Experimental implementation of a discrete-time quantum random walk on an NMR quantum-information processor

Ryan, Colm A.; Laforest, Martin; Boileau, Jean-Christian; Laflamme, Raymond

doi:10.1103/physreva.72.062317

Cited by 285 publications

(225 citation statements)

References 27 publications

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“…A quantum walk experiment carried out by Ryan et al used a 3 qubit NMR system to perform a quantum walk on a cycle of size N = 4 (Ryan et al 2005). This is actually a quantum computation of a quantum walk, since the three qubits are used to represent the binary number labelling the vertex (two qubits), and the qubit coin.…”

Section: Quantum Walks In Physical Systemsmentioning

confidence: 99%

Decoherence in quantum walks – a review

Kendon¹

2007

Math. Struct. in Comp. Science

327

385

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The development of quantum walks in the context of quantum computation, as generalisations of random walk techniques, has led rapidly to several new quantum algorithms. These all follow a unitary quantum evolution, apart from the final measurement. Since logical qubits in a quantum computer must be protected from decoherence by error correction, there is no need to consider decoherence at the level of algorithms. Nonetheless, enlarging the range of quantum dynamics to include non-unitary evolution provides a wider range of possibilities for tuning the properties of quantum walks. For example, small amounts of decoherence in a quantum walk on the line can produce more uniform spreading (a top-hat distribution), without losing the quantum speed up. This paper reviews the work on decoherence, and more generally on non-unitary evolution, in quantum walks and suggests what future questions might prove interesting to pursue in this area.

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Section: Quantum Walks In Physical Systemsmentioning

confidence: 99%

Decoherence in quantum walks – a review

Kendon¹

2007

Math. Struct. in Comp. Science

327

385

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“…Some aspects have been realized on the longitudinal modes of a linear optical resonator [7] and in a nuclear magnetic resonance experiment [8]. An implementation based on neutral atoms in a spin-dependent optical lattice[9, 10, 11] has resulted in an experiment recently.…”

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confidence: 99%

Quantum Walk of a Trapped Ion in Phase Space

Schmitz¹,

Matjeschk²,

Schneider³

et al. 2009

Phys. Rev. Lett.

474

448

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We implement the proof of principle for the quantum walk of one ion in a linear ion trap. With a single-step fidelity exceeding 0.99, we perform three steps of an asymmetric walk on the line. We clearly reveal the differences to its classical counterpart if we allow the walker/ion to take all classical paths simultaneously. Quantum interferences enforce asymmetric, non-classical distributions in the highly entangled degrees of freedom (of coin and position states). We theoretically study and experimentally observe the limitation in the number of steps of our approach, that is imposed by motional squeezing. We propose an altered protocol based on methods of impulsive steps to overcome these restrictions, in principal allowing to scale the quantum walk to several hundreds of steps.PACS numbers: 03.67. Ac, 05.40Fb, 0504Jc A quantum walk[1] is the deterministic quantum mechanical extension of a classical random walk. A simple classical version requires two basic operations: Tossing the coin (coin-operation), allowing for two possible and random outcomes. Dependent on this outcome, the walker performs a step to the right or left (stepoperation). In the quantum mechanical extension the operations allow for coherent superpositions of entangled coin and position states. After several iterations the probability to be in a certain position is determined by quantum mechanical interference of the walker state that leads to fundamentally different characteristics of the walk [2].The motivation for studying quantum walks is twofold. On the one hand, many classical algorithms include random walks. Examples can be found in biology, psychology, economics and physics, for example Einstein's simple model for Brownian motion [3]. The extension of the walk to quantum mechanics might allow for substantial speedup of related quantum versions [2], as in prominent algorithms suggested by Shor[4] and Grover [5] due to other quantum-subroutines. On the other hand, the quantum walk could lead to new insights into entanglement and decoherence in mesoscopic systems [6]. These topics might be explored by increasing the amount of walkers -even before any algorithm might benefit from the quantum random walk.Quantum walks have been thoroughly investigated theoretically and first attempts at implementation have been performed with a very limited amount of steps due to a lack of operation fidelity or fundamental restrictions within the protocol. Some aspects have been realized on the longitudinal modes of a linear optical resonator [7] and in a nuclear magnetic resonance experiment [8]. An implementation based on neutral atoms in a spin-dependent optical lattice[9, 10, 11] has resulted in an experiment recently. Other proposals considered an array of microtraps illuminated by a set of microlenses [12] and Bose-Einstein condensates [13]. Travaglione and Milburn[14] proposed a scheme for trapped ions to transfer the high operational fidelities [6] obtained in quantum information processing (QIP) into To implement the deterministic "tossing of t...

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“…Such regimes are important for example in systems in which energy or electrons are transferred from one loop or molecule to another, as they allow to generate quantum correlations between the different systems. Together with helping to understand and model the energy transfer and state transport processes in naturally occurring system, the recent experimental progress in creating quantum walks in various physical systems (NMR [39][40][41], cold ions [42,43], photons [44][45][46][47][48][49], and ultracold atoms [50]) will soon allow to study and engineer the processes we have described here in laboratory.…”

Section: Discussionmentioning

confidence: 99%

Noise-enhanced quantum transport on a closed loop using quantum walks

Chandrashekar

Busch

2014

Quantum Inf Process

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We study the effect of noise on the transport of a quantum state from a closed loop of n−sites with one of the sites as a sink. Using a discrete-time quantum walk dynamics, we demonstrate that the transport efficiency can be enhanced with noise when the number of sites in the loop is small and reduced when the number of sites in the loop grows. By using the concept of measurement induced disturbance we identify the regimes in which genuine quantum effects are responsible for the enhanced transport.

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Experimental implementation of a discrete-time quantum random walk on an NMR quantum-information processor

Cited by 285 publications

References 27 publications

Decoherence in quantum walks – a review

Decoherence in quantum walks – a review

Quantum Walk of a Trapped Ion in Phase Space

Noise-enhanced quantum transport on a closed loop using quantum walks

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