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  • Open Access

Regularization from superpositions of time evolutions

Yakir Aharonov1,2,3, Eliahu Cohen4,2,*, and Tomer Shushi5

  • 1Schmid College of Science and Technology, Chapman University, Orange, California 92866, USA
  • 2Institute for Quantum Studies, Chapman University, Orange, California 92866, USA
  • 3School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel
  • 4Faculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, 5290002 Ramat Gan, Israel
  • 5Center for Quantum Science and Technology, Department of Business Administration, Guilford Glazer Faculty of Business and Management, Ben-Gurion University of the Negev, Beer-Sheva, Israel

  • *Contact author: eliahu.cohen@biu.ac.il
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APS Open Sci. 1, 000049 – Published 23 June, 2026

DOI: https://doi.org/10.1103/4yq5-y6wf

Abstract

Short-time approximations and path integrals may be dominated by high-energy or large-field contributions, especially for singular interactions, motivating regulators that suppress such contributions while remaining removable. We show that smooth regulators of this kind can arise as conditional maps generated by interference in coherently controlled, postselected superpositions of time evolutions. In quantum mechanics, a Gaussian superposition of short-time translations produces a Gaussian energy filter that renders time-sliced kernels well behaved for singular potentials while recovering the target unitary dynamics when the regulator is removed and in the continuum limit. We also discuss a related momentum-space regulator obtained by coherently smearing a kinetic prefactor. In scalar quantum field theory, local Gaussian smearing of the quartic coupling induces a positive local ϕ8 term in the Euclidean action, providing a symmetry-compatible large-field stabilizer. We derive short-time error bounds, analyze multistep success probabilities, and discuss how the construction can be used as a removable regulator together with conventional ultraviolet regularization.

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APS Open Sci. 1, 000049– Published 23 June, 2026
Vol. 1
  • Received 6 April 2026
  • Accepted 15 June 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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