Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance

Vandersypen, L. M. K.; Steffen, Matthias; Breyta, Gregory; Yannoni, C. S.; Sherwood, Mark; Chuang, Isaac L.

doi:10.1038/414883a

Cited by 1,473 publications

(1,053 citation statements)

References 31 publications

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“…Two important quantum algorithms, the Shor algorithm [23], [24] and the Grover algorithm [25], [26] have been proposed in 1994 and 1996, respectively. 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.…”

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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Section: Introductionmentioning

confidence: 99%

Quantum Reinforcement Learning

Dong

Chen

2005

Lecture Notes in Computer Science

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“…Here a < N is a random number that has no common factors with N. Once M has been determined at least one factor of N can be found by computing the greatest common divisor of N and a M/2 ± 1. The quantum network for N = 15, a = 11 can be found in [10]. The quantum network contains Hadamard and CNOT gates and a network to perform the Fourier transform, containing Hadamard gates and controlled phase shifts.…”

Section: Factoring N = 15 Using Shor's Algorithmmentioning

confidence: 99%

Deterministic Event-based Simulation of Universal Quantum Computation

Michielsen

Raedt

2007

Springer Proceedings in Physics

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Summary. We demonstrate that locally connected networks of classical processing units that have primitive learning capabilities can be used to perform a deterministic, event-based simulation of universal quantum computation. The new simulation method is applied to implement Shor 's factoring algorithm. IntroductionThe basic ideas of quantum computation were formulated more than twenty years ago [1,2]. Ten years ago DiVincenzo has proven that the CNOT gate and single-qubit operations constitute a set of gates that can be used to construct a universal quantum computer [3]. This statement is equivalent to the one that a digital classical computer can be constructed by means of NAND gates only. Conventional computers can simulate the physical behavior of quantum computer hardware by solving the (time-dependent) Schrödinger equation [4,5]. However, the idea of building a quantum computer has lead to many advances in nanotechnology, making it possible to control individual ions, atoms, photons and the like and these single events cannot be described by quantum theory. In this paper we demonstrate how a quantum computer can be built from locally-connected networks of processing units with a primitive learning capability that deterministically generate events with frequencies that agree with the corresponding quantum mechanical probabilities.

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“…Extremely sub-wavelength metamaterials are also relevant to applications such as controlling spontaneous emission [27][28][29] and quantum information processing [30][31][32][33][34][35][36][37][38][39][40]. The light-matter interactions between free-space electromagnetic modes and quantum emitters are generally weak due to the small interaction cross-section of the latter.…”

Section: Introductionmentioning

confidence: 99%

Extremely Sub-Wavelength Negative Index Metamaterial

Zhang¹,

Usi²,

Khan³

et al. 2015

PIER

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Abstract-We present an extremely sub-wavelength negative index metamaterial structure operating at radio frequency. The unit cell of the metamaterial consists of planar spiral and meandering wire structures separated by dielectric substrate. The ratio of the free space wavelength to unit cell size in the propagation direction is record breaking 1733 around the resonance frequency. The proposed metamaterial also possesses the most extreme refractive index of −109 that has been recorded to date. Underlying magnetic and electric response originate from the spiral and meandering wire, respectively. We show that the meandering wire is the key element to improve the transparency of the negative index metamaterial.

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Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance

Cited by 1,473 publications

References 31 publications

Quantum Reinforcement Learning

Quantum Reinforcement Learning

Deterministic Event-based Simulation of Universal Quantum Computation

Extremely Sub-Wavelength Negative Index Metamaterial

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