Implementation of the Deutsch–Jozsa algorithm on an ion-trap quantum computer

Gulde, S.; Riebe, M.; Lancaster, G. P. T.; Becher, Christoph; Eschner, J.; Häffner, Hartmut; Schmidt-Kaler, F.; Chuang, Isaac L.; Blatt, R.

doi:10.1038/nature01336

Cited by 452 publications

(330 citation statements)

References 19 publications

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“…We then prepare the |0, DDD · · · D -state with N π-pulses on the carrier transition applied to ions #1 to #N , denoted by R C n (θ = π) (the notation is detailed in Gulde et al 15 ; we do not specify the phase of the pulses because its particular value is irrelevant in this context). Then this state is checked for vanishing fluorescence with a photomultiplier tube.…”

Section: Methodsmentioning

confidence: 99%

Scalable multiparticle entanglement of trapped ions

Häffner

Hänsel²,

Roos

et al. 2005

Nature

1,144

1,134

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Entanglement, its generation, manipulation and fundamental understanding is at the very heart of quantum mechanics. The phrase entanglement was coined by Erwin Schrödinger in 1935 for particles that are described by a common wave function where individual particles are not independent of each other but where their quantum properties are inextricably interwoven 1 . Entanglement properties of two and three particles have been studied extensively and are very well understood. Entanglement of four 2 and five 3 particles was demonstrated experimentally. However, both creation and characterization of entanglement become exceedingly difficult for multi-particle systems. Thus the availability of such multiparticle entangled states together with the full information on these states in form of their 1

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Section: Methodsmentioning

confidence: 99%

Scalable multiparticle entanglement of trapped ions

Häffner

Hänsel²,

Roos

et al. 2005

Nature

1,144

1,134

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“…The memory effects were further applied as important physical resources 28 to substantially improve the performance of the quantum algorithm with the assistance of the DD protection method. 26 The Deutsch-Jozsa algorithm, [38][39][40] which can be used to determine whether a coin is fair or fake in a single examination step, 40,41 is one of the seminal algorithms used to demonstrate the advantages of quantum computations. Experimentally, the refined Deutsch-Jozsa algorithm (RDJA) [38][39][40] was implemented with a single spin qubit of the NV center to study the memory effect of a non-Markovian environment, with a bidirectional flow of information between the spin qubit and the spin bath, as shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

Non-Markovianity-assisted high-fidelity Deutsch–Jozsa algorithm in diamond

et al. 2018

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The memory effects in non-Markovian quantum dynamics can induce the revival of quantum coherence, which is believed to provide important physical resources for quantum information processing (QIP). However, no real quantum algorithms have been demonstrated with the help of such memory effects. Here, we experimentally implemented a non-Markovianity-assisted highfidelity refined Deutsch-Jozsa algorithm (RDJA) with a solid spin in diamond. The memory effects can induce pronounced nonmonotonic variations in the RDJA results, which were confirmed to follow a non-Markovian quantum process by measuring the non-Markovianity of the spin system. By applying the memory effects as physical resources with the assistance of dynamical decoupling, the probability of success of RDJA was elevated above 97% in the open quantum system. This study not only demonstrates that the non-Markovianity is an important physical resource but also presents a feasible way to employ this physical resource. It will stimulate the application of the memory effects in non-Markovian quantum dynamics to improve the performance of practical QIP.npj Quantum Information (2018) 4:3 ; doi:10.1038/s41534-017-0053-z INTRODUCTION Based on quantum phenomena, such as superposition, correlation and entanglement, quantum information processing (QIP) has provided great advantages over its classical counterpart 1-3 in efficient algorithms, 4,5 secure communication, 6,7 and highprecision metrology. [8][9][10][11][12][13][14][15][16] However, quantum superposition and correlation are fragile in an open quantum system. Notorious decoherence, [17][18][19] which is caused by interactions with noisy environments, is a major hurdle in the realization of fault-tolerant coherent operation 20,21 and scalable quantum computation. To further expand the implementation of QIP in open quantum systems, full understanding and control of environmental interactions are required. 17,[22][23][24] Many techniques have been developed to address this issue, including decoherence-free subspaces, 25 dynamical decoupling (DD) 13,26 and the geometric approach. 27 However, actively utilizing the environmental interactions would represent a significant achievement, compared with passively shielding them.Usually, the interaction of an open quantum system with a noisy environment exhibits memory-less dynamics with an irreversible loss of quantum coherence, that can be described by the Born-Markov approximation. 28 However, because of strong system-environment couplings, structured or finite reservoirs, low temperatures, or large initial system-environment correlations, the dynamics of an open quantum system may deviate substantially from the Born-Markov approximation and follow a non-Markovian process. [28][29][30][31][32] In such a process, the pronounced memory effect, which is the primary feature of a non-Markovian environment, can be used to revive the genuine quantum properties, 28-34 such as quantum coherence and correlations. Consequently, improving the performance of QIP by utilizing memo...

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“…2 is interesting since it involves only n = 3 qubits and a few tens on quantum gates. Therefore this quantum computation seems to be accessible or close to the present capabilities of NMR-based [17,18] and ion-trap [19] quantum processors.…”

Section: Quantum Computing Of Dynamical Localizationmentioning

confidence: 81%

Quantum Computing and Information Extraction for Dynamical Quantum Systems

Benenti

Casati

Montangero

2004

Quantum Information Processing

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We discuss the simulation of a complex dynamical system, the so-called quantum sawtooth map model, on a quantum computer. We show that a quantum computer can be used to efficiently extract relevant physical information for this model. It is possible to simulate the dynamical localization of classical chaos and extract the localization length of the system with quadratic speed up with respect to any known classical computation. We can also compute with algebraic speed up the diffusion coefficient and the diffusion exponent both in the regimes of Brownian and anomalous diffusion. Finally, we show that it is possible to extract the fidelity of the quantum motion, which measures the stability of the system under perturbations, with exponential speed up.

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Implementation of the Deutsch–Jozsa algorithm on an ion-trap quantum computer

Cited by 452 publications

References 19 publications

Scalable multiparticle entanglement of trapped ions

Scalable multiparticle entanglement of trapped ions

Non-Markovianity-assisted high-fidelity Deutsch–Jozsa algorithm in diamond

Quantum Computing and Information Extraction for Dynamical Quantum Systems

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