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Fortschritte der Physik

Ion Trap Quantum Computer with Bichromatic Light

Anders Søndberg Sørensen, Klaus Mølmer

Published Sep 1, 2000• 6 citations
Publisher

Abstract

In the ion trap quantum computer, quantum bits are represented by the internal state of the trapped ions, and the collective vibrations of the ions are exploited for the coherent manipulation of the state of several bits. We have developed a method to perform gates on different ions by illuminating the ions with bichromatic light. Our gates are independent of the motional state of the ions and they may be applied to ions in any state or, e.g., thermal mixture of vibrational states. Moreover, our proposal allows the production of multiparticle entangled states even in situations without experimental access to the individual ions in the trap. Maximally entangled states of any number of ions are produced by simply illuminating all ions with the same beams of bichromatic light.

DOI
10.1002/1521-3978(200009)48:9/11<811::aid-prop811>3.0.co;2-y

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In the ion trap quantum computer, quantum bits are represented by the internal state of the trapped ions, and the collective vibrations of the ions are exploited for the coherent manipulation of the state of several bits. We have developed a method to perform gates on different ions by illuminating the ions with bichromatic light. Our gates are independent of the motional state of the ions and they may be applied to ions in any state or, e.g., thermal mixture of vibrational states. Moreover, our proposal allows the production of multiparticle entangled states even in situations without experimental access to the individual ions in the trap. Maximally entangled states of any number of ions are produced by simply illuminating all ions with the same beams of bichromatic light.
We propose an efficient method to produce multiparticle entangled states of ions in an ion trap for which a wide range of interesting effects and applications have been suggested. Our preparation scheme exploits the collective vibrational motion of the ions, but it works in such a way that this motion need not be fully controlled in the experiment. The ions may, e.g., be in thermal motion and exchange mechanical energy with a surrounding heat bath without detrimental effects on the internal state preparation. Our scheme does not require access to the individual ions in the trap.
We describe two schemes to manipulate the electronic qubit states of trapped ions independent of the collective vibrational state of the ions. The first scheme uses an adiabatic method, and thus is intrinsically slow. The second scheme takes the opposite approach and uses fast pulses to produce an effective direct coupling between the electronic qubits. This last scheme enables the simulation of a number of nonlinear quantum systems including systems that exhibit phase transitions, and other semiclassical bifurcations. Quantum tunnelling and entangled states occur in such systems.
In the system with ions confined both in a linear trap and in a high-QQQ single mode cavity, we present a simple quantum computing scheme by means of lasers and quantized cavity field, based on a previous proposal with bichromatic radiation [Phys. Rev. Lett. 82,82,82, 1971 (1999)]. The controlled-NOT gate operation can be performed by only three operations and it is independent of motional states of ions. Experimental feasibility for achieving our scheme is discussed.
Abstract We discuss how to simplify the Mølmer–Sørensen (MS) gate which is used for the trapped ion quantum computer. The original MS gate is implemented by illuminating two ions with bichromatic coherent light fields separately at the same time. In this paper, we propose a method for transforming a separable state of two ions into one of the Bell states by illuminating the two ions with monochromatic coherent light fields individually and this point is the advantage of our scheme over the original MS gate. The length of the execution time of our proposed gate is comparable to that of the original MS gate, however, numerical calculations show that our proposed gate is weakly sensitive to thermal fluctuations of the phonons. By giving another example of a simple two-ion gate that can generate entanglement but is strongly vulnerable to thermal fluctuations, we show that our simplified MS gate is more marked than usual.
Trapped ion systems are the leading candidate for quantum information processing because many of the critical components have already been demonstrated. Scaling trapped ion systems to large numbers of ions is currently believed possible, but much work remains to prove it. Microfabricated surface ion traps are increasing in popularity for their ease of mass production and their ability to manipulate individual ions and interact arbitrary pairs of ions. Even with the advent of scalable ion traps, detection of an individual ion trapped in a high vacuum poses a challenge. The internal state of the ion chosen for a quantum bit can be measured via exposure to a probe beam that causes one state to scatter light (a "bright" state), but not the other state (a "dark" state). In free space, a single ion acts like a point source that emits in all directions; a standard two inch lens system can only collect about 2% of the light emitted by the ion. Poor light collection results in a high error rate and slow determination of the internal state of the ion. Fast, high fidelity state detection is necessary for quantum error correction and loophole-free Bell experiments at short (less than 100\\,km) distances, and high efficiency collection is necessary to rapidly interconnect separate quantum computers. We demonstrate state detection fidelities of 99%, 99.856(8)% and 99.915(7) % which correspond to detection times of 10.5, 28.1 and 99.8 us, respectively.