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Renewal resetting of quantum dynamics: a classification for complete resets, a reduction for jump channels, and critical time scales

Anonymous

Published Oct 23, 2026• 0 citations
Publisher

Abstract

Unrefereed research candidate. A quantum system evolves under a fixed gate, step by step, and is occasionally reset; the waiting times between resets are independent and may have an infinite mean. Wald, Yao, Platini, Hooley and Carollo (Quantum 9, 1742, 2025, doi:10.22331/q-2025-05-13-1742) inferred from estimates and numerics how the averaged state behaves for the hazard r_n = gamma/(n+1)^alpha. This paper proves it: for alpha < 1 the state converges to a survival-weighted mixture, for alpha = 1 to the dephased state, and for alpha > 1 it approaches a rotating orbit and converges iff the reset state commutes with the gate. For complete resets the behaviour is classified for every renewal clock (finite mean, infinite mean, periodic, defective); a clock makes every finite-dimensional unitary reset system converge iff it is proper and aperiodic. This part is a short consequence of classical renewal theory. The claimed contributions are: the exact infinite-dimensional trace-norm defect 1 - m_pp (continuous spectral mass) for proper infinite-mean clocks, with no trace-norm convergent subsequence unless m_pp = 1; a laboratory-time reduction of imperfect resets (general jump channels, possibly noncommuting) to complete resetting at an effective state under a nonresonance condition (W), which is characterised, decidable for finitely supported clocks and open and dense, but is sufficient, not necessary, and not a classification; and uniform two-term asymptotics, endpoint and near-resonance crossovers for the critical clock gamma/(n+1), with practical time scales (dephasing can need more than 10^9 steps; numerical estimates). The archive contains the manuscript (PDF and LaTeX), a single deterministic verifier with its JSON report, semantic negative controls and SHA-256 sums. Assurance: written proofs; exact finite checks and labelled numerical checks; producer-side clean replay; internal AI-assisted review, AI-assisted adversarial audits before and after revision (OpenAI gpt-6-astra via Codex) and an AI-assisted verification re-review. This is not peer review, independent reproduction or formal verification. Creator: Anonymous. Prose, manuscript and data CC0-1.0; code MIT.

DOI
10.5281/zenodo.23580220

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Thermal ordering under Markovian relaxation: a finite-time criterion and its limits

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Unrefereed research candidate. When two copies of a system, one hotter and one cooler, relax in the same bath, the Markovian Mpemba effect is a crossing of their distances from equilibrium. This package gives a sufficient test that rules out such crossings at every time: if the dynamics and its time reverse preserve the cone of observables with nondecreasing arithmetic prefix means, cooling Gibbs preparations stay ordered for relative entropy (both orientations), squared Hellinger and Rényi divergences of order 0<α≤2, including for common schedules of noncommuting stages. For complete-graph bosonic population rates with common coupling, the test holds for every spectrum and bath temperature exactly when the spontaneous jump weight is concave; Ohmic baths with large enough cutoff, Drude–Lorentz and sub-Ohmic weights qualify on explicit ranges, super-Ohmic weights do not. A certified super-Ohmic example (J=d3) shows an actual relative-entropy crossing. Limits: an exact five-state cone-preserving example has a brief total-variation reversal, and for every N≥4 there are N-level systems with a slow-mode inversion although no proper induced subsystem shows one. The archive contains the 27-page manuscript (PDF and LaTeX), exact rational and interval certificates, a reproduction runner, semantic negative controls, CI and SHA-256 sums. Assurance: written proofs, exact certificates, internal AI-assisted review only (not peer review, independent reproduction or formal verification); the closest antecedent (Avitan et al. 2026) already excludes the slow-mode effect for Ohmic and sub-Ohmic spectra. Creator: Anonymous. Text and data CC0-1.0; code MIT.

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The Participating Clock: Conditioned Relational Dynamics as a Weak-Value Drive, and a Parameter-Free Second-Order Law

