Experimental realization of a Shor-type quantum algorithm

Chuang, Issac

doi:10.1364/icqi.2001.fqipa3

Cited by 11 publications

(15 citation statements)

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“…The fidelity is fundamentally limited by the combination ω ba τ which should be as large as possible. Using characteristic values of ω ba = 2π×6835 MHz and τ = 100 µs gives ω ba τ ∼ 4×10 6 input state decoherence error rotation error which is sufficiently large for high fidelity operation.…”

Section: Two-qubit Phase Gatementioning

confidence: 99%

“…While a useful processor remains far off, ground breaking experiments have demonstrated controlled evolution of a few qubits and implemented basic quantum algorithms for computation and error correction [2,3,4,5,6,7,8]. Among the range of physical systems that have been identified as candidates for implementing quantum logic the most extensive laboratory results so far have been obtained with cold trapped ions [9] and nuclear magnetic resonance (NMR) in macroscopic samples [10,11].…”

Section: Introductionmentioning

confidence: 99%

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Analysis of a quantum logic device based on dipole-dipole interactions of optically trapped Rydberg atoms

2005

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We present a detailed analysis and design of a neutral atom quantum logic device based on atoms in optical traps interacting via dipole-dipole coupling of Rydberg states. The dominant physical mechanisms leading to decoherence and loss of fidelity are enumerated. Our results support the feasibility of performing single and two-qubit gates at MHz rates with decoherence probability and fidelity errors at the level of 10 −3 for each operation. Current limitations and possible approaches to further improvement of the device are discussed.

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Section: Two-qubit Phase Gatementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of a quantum logic device based on dipole-dipole interactions of optically trapped Rydberg atoms

2005

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“…Entanglement, which seems the "spookiest" [6] to many people, has been argued to be the crucial quantum mechanical resource [7]. This belief informs, for example, the criticism that NMR experiments performed to date [8] have not actually realized quantum algorithms because at each timestep the state of the system can be described as a probabilistic ensemble of unentangled quantum states [9]. Lloyd [10] and Ahn, Weinacht & Bucksbaum [11] have recently suggested, however, that entanglement is not necessary for Grover's quantum search algorithm [4].…”

mentioning

confidence: 99%

Sophisticated Quantum Search Without Entanglement

Meyer¹

2000

Phys. Rev. Lett.

231

182

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Although entanglement is widely considered to be necessary for quantum algorithms to improve on classical ones, Lloyd has observed recently that Grover's quantum search algorithm can be implemented without entanglement, by replacing multiple particles with a single particle having exponentially many states. We explain that this maneuver removes entanglement from any quantum algorithm. But all physical resources must be accounted for to quantify algorithm complexity, and this scheme typically incurs exponential costs in some other resource(s). In particular, we demonstrate that a recent experimental realization requires exponentially increasing precision. There is, however, a quantum algorithm which searches a 'sophisticated' database (not unlike a Web search engine) with a single query, but which we show does not require entanglement even for multiparticle implementations.

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“…The basic requirement is that the experimenter has access to two states of a quantum system that can be effectively decoupled from environmental noise for a sufficiently long time, and that transitions between these two states can be controlled to simulate a number of elementary quantum gates (unitary transformations). Systems that have been investigated intensively are single photon systems, cavity QED, nuclear spins (using NMR in suitable molecules), atomic levels in ion traps, and Josephson rings [12,13,14]. We believe that if one could build one-dimensional spin J systems with J ≥ 3/2, which interact through an anisotropic interaction such as in the XXZ model, this would be a good starting point to encode qubits and unitary gates.…”

Section: Introductionmentioning

confidence: 99%

Isolated eigenvalues of the ferromagnetic spin-J XXZchain with kink boundary conditions

et al. 2008

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Abstract:We investigate the low-lying excited states of the spin J ferromagnetic XXZ chain with Ising anisotropy ∆ and kink boundary conditions. Since the third component of the total magnetization, M , is conserved, it is meaningful to study the spectrum for each fixed value of M . We prove that for J ≥ 3/2 the lowest excited eigenvalues are separated by a gap from the rest of the spectrum, uniformly in the length of the chain. In the thermodynamic limit, this means that there are a positive number of excitations above the ground state and below the essential spectrum.

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Experimental realization of a Shor-type quantum algorithm

Cited by 11 publications

References 0 publications

Analysis of a quantum logic device based on dipole-dipole interactions of optically trapped Rydberg atoms

Analysis of a quantum logic device based on dipole-dipole interactions of optically trapped Rydberg atoms

Sophisticated Quantum Search Without Entanglement

Isolated eigenvalues of the ferromagnetic spin-J XXZchain with kink boundary conditions

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