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  • Open Access

Higher-order Zeno sequences

Kasra Rajabzadeh Dizaji1,2,*, Leeseok Kim3, Milad Marvian3, and Christian Arenz1

  • *Contact author: krajabza@asu.edu
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Phys. Rev. Research 8, 023051 – Published 16 April, 2026

DOI: https://doi.org/10.1103/glcd-gm3v

Abstract

The quantum Zeno effect typically refers to freezing the dynamics of a quantum system through frequent observations. In general, quantum Zeno dynamics is obtained with an error of order O(1/N), where N is the number of projective measurements performed within a fixed evolution time. In this work, we develop higher-order Zeno sequences that achieve faster convergence to Zeno dynamics, yielding an improved error scaling of O(1/N2k), where k describes the order of the Zeno sequence. This is achieved by relating higher-order Zeno sequences to higher-order Trotter formulas that achieve similar convergence behavior. We leverage this relation to develop higher-order Zeno sequences for different manifestations of the quantum Zeno effect, including frequent projective measurements and unitary kicks. We go on to discuss achieving quantum Zeno dynamics through periodic control fields of high frequency. We explicitly develop control fields that yield a second-order type improvement in the Zeno error scaling and present shorter Zeno sequences. Finally, we discuss the connection to randomized and Uhrig dynamical decoupling to develop more efficient implementations in the weak-coupling regime.

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Phys. Rev. Research 8, 023051– Published 16 April, 2026
  • Received 2 December 2025
  • Accepted 18 March 2026
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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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