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arXiv:1104.2552 · Physical Review A

Single-qubit-gate error below 10 − 4 in a trapped ion

K. R. Brown, A. C. Wilson, Yves Colombe, C. Ospelkaus, Adam M. Meier, Emanuel H. Knill, Dietrich G. Leibfried, David J. Wineland

Published Sep 14, 2011• 214 citations
arXivHTMLPDF

Abstract

With a ${}^{9}{\mathrm{Be}}^{+}$ 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 ${}^{9}{\mathrm{Be}}^{+}$ 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.

DOI
10.1103/physreva.84.030303

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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×\else\texttimes\fi10\ensuremath−52.0(2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}2.0(2)\ifmmode×\else\texttimes\fi10\ensuremath−5, below the threshold estimate of 10\ensuremath−4{10}^{\ensuremath{-}4}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.
We report the achievement of single-qubit gates with sub-part-per-million error rates, in a trapped-ion ^{43}Ca^{+} hyperfine clock qubit. We explore the speed and fidelity trade-off for gate times 4.4≤t_{g}≤35 μs, and benchmark a minimum error per Clifford gate of 1.5(4)×10^{-7}. Calibration errors are suppressed to <10^{-8}, leaving qubit decoherence (T_{2}≈70 s), leakage, and measurement as the dominant error contributions. The ion is held above a microfabricated surface-electrode trap that incorporates a chip-integrated microwave resonator for electronic qubit control; the trap is operated at room temperature without magnetic shielding.
Trapped atomic ions are a promising candidate system for developing a quantum computer. All elementary operations for quantum information processing have al- ready been achieved in trapped-ion systems with errors below the “fault-tolerant threshold”, meaning that these errors are sufficiently small to be removed with quan- tum error correction. However, the preservation of quantum information over the short timescales that are relevant for quantum computing has not, to our knowledge, been measured before in trapped-ion qubits. Previous investigations have measured decoherence over long times and extrapolated an exponential decay model to short times. We directly measure the qubit memory error rate over short timescales, which is made possible by the high-fidelity single-qubit gates and state preparation and mea- surement in our system. Our qubit is a hyperfine “atomic clock” transition in 43Ca+, and gates are applied with near-field microwaves. We find that the assumption of exponential decay of qubit state coherence does not apply in our system. The data is fit well by a model of 1/f frequency noise with a low-frequency cutoff. The small- est memory error that we measure is 3(1)×10−6 over 2ms. The time at which our qubit memory error is 1×10−3, an important threshold for viable quantum error correction, is ≈400ms. We also present a design study into a new ion trap electrode geometry for applying near-field microwave two-qubit gates. This design features an ‘S’-shaped meander electrode to passively null the microwave field at the ions’ locations. It has improved isolation between the meander and other electrodes compared to previous work on this, which should reduce the sensitivity of the microwave field distribution to the boundary conditions of these electrodes. We show that the trap would allow for ion chains to be trapped, transported and split with feasible DC and RF voltages.
The trapped atomic ion qubits feature desirable properties for use in a quantum computer such as long coherence times, high qubit readout fidelity, and universal logic gates. While these essential properties have been demonstrated, the ability to scale a trapped ion quantum system has not yet been shown. The challenge of scaling the system calls for methods to realize high-fidelity logic gates in scalable trap structures. Surface electrode ion traps, that are microfabricated from a silicon substrate, provide a scalable platform for trapping ion qubits only if high-fidelity operations are achievable in these structures. Here, we present a system for trapping and manipulating ions in a scalable surface trap. Trapping times exceeding 20 minutes without laser cooling, and heating rates as low as 0.8 quanta/ms indicate stable trapping conditions in these microtraps. Coherence times of more than one second verify adequate qubit and control field stability. We demonstrate low-error single-qubit gates performed using stimulated Raman transitions driven by lasers that are tightly focused on the ion qubit. Digital feedback loops are implemented to control the driving field's amplitude and frequency. Gate errors are measured using a randomized benchmarking protocol for single qubit gates, where residual amplitude error in the control beam is compensated using various pulse sequence techniques. Using pulse compensation, we demonstrate single qubit gates with an average error per randomized Clifford group gate of 3.6(3)times10−43.6(3)\\times10^{-4}3.6(3)times10−4, which is below the fault-tolerant threshold for some error-correction schemes.
We trap individual 171 Yb + ions in a surface trap microfabricated on a silicon substrate, and demonstrate a complete set of high fidelity single qubit operations for the hyperfine qubit. Trapping times exceeding 20 min without laser cooling, and heating rates as low as 0.8 quanta ms −1 , indicate stable trapping conditions in these microtraps. A coherence time of more than 1 s, high fidelity qubit state detection and single qubit rotations are demonstrated. The observation of low heating rates and demonstration of high quality single qubit gates at room temperature are critical steps toward scalable quantum information processing in microfabricated surface traps.
We implement all single-qubit operations with fidelities significantly above the minimum threshold required for fault-tolerant quantum computing, using a trapped-ion qubit stored in hyperfine "atomic clock" states of 43 Ca þ .We measure a combined qubit state preparation and single-shot readout fidelity of 99.93%, a memory coherence time of T Ã 2 ¼ 50 sec, and an average single-qubit gate fidelity of 99.9999%.These results are achieved in a room-temperature microfabricated surface trap, without the use of magnetic field shielding or dynamic decoupling techniques to overcome technical noise.
We implement all single-qubit operations with fidelities significantly above the minimum threshold required for fault-tolerant quantum computing, using a trapped-ion qubit stored in hyperfine "atomic clock" states of ^{43}Ca^{+}. We measure a combined qubit state preparation and single-shot readout fidelity of 99.93%, a memory coherence time of T_{2}^{*}=50 sec, and an average single-qubit gate fidelity of 99.9999%. These results are achieved in a room-temperature microfabricated surface trap, without the use of magnetic field shielding or dynamic decoupling techniques to overcome technical noise.