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arXiv:1312.3227

Noise Studies of Driven Geometric Phase Gates with Trapped Ions

A Lemmer, A. Bermudez, M. B. Plenio

Published Dec 11, 2013• 2 citations
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Abstract

We present a study of the performance of the trapped-ion driven geometric phase gates introduced in [New J. Phys. 15, 083001 (2013)] when realized in a stimulated Raman transition. We show that the gate can achieve errors below the fault-tolerance threshold in the presence of laser intensity fluctuations. We also find that, in order to reduce the errors due to photon scattering below the fault-tolerance threshold, very intense laser beams are required to allow for large detunings in the Raman configuration without compromising the gate speed.

DOI
10.48550/arxiv.1312.3227

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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.
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We study photon scattering errors in stimulated Raman driven quantum logic gates. For certain parameter regimes, we find that previous simplified models of the process significantly overestimate the gate error rate due to photon scattering. This overestimate is shown to be due to previous models neglecting the detuning dependence of the scattered photon frequency and Lamb-Dicke parameter, a second scattering process, interference effects on scattering rates to metastable manifolds, and the counterrotating contribution to the Raman transition rate. The resulting improved model shows that there is no fundamental limit on gate error due to photon scattering for electronic ground-state qubits in commonly used trapped-ion species when the Raman laser beams are red detuned from the main optical transition. Additionally, photon scattering errors are studied for qubits encoded in the metastable D5/2{D}_{5/2}D5/2​ manifold, showing that gate errors below ${10}^{\ensuremath{-}4}$ are achievable for all commonly used trapped ions.
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The micromotion of ion crystals confined in Paul traps is usually considered an inconvenient nuisance, and is thus typically minimized in high-precision experiments such as high-fidelity quantum gates for quantum information processing (QIP). In this work, we introduce a particular scheme where this behavior can be reversed, making micromotion beneficial for QIP. We show that using laser-driven micromotion sidebands, it is possible to engineer state-dependent dipole forces with a reduced effect of off-resonant couplings to the carrier transition. This allows one, in a certain parameter regime, to devise entangling gate schemes based on geometric phase gates with both a higher speed and a lower error, which is attractive in light of current efforts towards fault-tolerant QIP. We discuss the prospects of reaching the parameters required to observe this micromotion-enabled improvement in experiments with current and future trap designs.