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arXiv:quant-ph/0611048 · Physical Review A

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

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

Published Apr 27, 2007• 167 citations
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Abstract

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.

DOI
10.1103/physreva.75.042329

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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 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.
High-fidelity and parallel realization in scalable platforms of the two-qubit entangling gates fundamental to universal quantum computing constitutes one of the largest challenges in implementing fault-tolerant quantum computation. Integrated optical addressing of trapped-ion qubits offers routes to scaling the high-fidelity optical control demonstrated to date in small systems. Here we show that in addition to scaling, capabilities practically enabled by integrated optics can substantially alleviate laser powers required for both light-shift (LS) and Molmer-Sorensen (MS) geometric phase gates acting on long-lived ground-state qubit encodings in a broad range of ion species. In the proposed gate schemes utilizing carrier nulling via ion positioning at phase-stable standing-wave (SW) nodes, our calculations suggest that suppressed spontaneous photon scattering at the SW node allows for gate drives operating at smaller Raman detunings, resulting in approximately an order-of-magnitude reduction in power requirement (and significantly larger in certain parameter regimes) for gates of a given duration and scattering-limited fidelity as compared to conventional running wave (RW)-based approaches. The SW schemes have the additional benefit of simultaneously eliminating undesired coherent couplings that typically limit gate speeds. Our work quantifies power requirements for multiple ion species and enhancements to be expected from carrier-nulled configurations practically enabled by integrated delivery, and informs experiments and systems for realization of fast and power-efficient laser-based entangling gates in scalable platforms.
Metastable qubits in atomic systems can enable large-scale quantum computing by simplifying hardware requirements and adding efficient erasure conversion to the preexisting toolbox of high-fidelity laser-based control. For trapped atomic ions, the fundamental error floor of this control is given by spontaneous Raman and Rayleigh scattering from short-lived excited states. We measure spontaneous Raman scattering rates out of a metastable D5/2{D}_{5/2}D5/2​ qubit manifold of a single trapped 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ion illuminated by 976 nm light that is $\ensuremath{-}44$ THz detuned from the dipole-allowed transition to the P3/2{P}_{3/2}P3/2​ manifold. This supports the calculation of error rates from both types of scattering during one- and two-qubit gates on this platform, thus demonstrating that infidelities less than ${10}^{\ensuremath{-}4}$ are possible.
Quantum logic gates performed via two-photon stimulated Raman transitions in ions and atoms are fundamentally limited by spontaneous scattering errors. Recent theoretical treatment of these processes has predicted no lower bound on the scattering-induced error rate of such gates when implemented with far-detuned lasers, while also providing an extension to metastable qubits. To validate this theoretical model, we provide experimental measurements of Raman scattering rates due to near- and far-detuned lasers for initial states in the metastable D5/2{D}_{5/2}D5/2​ level of 137Ba+^{137}\mathrm{Ba}^{+}137Ba+. The measured spontaneous Raman scattering rate is consistent with the theoretical prediction and suggests that metastable-level two-qubit gates with an error rate approximately equal to ${10}^{\ensuremath{-}4}$ are possible with laser excitation detuned by tens of terahertz or more.
Spontaneous Raman scattering from metastable states of Ba+^++
Quantum logic gates performed via two-photon stimulated-Raman transitions in ions and atoms are fundamentally limited by spontaneous scattering errors. Recent theoretical treatment of these scattering processes has predicted no lower bound on the error rate of such gates when implemented with far-detuned lasers, while also providing an extension to metastable qubits. To validate this theoretical model, we provide experimental measurements of Raman scattering rates due to near-, and far-detuned lasers for initial states in the metastable D5/2_{5/2}5/2​ level of 137^{137}137Ba+^++. The measured spontaneous Raman scattering rate is consistent with the theoretical prediction and suggests that metastable-level two-qubit gates with an error rate ≈10−4\approx10^{-4}≈10−4 are possible with laser excitation detuned by tens of terahertz or more.