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arXiv:2412.04421 · Physical Review Letters

Single-Qubit Gates with Errors at the 10 − 7 Level

Matthew C. Smith, A. D. Leu, K. Miyanishi, Mario F. Gely, D. M. Lucas

Published May 19, 2025• 35 citations
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Abstract

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.

DOI
10.1103/42w2-6ccy

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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.
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.
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.
The fidelity of laser-driven quantum logic operations on trapped ion qubits tend to be lower than microwave-driven logic operations due to the difficulty of stabilizing the driving fields at the ion location. Through stabilization of the driving optical fields and use of composite pulse sequences, we demonstrate high-fidelity single-qubit gates for the hyperfine qubit of a 171Yb+^{171}\text{Yb}^{+}171Yb+ ion trapped in a microfabricated surface-electrode ion trap. Gate error is characterized using a randomized benchmarking protocol and an average error per randomized Clifford group gate of $3.6(3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ is measured. We also report experimental realization of palindromic pulse sequences that scale efficiently in sequence length.
We use electronic microwave control methods to implement addressed single-qubit gates with high speed and fidelity, for 43Ca+^{43}{\mathrm{Ca}}^{+}43Ca+ hyperfine ``atomic clock'' qubits in a cryogenic (100 K) surface trap. For a single qubit, we benchmark an error of $1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ per Clifford gate (implemented using 600 ns $\ensuremath{\pi}/2$ pulses). For 2 qubits in the same trap zone (ion separation $5\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{m}$), we use a spatial microwave field gradient, combined with an efficient four-pulse scheme, to implement independent addressed gates. Parallel randomized benchmarking on both qubits yields an average error $3.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ per addressed $\ensuremath{\pi}/2$ gate. The scheme scales theoretically to larger numbers of qubits in a single register.
We demonstrate a two-qubit logic gate driven by near-field microwaves in a room-temperature microfabricated surface ion trap. We introduce a dynamically decoupled gate method, which stabilizes the qubits against fluctuating energy shifts and avoids the need to null the microwave field. We use the gate to produce a Bell state with fidelity 99.7(1)%, after accounting for state preparation and measurement errors. The gate is applied directly to ^{43}Ca^{+} hyperfine "atomic clock" qubits (coherence time T_{2}^{*}≈50 s) using the oscillating magnetic field gradient produced by an integrated microwave electrode.
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.