2026/01/31 by Yakir Aharonov, Eliahu Cohen, Tomer Shushi
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Model Reduction and Neural Networks #Numerical methods in inverse problems #quant-ph
paper · pdf · doi:10.1103/4yq5-y6wf
published as APS Open Science 1, 000049 (2026) · Updated version, 13 pages
arxiv created 2026/05/18 · openalex publication_date 2026/06/15 · openalex created_date 2026/06/16 · openalex updated_date 2026/07/21 · arxiv updated 2026/07/30
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 Vσ,Δt=e-iHΔt e-\frac12σ2Δt2H2, i.e. the desired unitary step multiplied by a Gaussian energy filter suppressing energies above order 1/(σΔt). This renders short-time kernels in time-sliced path-integral approximations well behaved for singular potentials, while the target unitary dynamics is recovered as σ→0 and (for fixed σ) also as Δt→0 at fixed t. In scalar QFT, a local Gaussian smearing of the quartic coupling induces a positive (σ2/2)ϕ8 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 σ (together with a conventional UV regulator) and removed by taking σ→0. We give short-time error bounds and analyze multi-step success probabilities.