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arXiv:quant-ph/9810039 · Physical Review Letters

Quantum Computation with Ions in Thermal Motion

Anders Søndberg Sørensen, Klaus Mølmer

Published Mar 1, 1999• 1,114 citations
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Abstract

We propose an implementation of quantum logic gates via virtual vibrational excitations in an ion-trap quantum computer. Transition paths involving unpopulated vibrational states interfere destructively to eliminate the dependence of rates and revolution frequencies on vibrational quantum numbers. As a consequence, quantum computation becomes feasible with ions whose vibrations are strongly coupled to a thermal reservoir.

DOI
10.1103/physrevlett.82.1971

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We propose an implementation of quantum logic gates via virtual vibrational excitations in an ion-trap quantum computer. Transition paths involving unpopulated vibrational states interfere destructively to eliminate the dependence of rates and revolution frequencies on vibrational quantum numbers. As a consequence, quantum computation becomes feasible with ions whose vibrations are strongly coupled to a thermal reservoir.
We propose a universal quantum computation scheme for trapped ions in thermal motion via the technique of adiabatic passage, which incorporates the advantages of both the adiabatic passage and the model of trapped ions in thermal motion. Our scheme is immune from the decoherence due to spontaneous emission from excited states as the system in our scheme evolves along a dark state. In our scheme the vibrational degrees of freedom are not required to be cooled to their ground states because they are only virtually excited. It is shown that the fidelity of the resultant gate operation is still high even when the magnitude of the effective Rabi frequency moderately deviates from the desired value.
Decoherence is studied in an attractive proposal for an actual implementation of a quantum computer based on trapped ions.Emphasis is placed on the decoherence arising from the vibrational motion of the ions, which is compared with that due to spontaneous emission from excited states of the ions. The calculations is made tractable by exploiting the vast difference in time scales between the vibrational excitations and the intra-ionic electronic excitations. Since the latter are several orders of magnitude faster, an adiabatic approximation is used to integrate them out and find the inclusive probability for the electronic state of the ions to evolve as it would in the absence of vibrational coupling, and the ions to evolve into any state whatsoever. The decoherence time is found at zero temperature and for any number of ions N in the computer. Comparison is made with the spontaneous emission decoherence, and the implications for how trap voltages and other parameters should be scaled with N are discussed.
We suggest a fast two-qubit quantum logic gates for trapped ions in thermal motion via geometric phase shifts. In the scheme, several vibrational modes are simultaneously displaced by driving the ions with a single off-resonant standing-wave laser. Under certain conditions, all the vibrational modes simultaneously return to the original points in the phase spaces along corresponding closed paths depending on the electronic states, producing a geometric phase gate. During the gate operation, the ions undergo no electronic transitions and the gate time might be shorter than the period of the center-of-mass vibration.
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.