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Version 3 (2026-08). One correction, chair-directed after an independent text-only rebuild: the setting's conventions dictionary is regenerated from the code of record. The pointer packet is an ENERGY-basis Gaussian launched at tick zero (v1/v2 described it as a tick-space packet of tick-width sigma_n; the temporal width is in fact the inverse, NC/(4 pi sigma_n) ticks); the tick-state sign convention, the second geometry's sigma_n = 3, the twin/control definitions, and the post-selection probabilities are now printed; a standing text-only rebuild gate (fresh implementation from the setting paragraph alone, matching the exact conditioned state at 3.5e-14) guards the dictionary. Every published number stands (the independent rebuild reproduced the NC = 24 physics cold, the lane's first exterior verification, recorded in the data-and-code paragraph); the dictionary was broken. The methods law is minted program-wide: a geometry prints its dictionary, generated from the code, never transcribed. Version 2 (2026-08). Changes from v1: the clock-width profile is completed end to end: v1's spike-plus-plateau is the interior of a measured disturbance VALLEY with an optimal clock width (minimum at sigma_n* = 2.5; the broad side rises 93x by sigma_n = 24, tracked by the value law against exact evolution at ratios 0.985 and 0.995), so the least-disturbing clock is neither time-sharp nor energy-sharp; a pre-registered identification of the plateau with the sharp-clock limit was killed by a factor of 160 and is ledgered; the open problems are re-posed at the valley's optimum. When a finite quantum clock gates a register's interactions and the run is conditioned on the clock's final reading, the register's conditioned dynamics is derived at two orders and machine-verified against exact evolution. First order: the drive is the complex Aharonov-Albert-Vaidman weak value of the gating window projector (real part = Hermitian envelope, imaginary part = post-selection reweighting); a twin evolved under this envelope removes the entire first-order mismatch a mean-envelope control retains (state-metric deficits g^1.1 vs g^2.1, factor 56 at g = 0.1). Second order: the deficit is governed by the connected two-time window correlator under post-selection, resolved along the interaction picture; the resulting parameter-free value law matches measured deficits at ratios 0.92-1.05 across the clock-width grid and at a second geometry (1.03-1.07). The when/what trade-off of a participating clock is promoted from confounded excess to derived law: the disturbance is the connected fluctuation of the clock's timing answer, its clock-width profile is a predicted spike-plus-plateau (not a power law), and two earlier exponent claims are superseded with the reconciliation recorded. Two honest derivation failures (equal-time invisibility resurrected by the interaction picture; the kernel belonging inside the integral) are ledgered as the steps that located the law.

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An eight-point obstruction to universality of RBM(4,3)

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Unrefereed candidate, Anonymous, version 0.2.0-candidate. A finite integer certificate and written analytic argument establish a necessary leakage inequality on the full classical real binary RBM(4,3) visible closure, an eight-point obstruction to universality, a strictly positive excluded law, and non-sharp total-variation lower bounds. A contrasting exact construction represents every distribution on the specified parity-plus-one support. At least four hidden units are necessary; four-hidden sufficiency, smallest excluded support, complete classification, practical training penalties and historical priority are not established. The archive includes solver-free standard-library checkers, exact data, manuscript and PDF, normal/optimized hostile regression controls, source comparison, and one five-role coordinated AI internal editorial round. Producer checks and coordinated reconstruction are not unaffiliated reproduction, human specialist endorsement, journal peer review, or formal verification. The supplied external AI review reports a separate reconstruction but its linked audit ZIP was not retrieved. Original prose and data are CC0; code is MIT; upstream terms are preserved in LICENSES.md. The frozen editorial submission is included separately for audit and is superseded by the final release archive.

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Stochastic resetting in discrete-time quantum dynamics: steady states and correlations in few-qubit systems

Sascha Wald, Louie Hong Yao, Thierry Platini +2 more

Time evolution in several classes of quantum devices is generated through the application of quantum gates. Resetting is a critical technological feature in these systems allowing for mid-circuit measurement and complete or partial qubit reset. The possibility of realizing discrete-time reset dynamics on quantum computers makes it important to investigate the steady-state properties of such dynamics. Here, we explore the behavior of generic discrete-time unitary dynamics interspersed by random reset events. For Poissonian resets, we compute the stationary state of the process and demonstrate, by taking a weak-reset limit, the existence of "resonances" in the quantum gates, allowing for the emergence of steady state density matrices which are not diagonal in the eigenbasis of the generator of the unitary gate. Such resonances are a genuine discrete-time feature and impact on quantum and classical correlations even beyond the weak-reset limit. Furthermore, we consider non-Poissonian reset processes and explore conditions for the existence of a steady state. We show that, when the reset probability vanishes sufficiently rapidly with time, the system does not approach a steady state. Our results highlight key differences between continuous-time and discrete-time stochastic resetting and may be useful to engineer states with controllable correlations on existing devices.

