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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Prolonging qubit coherence: dynamical decoupling schemes studied in a Penning ion trap

Hermann Uys, Michael J. Biercuk, Aaron P. VanDevender, Nobuyasu Shiga, Wayne M. Itano, J. J. Bollinger

Published Jan 7, 2009• 1 citation
Publisher

Abstract

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.

DOI
10.1117/12.823179

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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.
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 study pulse sequences that dynamically decouple 9 1. Summary Efficient suppression of decoherence is a key challenge in many experiments aiming to exploit features of quantum mechanics. Many techniques to this end were developed, and are today widely employed, in the nuclear magnetic resonance community. Improving these capabilities are becoming increasingly relevant in the field of quantum information science, in which stringent fidelity requirements exist for the implementation of fault- tolerant quantum computing. Here we report the implementation of new techniques for the suppression of decoherence (1). In particular we use adaptive measurement feedback to optimize the delay times between applied decoupling pulses. We find that the pulse sequences so obtained outperform known sequences in certain noise environments (2,3). This study hints at the potential power of using adaptive feedback in the context of noise suppression. Figure 1: (a) Comparison of 6π-pulse CPMG (open circles), UDD (black triangles) and a sequence optimized via measurement feedback (green squares) at a free evolution time of = 2.4 ms. The gray arrow indicates the improvement gained over UDD at that time. Note the log scale. The blue line with vertical dashes represents a LODD simulation adjusting the pulse timings to give optimum error suppression at each point along the curve. It shows an improvement of at least an order of magnitude over UDD at most times. The timing of each pulse sequence (relative to each corresponding total free evolution time) is shown in (b) on the same time axis. The dotted lines in (b) show the pulse timings of the UDD sequence. The horizontal dashed line in (a) indicates the current detection threshold of our system. In all cases the same ohmic spectrum with a sharp cutoff around 500 Hz was used. 2. References
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.
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.
Dynamical decoupling (DD) emerges as a promising tool to suppress decoherence of quantum systems by eliminating the system-environment coupling. We investigate its power in combating pure dephasing of a qubit under random classical noise. Interestingly, the decoherence rate can be viewed as the interplay between noise spectrum and a controllable filter function. More specifically, the filter function is determined by the DD sequence we employed. Here we take Uhrig DD (UDD) as a benchmark sequence to illustrate the filtering process. We find that UDD sequence works as a perfect dynamical filter for low-frequency noise. For spectrum with hard cutoff, UDD increases the performance order by order with linearly increased number of pulses. However, for noise spectrum with soft cutoff, the required pulse number grows exponentially.
We describe experimental and theoretical studies of open-loop quantum control techniques known as dynamical decoupling (DD) for the suppression of decoherence-induced errors in quantum systems. Our experiments on trapped atomic ion qubits demonstrate that it is possible to optimize the construction of DD sequences for a given noise power spectral density. Studies of novel sequences derived analytically or through numerical optimization – while maintaining fixed control resources – demonstrate large gains in our ability to preserve quantum coherence in arbitrary noise environments.