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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Error-resistant Single Qubit Gates with Trapped Ions

Nuala Timoney, Vladimir Elman, C. Weiss, M. Johanning, C. Wunderlich, Werner Neuhauser

Published Jun 1, 2007• 16 citations
Publisher

Abstract

This study presents single qubit gates with trapped ions that are robust against experimental imperfections over a wide range of parameters. In particular it is shown that errors caused by an inaccurate setting of either frequency, amplitude, or duration of the driving field, or of a combination of these errors are tolerable when a suitable sequence of radiation pulses, or a shaped pulse is applied instead of, for instance, a single rectangular pi-pulse. Thus an essential prerequisite for scalable quantum computation with trapped ions is demonstrated.

DOI
10.1109/cleoe-iqec.2007.4386765

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This study presents single qubit gates with trapped ions that are robust against experimental imperfections over a wide range of parameters. In particular it is shown that errors caused by an inaccurate setting of either frequency, amplitude, or duration of the driving field, or of a combination of these errors are tolerable when a suitable sequence of radiation pulses, or a shaped pulse is applied instead of, for instance, a single rectangular pi-pulse. Thus an essential prerequisite for scalable quantum computation with trapped ions is demonstrated.
Coherent operations with individual trapped Yb+{\text{Yb}}^{+}Yb+ ions are demonstrated that are robust against variations in experimental parameters and intrinsically indeterministic system parameters. In particular, pulses developed using optimal control theory are demonstrated with trapped ions. Their performance as a function of error parameters is systematically investigated and compared to composite pulses. Such pulses are basic building blocks for single and multiqubit quantum gates.
Highly-localized light-matter interactions are necessary for scaling trapped-ion architectures. In hyperfine qubits, counterpropagating beams generate entangling gates by coupling with motion, but this effect is undesirable during single-qubit operations. For that reason, single-qubit gates are traditionally implemented with copropagating beams, and the coexistence of two beam geometries adds hardware and computational overhead. In an effort towards collective performance improvement with minimal overhead, we design and implement pulse-amplitude and dephasing robust dynamically corrected gates using Space Curve Quantum Control (SCQC) and compare them against the constant-amplitude gate implementation. We perform gate set tomography on a four-qubit trapped-ion register, and we discover more than 50% error reduction when robust pulses are used. We find that counterpropagating robust gates often outperform their copropagating counterparts and reach error rates as low as (3.59±1.25)⋅10−3(3.59 \pm 1.25)\cdot 10^{-3}(3.59±1.25)⋅10−3, using diamond distance as a metric. This value establishes a laser-driven-gate error reference and is merely an order of magnitude higher than the best reported microwave\textit{microwave}microwave gate on a single\textit{single}single ion. Additional experiments reveal that robust pulses can effectively suppress non-Markovian errors that grow during runtime. Our work challenges the widely accepted belief that copropagating gates should be preferred for their weak motional coupling and invites the adoption of high-performance robust pulses that suppress multiple noise sources of the trapped-ion error budget.
Physical qubits in experimental quantum information processors are inevitably exposed to different sources of noise and imperfections, which lead to errors that typically accumulate hindering our ability to perform long computations reliably. Progress towards scalable and robust quantum computation relies on exploiting quantum error correction (QEC) to actively battle these undesired effects. In this work, we present a comprehensive study of crosstalk errors in a quantum-computing architecture based on a single string of ions confined by a radio-frequency trap, and manipulated by individually-addressed laser beams. This type of errors affects spectator qubits that, ideally, should remain unaltered during the application of single- and two-qubit quantum gates addressed at a different set of active qubits. We microscopically model crosstalk errors from first principles and present a detailed study showing the importance of using a coherent vs incoherent error modelling and, moreover, discuss strategies to actively suppress this crosstalk at the gate level. Finally, we study the impact of residual crosstalk errors on the performance of fault-tolerant QEC numerically, identifying the experimental target values that need to be achieved in near-term trapped-ion experiments to reach the break-even point for beneficial QEC with low-distance topological codes.
Fault-tolerant quantum computing requires high-fidelity quantum gates that are resilient to control errors and device imperfections. Here, we develop energy-optimal control pulses for single-qubit gates that are simultaneously robust against frequency detuning and waveform inhomogeneities while also suppressing leakage outside the computational subspace. Combining the optimized pulse envelopes with an adaptive control scheme, we experimentally demonstrate optimal robust gates on a superconducting quantum processor. For a gate duration of 90ns, we achieve fidelities above 99.9% for the X gate and 99.6% for Hadamard-type gates. For the X gate, we maintain fidelities above 99.5% for simultaneous drive-amplitude variations up to 20% and qubit detuning up to 4 MHz. This robustness outperforms that of conventional Gaussian pulses by an order of magnitude, without much difference in peak gate fidelity. These results establish a route towards robust single-qubit control in large-scale quantum processors, advancing the development of fault-tolerant quantum computing.
With a 9Be+{}^{9}{\mathrm{Be}}^{+}9Be+ trapped-ion hyperfine-state qubit, we demonstrate an error probability per randomized single-qubit gate of $2.0(2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$, below the threshold estimate of ${10}^{\ensuremath{-}4}$ commonly considered sufficient for fault-tolerant quantum computing. The 9Be+{}^{9}{\mathrm{Be}}^{+}9Be+ ion is trapped above a microfabricated surface-electrode ion trap and is manipulated with microwaves applied to a trap electrode. The achievement of low single-qubit-gate errors is an essential step toward the construction of a scalable quantum computer.
Two-qubit gate performance is vital for scaling up ion-trap quantum computing. Optimized quantum control is needed to achieve reductions in gate duration and gate error rate. We describe two-qubit gates with addressed Raman beams within a linear trapped-ion chain by a quantum master equation (QME). The QME incorporates the single-ion two-photon effective Rabi frequency, Autler-Townes and vibrational Bloch-Siegert energy shifts, off-resonant transitions, Raman and Rayleigh scattering, laser-power fluctuations, motional heating, cross-Kerr phonon coupling, laser spillover, asymmetric addressing beams, and an imperfect initial motional ground state, with no fitting parameters, whereas state-of-the-art methods are oblivious to these effects in the gate design procedure. We employ global optimization to design pulse sequences for achieving a robust rapid two-qubit gate for a simulated chain of seven trapped 171Yb+^{171}\mathrm{Yb}^{+}171Yb+ ions by optimizing over numerically integrated QME solutions. Here, robust means resilient against slow drift of motional frequencies, and rapid means gate execution where the effective Rabi frequency is comparable to the detuning of the laser from the ion's bare electronic transition. Our robust quantum control delivers rapid high-quality two-qubit gates in long ion chains, enabling scalable quantum computing with trapped ions.