Quantum Mechanics Helps in Searching for a Needle in a Haystack

Grover, Lov K.

doi:10.1103/physrevlett.79.325

Cited by 3,902 publications

(3,440 citation statements)

References 11 publications

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“…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%

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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confidence: 99%

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

Das

Kumar

2005

Journal of Magnetic Resonance

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“…Grover's search algorithm can search (with high probability) any state of an N-qubit system in O( √ 2 N ) iterations [5]. Each iteration has two steps, namely 'conditional sign-flip' and 'inversion about average'.…”

Section: Simulationsmentioning

confidence: 99%

“…This step can be realized by applying a Hadamard gate 'H' (on all qubits) before and after a conditional phase shift C 000 (π) gate, hence Λ = HC 000 (π)H [5,13]. It may be noted that the C 000 (π) gate is required because we started with |000 pseudo-pure state, whereas if one starts with another pseudo-pure state, say |001 , then the corresponding phase shift gate C 001 (π) will be required.…”

Section: Simulationsmentioning

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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“…• Four is also the largest number of states which can be uniquely identified by a single yes/no question in a quantum search algorithm (Grover 1997).…”

Section: Structural Informationmentioning

confidence: 99%

“…Proline is the special amino acid in class II, involved in trans-cis transformations, while cysteine is the special amino acid in class I, involved in tying together far separated regions of the polypeptide chain.) A look at the optimal solutions of the quantum search algorithm (Grover 1997) brings out another interesting feature. Living organisms form DNA and polypeptide chains by joining their building blocks together in sequential assembly line operations.…”

Section: Putting Things Togethermentioning

confidence: 99%

Carbon — the first frontier of information processing

Patel

2002

J Biosci

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Information is often encoded as an aperiodic chain of building blocks.Modern digital computers use bits as the building blocks, but in general the choice of building blocks depends on the nature of the information to be encoded. What are the optimal building blocks to encode structural information? This can be analysed by substituting the operations of addition and multiplication of conventional arithmetic with translation and rotation.It is argued that at the molecular level, the best component for encoding discretised structural information is carbon. Living organisms discovered this billions of years ago, and used carbon as the back-bone for constructing proteins that function according to their structure. Structural analysis of polypeptide chains shows that an efficient and versatile structural language of 20 building blocks is needed to implement all the tasks carried out by proteins. Properties of amino acids indicate that the present triplet genetic code was preceded by a more primitive one, coding for 10 amino acids using two nucleotide bases.Keywords. Amino acid; aminoacyl-tRNA synthetase; computation; genetic code; information; lattice models; protein structure; quantum search; tetrahedral geometry Structural informationIt is a characteristic of living organisms to acquire information, interpret it and pass it on, often using it and refining it along the way. This information can be in various forms or languages. It can be genetic information passed on from the parent to the offspring, sensory information conveyed by the sense organ to the brain, linguistic information communicated by one being to another, or numerical data entered in a computer for later use. It is advantageous to process the information efficiently, and not in any haphazard manner. In case of living organisms, Darwinian selection during evolution can be considered the driving force for such optimisation. In general, information processing is optimised following two guidelines: minimisation of physical resources (time as well as space), and minimisation of errors.A striking feature of all the forms of information listed above is that the messages are represented as aperiodic chains of discrete building blocks. Such a representation, called digitisation of the message, is commonplace due to its many advantages. Discretisation makes it possible to correct errors arising from local disturbances, and so it is desirable even when the underlying physical variables are continuous (e.g. voltages and currents in computers). It is also easier to handle several variables each spanning a small range than a single variable covering a large range. Any desired message can then be constructed by putting together as many as necessary of the smaller range variables, while the instruction set required to manipulate each variable is substantially simplified. This simplification means that only a limited number of processes have to be physically implemented leading to high speed computation. An important question, therefore, is to figure out the best way...

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Quantum Mechanics Helps in Searching for a Needle in a Haystack

Cited by 3,902 publications

References 11 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

Carbon — the first frontier of information processing

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