non-adiabatic geometric phase for quantum computing by NMR

Use of non-adiabatic geometric phase for quantum computing by NMR

Implementation of conditional phase-shift gate for quantum information processing by NMR, using transition-selective pulses

Toward a charge-transfer model of neuromolecular computing

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