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arXiv:1009.6189 · Journal of Physics B Atomic Molecular and Optical Physics

Keeping a single qubit alive by experimental dynamic decoupling

D. J. Szwer, S. C. Webster, Andrew M. Steane, D M Lucas

Published Dec 23, 2010• 51 citations
arXivHTMLPDF

Abstract

We demonstrate the use of dynamic decoupling techniques to extend the coherence time of a single memory qubit by nearly two orders of magnitude. By extending the Hahn spin-echo technique to correct for unknown, arbitrary polynomial variations in the qubit precession frequency, we show analytically that the required sequence of π-pulses is identical to the Uhrig dynamic decoupling (UDD) sequence. We compare UDD and Carr–Purcell–Meiboom–Gill (CPMG) sequences applied to a single 43 Ca + trapped-ion qubit and find that they afford comparable protection in our ambient noise environment.

DOI
10.1088/0953-4075/44/2/025501

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We demonstrate the use of dynamic decoupling techniques to extend the coherence time of a single memory qubit by nearly two orders of magnitude. By extending the Hahn spin-echo technique to correct for unknown, arbitrary polynomial variations in the qubit precession frequency, we show analytically that the required sequence of π-pulses is identical to the Uhrig dynamic decoupling (UDD) sequence. We compare UDD and Carr–Purcell–Meiboom–Gill (CPMG) sequences applied to a single 43 Ca + trapped-ion qubit and find that they afford comparable protection in our ambient noise environment.
We present a detailed experimental study of the Uhrig dynamical decoupling (UDD) sequence in a variety of noise environments. Our qubit system consists of a crystalline array of 9Be+{^{9}\text{B}\text{e}}^{+}9Be+ ions confined in a Penning trap. We use an electron-spin-flip transition as our qubit manifold and drive qubit rotations using a 124 GHz microwave system. We study the effect of the UDD sequence in mitigating phase errors and compare against the well known Carr-Purcell-Meiboom-Gill-style multipulse spin echo as a function of pulse number, rotation axis, noise spectrum, and noise strength. Our results agree well with theoretical predictions for qubit decoherence in the presence of classical phase noise, accounting for the effect of finite-duration $\ensuremath{\pi}$ pulses. Finally, we demonstrate that the Uhrig sequence is more robust against systematic over- or under-rotation and detuning errors than is multipulse spin echo, despite the precise prescription for pulse timing in UDD.
Decoherence is a primary barrier to practical quantum computation, causing quantum states to degrade through phase randomization and irreversible energy relaxation. This study presents a simulation-based evaluation of echo-based dynamical decoupling (DD) pulse sequences as a software-level mitigation strategy in single-qubit systems. Using the Qiskit Aer density matrix simulator, four strategies—baseline, Hahn Echo, Carr-Purcell-Meiboom-Gill (CPMG), and Mixed Synchronization—were evaluated across low-frequency phase noise, high-frequency phase noise, and combined T₁ + T₂ noise regimes. Hahn Echo restored mean fidelity to 100.00% under low-frequency noise (baseline: 57.90%), while CPMG achieved 97.62% under high-frequency noise (baseline: 2.45%). Under combined noise, all strategies showed limited improvement, with Mixed-Sync reaching 65.34% versus 60.95%. Coefficient of variation (CV) analysis across 500 Monte Carlo trials showed that CPMG reduced purity-decay variance threefold under high-frequency noise, with bootstrap confidence intervals confirming statistical significance. Time-resolved analysis showed that CPMG suppressed variance growth throughout evolution, reducing variance growth from +267% (baseline) to +89%, while baseline and Hahn Echo exhibited progressive amplification of variance. These results show that dynamical decoupling influences the temporal structure of noise, not just mean fidelity. In T₂-dominated regimes, pulse sequences constrain variability; in mixed regimes, they partially shape it; and in T₁-dominated regimes, both mean performance and variability converge to hardware-limited behavior. DD effectively corrects reversible phase errors but cannot overcome irreversible T₁ loss, with implications for NISQ circuit design.
Recent studies have shown that applying a sequence of Hahn spin-echo pulses to a qubit system at judiciously chosen intervals can, in certain noise environments, greatly improve the suppression of phase errors compared to traditional dynamical decoupling approaches. By enforcing a simple analytical condition, we obtain sets of dynamical decoupling sequences that are designed for optimized noise filtration, but are independent of the noise spectrum up to a single scaling factor set by the coherence time of the system. These sequences are tested in a model qubit system, ;{9}Be;{+} ions in a Penning trap. Our combined theoretical and experimental studies show that in high-frequency-dominated noise environments with sharp high-frequency cutoffs this approach may suppress phase errors orders of magnitude more efficiently than comparable techniques can.
We present a study of dynamical decoupling schemes for the suppression of phase errors from various noise environments using ions in a Penning trap as a model ensemble of qubits. By injecting frequency noise we demonstrate that in an ohmic noise spectrum with a sharp, high-frequency cutoff the recently proposed UDD decoupling sequence gives noise suppression superior to the traditional CPMG technique. Under only the influence of ambient magnetic field fluctuations with a 1/ω4 power spectrum, we find little benefit from using the UDD sequence, consistent with theoretical predictions for dynamical decoupling performance in the presence of noise spectra with soft cutoffs. Finally, we implement an optimization algorithm using measurement feedback, demonstrating that local optimization of dynamical decoupling can further lead to significant gains in error suppression over known sequences.
We experimentally demonstrate coherence recovery of singlet-triplet superpositions by interlacing qubit rotations between Carr-Purcell (CP) echo sequences. We then compare the performance of Hahn, CP, concatenated dynamical decoupling (CDD), and Uhrig dynamical decoupling for singlet recovery. In the present case, where gate noise and drift combined with spatially varying hyperfine coupling contribute significantly to dephasing, and pulses have limited bandwidth, CP and CDD yield comparable results, with T(2)∼80 μs.