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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Geometric phase gate with a quantized driving field

Shabnam Siddiqui, Julio R. Gea-Banacloche

Published May 5, 2006• 0 citations
Publisher

Abstract

We have studied the performance of a geometric phase gate with a quantized driving field numerically, and developed an analytical approximation that yields some preliminary insight on the way the qubit becomes entangled with the driving field.
DOI
10.1117/12.665010

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We study the performance of an adiabatic geometric phase gate with a quantized driving field numerically and develop an analytical approximation that shows how the qubit becomes entangled with the driving field. This results in a scaling of the gate error probability versus the energy in the control field that has the same form as that found for dynamic, nonadiabatic gates, but with a prefactor that would typically be several orders of magnitude larger, because of the adiabaticity constraint. In the approximation we have used, which should be valid for sufficiently large control fields, the main source of decoherence (and hence error) is the ``which path'' information carried by the photons that would be radiated by the driven qubit.
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Abstract We describe a hybrid laser–microwave scheme to implement two-qubit geometric phase gates in crystals of trapped ions. The proposed gates can attain errors below the fault-tolerance threshold in the presence of thermal, dephasing, laser-phase and microwave-intensity noise. Moreover, our proposal is technically less demanding than previous schemes, since it does not require a laser arrangement with interferometric stability. The laser beams are tuned close to a single vibrational sideband to entangle the qubits, while strong microwave drivings provide the geometric character to the gate, and thus protect the qubits from these different sources of noise. A thorough analytic and numerical study of the performance of these gates in realistic noisy regimes is presented.