arXiv:2410.11497•Quantum•May 13, 2025•11 citations
Unrefereed research candidate. A quantum system evolves under a fixed gate, step by step, and is occasionally reset; the waiting times between resets are independent and may have an infinite mean. Wald, Yao, Platini, Hooley and Carollo (Quantum 9, 1742, 2025, doi:10.22331/q-2025-05-13-1742) inferred from estimates and numerics how the averaged state behaves for the hazard r_n = gamma/(n+1)^alpha. This paper proves it: for alpha < 1 the state converges to a survival-weighted mixture, for alpha = 1 to the dephased state, and for alpha > 1 it approaches a rotating orbit and converges iff the reset state commutes with the gate. For complete resets the behaviour is classified for every renewal clock (finite mean, infinite mean, periodic, defective); a clock makes every finite-dimensional unitary reset system converge iff it is proper and aperiodic. This part is a short consequence of classical renewal theory. The claimed contributions are: the exact infinite-dimensional trace-norm defect 1 - m_pp (continuous spectral mass) for proper infinite-mean clocks, with no trace-norm convergent subsequence unless m_pp = 1; a laboratory-time reduction of imperfect resets (general jump channels, possibly noncommuting) to complete resetting at an effective state under a nonresonance condition (W), which is characterised, decidable for finitely supported clocks and open and dense, but is sufficient, not necessary, and not a classification; and uniform two-term asymptotics, endpoint and near-resonance crossovers for the critical clock gamma/(n+1), with practical time scales (dephasing can need more than 10^9 steps; numerical estimates). The archive contains the manuscript (PDF and LaTeX), a single deterministic verifier with its JSON report, semantic negative controls and SHA-256 sums. Assurance: written proofs; exact finite checks and labelled numerical checks; producer-side clean replay; internal AI-assisted review, AI-assisted adversarial audits before and after revision (OpenAI gpt-6-astra via Codex) and an AI-assisted verification re-review. This is not peer review, independent reproduction or formal verification. Creator: Anonymous. Prose, manuscript and data CC0-1.0; code MIT.
Unrefereed research candidate. When two copies of a system, one hotter and one cooler, relax in the same bath, the Markovian Mpemba effect is a crossing of their distances from equilibrium. This package gives a sufficient test that rules out such crossings at every time: if the dynamics and its time reverse preserve the cone of observables with nondecreasing arithmetic prefix means, cooling Gibbs preparations stay ordered for relative entropy (both orientations), squared Hellinger and Rényi divergences of order 0<α≤2, including for common schedules of noncommuting stages. For complete-graph bosonic population rates with common coupling, the test holds for every spectrum and bath temperature exactly when the spontaneous jump weight is concave; Ohmic baths with large enough cutoff, Drude–Lorentz and sub-Ohmic weights qualify on explicit ranges, super-Ohmic weights do not. A certified super-Ohmic example (J=d3) shows an actual relative-entropy crossing. Limits: an exact five-state cone-preserving example has a brief total-variation reversal, and for every N≥4 there are N-level systems with a slow-mode inversion although no proper induced subsystem shows one. The archive contains the 27-page manuscript (PDF and LaTeX), exact rational and interval certificates, a reproduction runner, semantic negative controls, CI and SHA-256 sums. Assurance: written proofs, exact certificates, internal AI-assisted review only (not peer review, independent reproduction or formal verification); the closest antecedent (Avitan et al. 2026) already excludes the slow-mode effect for Ohmic and sub-Ohmic spectra. Creator: Anonymous. Text and data CC0-1.0; code MIT.
Version 3 (2026-08). One correction, chair-directed after an independent text-only rebuild: the setting's conventions dictionary is regenerated from the code of record. The pointer packet is an ENERGY-basis Gaussian launched at tick zero (v1/v2 described it as a tick-space packet of tick-width sigma_n; the temporal width is in fact the inverse, NC/(4 pi sigma_n) ticks); the tick-state sign convention, the second geometry's sigma_n = 3, the twin/control definitions, and the post-selection probabilities are now printed; a standing text-only rebuild gate (fresh implementation from the setting paragraph alone, matching the exact conditioned state at 3.5e-14) guards the dictionary. Every published number stands (the independent rebuild reproduced the NC = 24 physics cold, the lane's first exterior verification, recorded in the data-and-code paragraph); the dictionary was broken. The methods law is minted program-wide: a geometry prints its dictionary, generated from the code, never transcribed. Version 2 (2026-08). Changes from v1: the clock-width profile is completed end to end: v1's spike-plus-plateau is the interior of a measured disturbance VALLEY with an optimal clock width (minimum at sigma_n* = 2.5; the broad side rises 93x by sigma_n = 24, tracked by the value law against exact evolution at ratios 0.985 and 0.995), so the least-disturbing clock is neither time-sharp nor energy-sharp; a pre-registered identification of the plateau with the sharp-clock limit was killed by a factor of 160 and is ledgered; the open problems are re-posed at the valley's optimum. When a finite quantum