We study the performance of composite pulses in the presence of time-varying control noise on a single qubit. These protocols, originally devised only to correct for static, systematic errors, are shown to be robust to time-dependent non-Markovian noise in the control field up to frequencies as high as ∼10% of the Rabi frequency. Our study combines a generalized filter-function approach with asymptotic dc-limit calculations to give a simple analytic framework for error analysis applied to a number of composite-pulse sequences relevant to nuclear magnetic resonance as well as quantum information experiments. Results include examination of recently introduced concatenated composite pulses and dynamically corrected gates, demonstrating equivalent first-order suppression of time-dependent fluctuations in amplitude and/or detuning, as appropriate for the sequence in question. Our analytic results agree well with numerical simulations for realistic 1/f noise spectra with a roll-off to 1/f 2 , providing independent validation of our theoretical insights.

The fidelity of laser-driven quantum logic operations on trapped ion qubits tend to be lower than microwavedriven 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 171 Yb + 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) × 10 −4 is measured. We also report experimental realization of palindromic pulse sequences that scale efficiently in sequence length. The trapped atomic ion qubits feature desirable properties for use in a quantum computer such as long coherence times [1], high-fidelity qubit measurement [2], and universal logic gates [3]. The quality of quantum logic gate operations on trapped ion qubits has been limited by the stability of the control fields at the ion location used to implement the gate operations. For this reason, the logic gates utilizing microwave fields [4][5][6][7] have shown gate fidelities several orders of magnitude better than those using laser fields [8][9][10]. The laser beams used to drive either Raman gates for a hyperfine ion qubit or optical gates between metastable qubit states are subject to severe wave-front distortion in air due to turbulence, leading to amplitude and phase fluctuations of the optical field at the ion location that limited the gate fidelity in the 0.5% range [8,11].Microfabricated surface-electrode ion traps, where atomic ions are trapped above a two-dimensional surface of electrodes, can provide a scalable platform on which to build an ion-based quantum computer [12,13]. Experiments using surface traps have demonstrated coherence times of more than 1 s [14], state detection with fidelities greater than 99.9% [2], and low-error single-qubit gates [ 2.0(2) × 10 −5 ] using integrated microwave waveguides [4,7]. Use of high-power UV lasers close to the trap surface can lead to substantial charging due to unwanted exposure [15]. The recent development of single-mode fibers capable of delivering high-power UV laser beams [16] opens the possibility of significantly reducing the free-space UV beam path length and delivering a clean spatial mode to the ions, eliminating unwanted scattering off nearby trap structures.Here we demonstrate low-error single-qubit gates performed using stimulated Raman transitions on an ion qubit trapped in a microfabricated chip trap. Gate errors are measured using a randomized benchmarking protocol [8,17,18], where amplitude error in the control beam is compensated using various pulse sequence techniques [19,20]. Using B2 compensation [19], we demonstrate single-qubit gates with an average error per randomized Clifford group gate of 3.6(3) × 10 −4 . We also show that compact palindromic pulse compensation sequences (PDn) [20] compensate for amplitude errors as designed. Two hyperfin...

We schedule the Steane [[7,1,3]] error correction on a model ion trap architecture with ballistic transport. We compare the level one error rates for syndrome extraction using the Shor method of ancilla prepared in verified cat states to the DiVincenzo-Aliferis method without verification. The study examines how the quantum error correction circuit latency and error vary with the number of available ancilla and the choice of protocol for ancilla preparation and measurement. We find that with few exceptions the DiVincenzo-Aliferis method without cat state verification outperforms the standard Shor method. We also find that additional ancilla always reduces the latency but does not significantly change the error due to the high memory fidelity.