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Optimally Band-Limited Noise Filtering for Single-Qubit Gates

Yasuo Oda1,*, Dennis Lucarelli2, Kevin Schultz3, B. David Clader3,†, and Gregory Quiroz1,3

  • 1William H. Miller III Department of Physics & Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
  • 2Department of Physics, American University
  • 3Johns Hopkins University Applied Physics Laboratory

  • *yoda2@jhu.edu
  • †Current affiliation: Goldman Sachs & Co.
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Phys. Rev. Applied 19, 014062 – Published 23 January, 2023

DOI: https://doi.org/10.1103/PhysRevApplied.19.014062

Abstract

We introduce a quantum control protocol that produces smooth, experimentally implementable control sequences optimized to combat temporally correlated noise for single-qubit systems. The control ansatz is specifically chosen to be a functional expansion of discrete prolate spheroidal sequences, a discrete time basis known to be optimally concentrated in time and frequency, and quite attractive when faced with experimental control hardware constraints. We leverage the filter function formalism to transform the control problem into a filter design problem, and show that the frequency response of a quantum system can be carefully tailored to avoid the most relevant dynamical contributions of noise processes. Using gradient ascent, we obtain optimized filter functions and exploit them to elucidate important details about the relationship between filter function design, control bandwidth, and noise characteristics. In particular, we identify regimes of optimal noise suppression and, in turn, optimal control bandwidth directly proportional to the size of the frequency bands where the noise power is large. In addition to providing guiding principles for filter design, our approach enables the development of controls that simultaneously yield robust noise filtering and high-fidelity single-qubit logic operations in a wide variety of complex noise environments.

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Phys. Rev. Applied 19, 014062– Published 23 January, 2023
  • Received 15 June 2022
  • Accepted 15 November 2022
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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