clock gates a register's interactions and the run is conditioned on the clock's final reading, the register's conditioned dynamics is derived at two orders and machine-verified against exact evolution. First order: the drive is the complex Aharonov-Albert-Vaidman weak value of the gating window projector (real part = Hermitian envelope, imaginary part = post-selection reweighting); a twin evolved under this envelope removes the entire first-order mismatch a mean-envelope control retains (state-metric deficits g^1.1 vs g^2.1, factor 56 at g = 0.1). Second order: the deficit is governed by the connected two-time window correlator under post-selection, resolved along the interaction picture; the resulting parameter-free value law matches measured deficits at ratios 0.92-1.05 across the clock-width grid and at a second geometry (1.03-1.07). The when/what trade-off of a participating clock is promoted from confounded excess to derived law: the disturbance is the connected fluctuation of the clock's timing answer, its clock-width profile is a predicted spike-plus-plateau (not a power law), and two earlier exponent claims are superseded with the reconciliation recorded. Two honest derivation failures (equal-time invisibility resurrected by the interaction picture; the kernel belonging inside the integral) are ledgered as the steps that located the law.
Unrefereed research candidate. When m identical copies of a quantum state of light are measured with Gaussian measurements (linear optics, Gaussian auxiliary modes, homodyne detection), measuring the copies jointly can give more Fisher information than measuring them one by one (Navarro, Morelli, Sanz and Mehboudi, arXiv:2512.20534), who left finite-copy optimality open. For every smooth family of pure single-mode Gaussian states and every m, this package proves the exact maximum of the Fisher information over all fixed (non-adaptive) Gaussian measurements, including ancilla-assisted schemes: a one-angle formula attained by concentrating the mean into one bright output and homodyne detection of every output. It also gives the exact optimum when measurement-seed squeezing is capped (in normalised coordinates), the exact shortfall from the quantum Fisher information (nondecreasing in m, at most one copy's variance information λ2/2, with an explicit limit), and a necessary and sufficient condition for strict collective advantage. The archive contains the 9-page manuscript (PDF and LaTeX), numerical checks with semantic negative controls, CI and SHA-256 sums. Assurance: written proofs; internal AI-assisted review only (not peer review, independent reproduction or formal verification); bounded prior-art search. Mixed states, multimode tangents and adaptive strategies are not covered. Creator: Anonymous. Text CC0-1.0; code MIT.
Unrefereed candidate, Anonymous, version 0.2.0-candidate. A finite integer certificate and written analytic argument establish a necessary leakage inequality on the full classical real binary RBM(4,3) visible closure, an eight-point obstruction to universality, a strictly positive excluded law, and non-sharp total-variation lower bounds. A contrasting exact construction represents every distribution on the specified parity-plus-one support. At least four hidden units are necessary; four-hidden sufficiency, smallest excluded support, complete classification, practical training penalties and historical priority are not established. The archive includes solver-free standard-library checkers, exact data, manuscript and PDF, normal/optimized hostile regression controls, source comparison, and one five-role coordinated AI internal editorial round. Producer checks and coordinated reconstruction are not unaffiliated reproduction, human specialist endorsement, journal peer review, or formal verification. The supplied external AI review reports a separate reconstruction but its linked audit ZIP was not retrieved. Original prose and data are CC0; code is MIT; upstream terms are preserved in LICENSES.md. The frozen editorial submission is included separately for audit and is superseded by the final release archive.
Time evolution in several classes of quantum devices is generated through the application of quantum gates. Resetting is a critical technological feature in these systems allowing for mid-circuit measurement and complete or partial qubit reset. The possibility of realizing discrete-time reset dynamics on quantum computers makes it important to investigate the steady-state properties of such dynamics. Here, we explore the behavior of generic discrete-time unitary dynamics interspersed by random reset events. For Poissonian resets, we compute the stationary state of the process and demonstrate, by taking a weak-reset limit, the existence of "resonances" in the quantum gates, allowing for the emergence of steady state density matrices which are not diagonal in the eigenbasis of the generator of the unitary gate. Such resonances are a genuine discrete-time feature and impact on quantum and classical correlations even beyond the weak-reset limit. Furthermore, we consider non-Poissonian reset processes and explore conditions for the existence of a steady state. We show that, when the reset probability vanishes sufficiently rapidly with time, the system does not approach a steady state. Our results highlight key differences between continuous-time and discrete-time stochastic resetting and may be useful to engineer states with controllable correlations on existing devices.