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Efficient adaptive Bayesian estimation of a slowly fluctuating Overhauser field gradient
by Jacob Benestad, Jan A. Krzywda, Evert van Nieuwenburg, Jeroen Danon
Submission summary
| Authors (as registered SciPost users): | Jacob Benestad |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2309.15014v2 (pdf) |
| Code repository: | https://github.com/jacobdben/efficient-bayesian-estimation |
| Date submitted: | 2023-10-03 10:15 |
| Submitted by: | Benestad, Jacob |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Slow fluctuations of Overhauser fields are an important source for decoherence in spin qubits hosted in III-V semiconductor quantum dots. Focusing on the effect of the field gradient on double-dot singlet-triplet qubits, we present two adaptive Bayesian schemes to estimate the magnitude of the gradient by a series of free induction decay experiments. We concentrate on reducing the computational overhead, with a real-time implementation of the schemes in mind. We show how it is possible to achieve a significant improvement of estimation accuracy compared to more traditional estimation methods. We include an analysis of the effects of dephasing and the drift of the gradient itself.
Current status:
Reports on this Submission
Report
In the present manuscript, the authors developed and benchmarked adaptive methods to optimize the Bayesian estimation of a slowly fluctuating Overhauser field. The scheme is tailored to work with state-of-the-art field-programmable gate arrays (FPGAs) for fast real-time feedback in the experiment.
In singlet-triplet qubits, information about the Overhauser field gradient can be extracted through a free induction decay (FID) experiment, which yields a binary measurement result depending on the field gradient strength and the FID time. The outcome of such a measurement can then be used to perform a Bayesian update on an estimate of the field gradient distribution. The speed at which one can gain certainty about the field gradient crucially depends on the chosen FID times and initial distribution.
In this work, the authors develop a greedy approach that describes the field gradient by a (bimodal) Gaussian distribution and adaptively pick the FID times of the next iteration by minimizing the expected variance. Here the distribution after the application of Bayes’ rule is found through a fit. Using the method of moments for the fit, the authors are able to find approximate analytic expressions for the optimal FID times. Simulating the estimation protocol for a realistic set of parameters, the authors find that it significantly outperforms a standard non-adaptive approach. The authors further improve the performance of the scheme by training a compact neural network to find the optimal FID times in the parameter regime where the approximate analytic solution breaks down. Finally, the authors analyze the optimal number of FID iterations given that the estimated parameter is drifting and describe how previous estimates can be used to improve the initial guess of the gradient field in the next iteration.
Overall, the paper is well written and as far as I can judge scientifically sound. It is also highly relevant as offers an efficient estimation protocol that can be run on a FPGA for fast feedback. I recommend publication and only have some minor comments.
Requested changes
(1) Maybe one could mention that Eq. (15) is just Eq. (4) multiplied with the results in Eq. (13). I was also wondering why T in Eq. (4) is replaced by alpha_n in Eq. (15).
(2) The experiment time Te in Fig. 3 has no unit. Should it be multiplied by sigma_K as in Fig. 4?