Decoherence Bounds on Quantum Computation with Trapped Ions

Hughes, Richard; James, Daniel F. V.; Knill, Emanuel; Laflamme, Raymond; Petschek, A. G.

doi:10.1103/physrevlett.77.3240

Cited by 89 publications

(85 citation statements)

References 17 publications

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“…We have not considered the effects of decoherence during the gate operations, such as thermalization of the phonon modes, spontaneous emission etc.. The fundamental limits, however, will allow one to perform many gate operations during the decoherence time [8,12].…”

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confidence: 99%

Quantum Gates with “Hot” Trapped Ions

1998

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We propose a scheme to perform a fundamental two-qubit gate between two trapped ions using ideas from atom interferometry. As opposed to the scheme considered by J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995), it does not require laser cooling to the motional ground state.Quantum computation allows the development of polynomial-time algorithms for computational problems such a prime factoring, which have previously been viewed as intractable [1]. This has motivated studies into the feasibility of actual implementation of quantum computers in physical systems [2]. The task of designing a QC is equivalent to finding a physical realization of quantum gates between a set of qubits, where a qubit refers to a two-level system {|0 , |1 }. Any operation can be decomposed into rotations on a single qubit and a universal two-bit gate, e.g. a gate defined bŷImplementation of a quantum computer requires precise control of the Hamiltonian operations and a high degree of coherence. Achieving the conditions for quantum computation is extremely demanding, and only a few systems have been identified as possible candidates to build small scale models in the lab [1][2][3][4]. One of the most promising examples is a string of cold ions stored in a linear trap [3]. In this ion trap quantum computer qubits are stored in long-lived internal atomic ground states. Single bit operations in this system are accomplished by directing different laser beams to each of the ions, and a fundamental gate operation is implemented by exciting the collective quantized motion of the ions with lasers, where the exchange of phonons serves as a data bus to transfer quantum information between the qubits. Prospects of building small ion trap quantum computers in the near future are good, but the question remains whether stringent requirements in implementing two bit quantum gates can be relaxed: while decoherence of the qubit stored in the atomic ground state is not an issue, cooling of ions to the vibrational ground state to prepare a pure initial state for the collective phonon mode remains a challenge [5]. The question arises whether quantum gates can be performed starting from thermal or mixed states of phonon modes. The task of implementing quantum computing in "hot" systems seems particularly timely in view of the recent interest in NMR quantum computing [4], where quantum states are stored as pseudo-pure states in an ensemble of "hot" spins.In this Letter we will discuss the implementation of a universal two-bit gate between two ions in a linear trap with the phonon modes initially in a thermal (mixed) state. The novel concept behind the gate operation is to implement conditional dynamics based on atom interferometry of two entangled atoms [6,7]. The two-bit gate operation proceeds as follows: ion 2 is kicked left or right depending on its internal state with laser light (see Fig. 1(a) at t = 0). Thus the ion 1 will experience a kick via the Coulomb repulsion conditional to the internal state of the first ion. The corresponding wave p...

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confidence: 99%

Quantum Gates with “Hot” Trapped Ions

1998

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“…Furthermore, calculations suggest that it should be possible to trap 20 or more Calcium ions in a linear configuration and manipulate their quantum states by lasers on short enough time scales that many quantum logic operations may be performed before coherence is lost. Only by experiment can the theoretical estimates of performance be confirmed [36,37]. Until all of the sources of experimental error in real devices are thoroughly investigated, it will be impossible to determine what ion and addressing scheme enables one to build the best quantum computer or, indeed, whether it is possible to build a useful quantum computer with cold trap ions at all.…”

Section: Discussionmentioning

confidence: 99%

Trapped Ion Quantum Computer Research at Los Alamos

James

Gulley

Holzscheiter

et al. 1999

Quantum Computing and Quantum Communications

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“…If we set a limit s for the smallest permissible seperation of the closest ions in the string during processing, we obtain [15,4].…”

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confidence: 99%

Speed of ion-trap quantum-information processors

Steane¹,

Roos²,

Stevens³

et al. 2000

Phys. Rev. A

117

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We investigate theoretically the speed limit of quantum gate operations for ion trap quantum information processors. The proposed methods use laser pulses for quantum gates which entangle the electronic and vibrational degrees of freedom of the trapped ions. Two of these methods are studied in detail and for both of them the speed is limited by a combination of the recoil frequency of the relevant electronic transition, and the vibrational frequency in the trap. We have experimentally studied the gate operations below and above this speed limit. In the latter case, the fidelity is reduced, in agreement with our theoretical findings.

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Decoherence Bounds on Quantum Computation with Trapped Ions

Cited by 89 publications

References 17 publications

Quantum Gates with “Hot” Trapped Ions

Quantum Gates with “Hot” Trapped Ions

Trapped Ion Quantum Computer Research at Los Alamos

Speed of ion-trap quantum-information processors

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