Experimental Implementation of Fast Quantum Searching

Chuang, Isaac L.; Gershenfeld, Neil; Kubinec, Mark G.

doi:10.1103/physrevlett.80.3408

Cited by 643 publications

(554 citation statements)

References 15 publications

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“…The errors are mainly due to errors in long low power rf pulses (transition selective), during which relaxation and evolution adds to the errors. However, the errors in the present experiment are comparable to those performed earlier using J-evolution [13].…”

Section: Methodssupporting

confidence: 86%

“…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%

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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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Section: Methodssupporting

confidence: 86%

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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“…Grover's search algorithm has been earlier demonstrated by several workers by NMR, all using dynamic phase [30,[42][43][44]39]. The quantum circuit for implementing Grover's search algorithm on two qubit system is given in figure 7(a).…”

Section: Grover's Search Algorithmmentioning

confidence: 99%

“…Figure captions [42,30]. The U x and U 00 phase gates were implemented by non-adiabatic geometric phase using selective excitation by 13.2 ms (6/J) long Gaussian shaped pulses.…”

Section: Acknowledgmentmentioning

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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“…The Shor algorithm can give an exponential speedup for factoring large integers into prime numbers and it has been realized [27] for the factorization of integer 15 using nuclear magnetic resonance (NMR). The Grover algorithm can achieve a square speedup over classical algorithms in unsorted database searching and its experimental implementations have also been demonstrated using NMR [28]- [30] and quantum optics [31], [32] for a system with four states. Some methods have also been explored to connect quantum computation and machine learning.…”

Section: Introductionmentioning

confidence: 99%

Quantum Reinforcement Learning

Dong

Chen

2005

Lecture Notes in Computer Science

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Abstract-The key approaches for machine learning, especially learning in unknown probabilistic environments are new representations and computation mechanisms. In this paper, a novel quantum reinforcement learning (QRL) method is proposed by combining quantum theory and reinforcement learning (RL). Inspired by the state superposition principle and quantum parallelism, a framework of value updating algorithm is introduced. The state (action) in traditional RL is identified as the eigen state (eigen action) in QRL. The state (action) set can be represented with a quantum superposition state and the eigen state (eigen action) can be obtained by randomly observing the simulated quantum state according to the collapse postulate of quantum measurement. The probability of the eigen action is determined by the probability amplitude, which is parallelly updated according to rewards. Some related characteristics of QRL such as convergence, optimality and balancing between exploration and exploitation are also analyzed, which shows that this approach makes a good tradeoff between exploration and exploitation using the probability amplitude and can speed up learning through the quantum parallelism. To evaluate the performance and practicability of QRL, several simulated experiments are given and the results demonstrate the effectiveness and superiority of QRL algorithm for some complex problems. The present work is also an effective exploration on the application of quantum computation to artificial intelligence.Index Terms-quantum reinforcement learning, state superposition, collapse, probability amplitude, Grover iteration.

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Experimental Implementation of Fast Quantum Searching

Cited by 643 publications

References 15 publications

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

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

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

Quantum Reinforcement Learning

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