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Bulletin of the American Physical Society

Error in trapped-ion quantum gates due to spontaneous photon scattering

Roee Ozeri, C. Langer, John D. Jost, R. B. Blakestad, J. Britton, John Chiaverini, David B. Hume, Wayne M. Itano, E. Knill, Dietrich G. Leibfried, R. Reichle, Signe Louise Seidelin, Janus H. Wesenberg, David J. Wineland

Published May 17, 2006• 0 citations
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We analyze the error in trapped-ion, hyperfine qubit, quantum gates due to spontaneous scattering of photons from the gate laser beams. We investigate single-qubit rotations that are based on stimulated Raman transitions and two-qubit entangling phase gates that are based on spin-dependent optical dipole forces. This error is compared between different ion species currently being investigated as possible quantum-information carriers. For both gate types we show that with attainable laser powers the scattering error can be reduced to below current estimates of the fault-tolerance error threshold.
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.
We construct a detailed microscopic noise model for multi-qubit (MQ) gate operations in the context of trapped ion architecture with all-to-all connectivity. We find that phonon heating and motional dephasing are well captured by effective single- and two-qubit error channels that can, in principle, act between arbitrary pairs of qubits. Nevertheless, the median magnitude of two-qubit errors between uncoupled qubits is substantially smaller than that of errors between gate-coupled qubits. Errors associated with photon scattering are shown to solely propagate to qubits participating in gate operations. Lastly, we combine all noise sources, assigned with experimentally relevant parameters, and explore the scalability of a quantum error correction (QEC) scheme based on the rotated surface code, as a function of error rates and code size. Our analysis bridges device-level physics and QEC performance for MQ gates in trapped-ion architectures.