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Efficient Qubit Calibration by Binary-Search Hamiltonian Tracking

Fabrizio Berritta1,2, Jacob Benestad3, Lukas Pahl1,4, Melvin Mathews1,5, Jan A. Krzywda6, Réouven Assouly1, Youngkyu Sung1,4, David K. Kim7, Bethany M. Niedzielski7 et al.

Kyle Serniak1,7, Mollie E. Schwartz7, Jonilyn L. Yoder7, Anasua Chatterjee2,8, Jeffrey A. Grover1, Jeroen Danon3, William D. Oliver1,4,9, and Ferdinand Kuemmeth2,10,11,*

  • *Contact author: ferdinand.kuemmeth@ur.de
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PRX Quantum 6, 030335 – Published 26 August, 2025

DOI: https://doi.org/10.1103/77qg-p68k

Abstract

We present and experimentally implement a real-time protocol for calibrating the frequency of a resonantly driven qubit, achieving exponential scaling in calibration precision with the number of measurements, up to the limit imposed by decoherence. The real-time processing capabilities of a classical controller dynamically generate adaptive probing sequences for qubit-frequency estimation. Each probing evolution time and drive frequency are calculated to divide the prior probability distribution into two branches, following a locally optimal strategy that mimics a conventional binary search. The scheme does not require repeated measurements at the same setting, as it accounts for state preparation and measurement errors. Its use of a parametrized probability distribution favors numerical accuracy and computational speed. We show the efficacy of the algorithm by stabilizing a flux-tunable transmon qubit, leading to improved coherence and gate fidelity. As benchmarked by gate-set tomography, the field-programmable gate array (FPGA) powered control electronics partially mitigates non-Markovian noise, which is detrimental to quantum error correction. The mitigation is achieved by dynamically updating and feeding forward the qubit frequency. Our protocol highlights the importance of feedback in improving the calibration and stability of qubits subject to drift and can be readily applied to other qubit platforms.

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Popular Summary

Quantum computing and quantum sensing rely on the development of quantum devices. As quantum devices are sensitive to changes in their environment, they can easily lose their intended quantum properties, a phenomenon known as quantum decoherence. To calibrate quantum devices, one can apply feedback by estimating uncontrolled environmental noise in real time. This is an important task for many platforms such as superconducting qubits, spin qubits, trapped atoms, and others.

In this study, a protocol is presented for an efficient real-time Hamiltonian estimation of a superconducting qubit. Real-time Bayesian Hamiltonian estimation is performed using a field-programmable gate array (FPGA) based on single-shot readout classification. Even though the qubit frequency fluctuates over time because of flux noise (which normally would cause decoherence), it is estimated on the fly by updating its probability distribution according to a binary-search algorithm. The FPGA then adapts the free-evolution time and drive frequency of the microwave pulses accordingly, resulting in improved qubit performance with fewer than ten measurements.

This study introduces a new protocol that employs a binary-search Hamiltonian-estimation protocol aimed at mitigating the effects of decoherence and drift of solid-state qubits affected by low-frequency noise.

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PRX Quantum 6, 030335– Published 26 August, 2025
  • Received 10 January 2025
  • Revised 26 May 2025
  • Accepted 14 July 2025
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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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