Fast quantum gates for cold trapped ions

Jonathan, Daniel; Plenio, Martin B.; Knight, Peter

doi:10.1103/physreva.62.042307

Cited by 159 publications

(177 citation statements)

References 26 publications

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“…The present work shows that the CNOT gate between different ions can be realized by using a three-step pulse process, which is simpler than the previous schemes which usually employed either five pulses [6,13], six pulses [15] or seven-step operations [16]. (8) for m = 0.…”

Section: A Two-qubit Controlled Operationsmentioning

confidence: 99%

“…(12)(13)(14)(15)) that E = 1 for α 2 /α 1 = √ 2 ± 1. This implies that two-qubit maximally entangled states can be generated deterministically by using a single-step operation beyond the LD limit.…”

Section: B Two-qubit Entangled Statesmentioning

confidence: 99%

“…[20,22]) to be easily addressed by different laser beams, i.e., each ion can be illuminated individually by a separate leaser beam. The communication and logic operations between qubits are usually performed by exciting or de-exciting quanta of the collective vibration (i.e., the shared phonon) modes, which act as the information bus (see, e.g., [6,13,15]). …”

Section: Conditional Quantum Dynamics For Two Trapped Ions Drivenmentioning

confidence: 99%

“…In the past few years, several key features of the proposal in [6], including the production of entangled states and the implementation of quantum controlled operations between a pair of trapped ions, have already been experimentally demonstrated * lfwei@riken.jp † fnori@riken.jp ‡ Permanent address [5,8,9,10]. Also, several alternative theoretical schemes (see, e.g., [11,12,13,14,15,16,17]) have been developed for overcoming various difficulties in realizing a practical iontrap quantum information processor.…”

Section: Introductionmentioning

confidence: 99%

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An efficient single-step scheme for manipulating quantum information of two trapped ions beyond the Lamb–Dicke limit

Wei¹,

Nori²

2003

Physics Letters A

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Section: A Two-qubit Controlled Operationsmentioning

confidence: 99%

Section: B Two-qubit Entangled Statesmentioning

confidence: 99%

Section: Conditional Quantum Dynamics For Two Trapped Ions Drivenmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An efficient single-step scheme for manipulating quantum information of two trapped ions beyond the Lamb–Dicke limit

Wei¹,

Nori²

2003

Physics Letters A

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“…Any operation that requires coupling between motion and internal dynamics and thus usually requires optical radiation can be carried out using radiation in the rf or mw regime. For example, conditional quantum dynamics on a collection of qubits may be implemented according to the schemes proposed in [17,41,42].…”

Section: A Adding a Driving Fieldmentioning

confidence: 99%

Conditional Spin Resonance with Trapped Ions

Wunderlich¹

2002

Laser Physics at the Limits

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Internal states of different ions in an electrodynamic trap are coupled when a static magnetic field is applied -analogous to spin-spin coupling in molecules used for NMR. This spin-spin interaction can be used, for example, to implement quantum logic operations in ion traps using NMR methods. The collection of trapped ions can be viewed as a N -qubit molecule with adjustable coupling constants. I. MOTIVATIONDigital information processing builds upon elementary physical elements ("bits") that may occupy either one of two possible states labelled 0 and 1, respectively. If a quantum system, for example, an individual atom having discrete energy eigenstates, is chosen as elementary switch ("qubit" ), then the general state of this system will be a superposition of the two computational basis states, i.e. the states chosen to represent the logic 0 and 1. When applying the superposition principle to a register comprising N qubits, one immediately sees that such a register can exist in a superposition of 2 N states thus representing 2 N binary encoded numbers simultaneously. Any operation on this register will act on all states at once, effecting parallel processing on an exponentially growing (with N ) number of states. The outcome of a measurement on this register after such an operation will, of course, yield just one out of 2 N possible results with a certain probability.In order to take advantage of quantum parallelism for efficient computing, a second ingredient is necessary: interference. A useful quantum algorithm has to exploit this parallelism, and, at the same time, make different computational paths interfere such that only the correct result survives after the last computational step [1]. An important example is Shor's algorithm for the factorization of large numbers [2]. Once created, coherent superpositions have to remain intact while a quantum algorithm is carried out, i.e. qubits must not in an uncontrollable way interact with their environment. This would lead to decoherence, an important issue, not only in the realm of quantum information processing (QIP), but also related to the notion of measurement in quantum mechanics [3,4].A quantum computer is ideally suited for the simulation of quantum mechanical systems [5,6], for example, to determine eigenvalues and eigenvectors of many-body systems [7]. Calculating the dynamics of chaotic systems is another useful line of action for a quantum computer, even for one that consists of only a few qubits [8]. Beneficial both for fundamental research and applications is the ability of a quantum computer -comprising a modest number of qubits and working with limited accuracy -to simulate the dynamics of a macroscopic ensemble of classical particles, a task not suitable even for modern supercomputers [9].In the course of a quantum computation entangled states of qubits are created exhibiting correlations between individual qubits that possess no classical analog. Fundamental questions concerning the role of entanglement, not only in QIP, but also in the framewor...

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Quantum Computing with Trapped Ions, Atoms and Light

Steane

Lucas

2000

Fortschr. Phys.

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We first consider the basic requirements for a quantum computer, arguing for the attractiveness of nuclear spins as information‐bearing entities, and light for the coupling which allows quantum gates. We then survey the strengths of and immediate prospects for quantum information processing in ion traps. We discuss decoherence and gate rates in ion traps, comparing methods based on the vibrational motion with a method based on exchange of photons in cavity QED. We then sketch the main features of a quantum computer designed to allow an algorithm needing 106 Toffoli gates on 100 logical qubits. We find that around 200 ion traps linked by optical fibres and high‐finesse cavities could perform such an algorithm in a week to a month, using components at or near current levels of technology.

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Fast quantum gates for cold trapped ions

Cited by 159 publications

References 26 publications

An efficient single-step scheme for manipulating quantum information of two trapped ions beyond the Lamb–Dicke limit

An efficient single-step scheme for manipulating quantum information of two trapped ions beyond the Lamb–Dicke limit

Conditional Spin Resonance with Trapped Ions

Quantum Computing with Trapped Ions, Atoms and Light

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