Regularization from Superpositions of Time Evolutions

Quantum Physics arXiv:2601.04685 (quant-ph) [Submitted on 8 Jan 2026] Title:Regularization from Superpositions of Time Evolutions Authors:Eliahu Cohen, Tomer Shushi View a PDF of the paper titled Regularization from Superpositions of Time Evolutions, by Eliahu Cohen and 1 other authors View PDF HTML (experimental) Abstract:Short-time approximations and path integrals can be dominated by high-energy or large-field contributions, especially in the presence of singular interactions, motivating regulators that are suppressive yet removable. Standard regulators typically impose such suppressions by hand (e.g. cutoffs, higher-derivative terms, heat-kernel smearing, lattice discretizations), while here we show that closely related smooth filters can arise as the conditional map produced by interference in a coherently controlled, postselected superposition of evolutions. A successful postselection implements a single heralded operator that is a coherent linear combination of time-evolution operators. For a Gaussian superposition of time translations in quantum mechanics, the postselected step is $V_{\sigma,\Delta t}=e^{-iH\Delta t}\,e^{-\frac12\sigma^2\Delta t^2H^2}$, i.e.\ the desired unitary step multiplied by a Gaussian energy filter suppressing energies above order $1/(\sigma\Delta t)$. This renders short-time kernels in time-sliced path-integral approximations well behaved for singular potentials, while the target unitary dynamics is recovered as $\sigma\to0$ and (for fixed $\sigma$) also as $\Delta t\to0$ at fixed $t$. In scalar QFT, a local Gaussian smearing of the quartic coupling induces a positive $(\sigma^2/2)\phi^8$ term in the Euclidean action, providing a symmetry-compatible large-field stabilizer; it is naturally viewed as an irrelevant operator whose effects can be renormalized at fixed $\sigma$ (together with a conventional UV regulator) and removed by taking $\sigma\to0$. We give short-time error bounds and analyze multi-step success probabilities. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.04685 [quant-ph] (or arXiv:2601.04685v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.04685 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Eliahu Cohen [view email] [v1] Thu, 8 Jan 2026 07:54:22 UTC (14 KB) Full-text links: Access Paper: View a PDF of the paper titled Regularization from Superpositions of Time Evolutions, by Eliahu Cohen and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)