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Decoherence from the Vacuum Code: Exact Dephasing Laws, a Revival Dichotomy, and a Tracking Band in the SelectionStitch Model

Raghu Kulkarni

Published Aug 22, 2026• 0 citations
Publisher
DOI
10.13140/rg.2.2.21034.99521

Related papers

Decoherence from the Vacuum Code: Exact Dephasing Laws, a Revival Dichotomy, and a Tracking Band in the Selection–Stitch Model

Raghu Kulkarni

A companion paper predicted a two-step quantum–classical threshold at 13.1–22.6 μg from a close-packed vacuum lattice, resting on a stated hypothesis (P3): the lattice sustains a coherent mass excitation only while it can resolve the excitation's Compton wavelength. Here we derive as much of that structure as the lattice's own error-correcting code permits, working exactly on the [[3L_s^3, 2L_s^3+2, 3]] CSS family. Results: (1) an exact dephasing law — the vacuum code's own syndrome extraction dephases center-of-mass superpositions of edge-supported excitations at a rate set by the weight variance of the stabilizer group on the excitation's support; (2) a revival dichotomy theorem — at clock phase π per cycle, coherence is exactly 1 or exactly 0, decided by a one-line kernel criterion; (3) exact locality and composite laws — the composite clock runs at total mass because rest energies add, and dephasing is exactly additive beyond contact range, with a subadditive co-monitoring correction at contact; (4) a tracking band, conditional on one isolated dynamical assumption: if passive verification gives way to active checking at phase aliasing, the crossover spans m_alias = h/(8Lc) = 10.3 μg to m_wrap = h/(4Lc) = 20.5 μg — a cadence-derived band that the geometric window 13.1–22.6 μg overlaps without coinciding, so two independently constructed mechanisms select the same narrow microgram regime; and (5) the calibration foundation — the vacuum's entanglement obeys an exact area law on flat cuts, and for ball regions the exactly derived staircase factor of 3/2 is numerically compensated by inter-facet correlations to 10–15% at the tested sizes, with exactness of the compensation conjectured. What is not derived is stated with equal care: the existence of the passive-to-active transition is postulated, not derived, and the precise geometric endpoints and their √3 ratio remain inputs. Every claim carries a status tag.

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Irreversibility and Dephasing from Vacuum Fluctuations

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Exploratory Benchmark — Applied Quantum Computing Track This record presents an exploratory benchmark in the applied quantum computing track of the Radial Coherential Dynamics (RCD) research program. Building upon the previously published decoherence suppression model (Topological Decoherence Suppression via Coherential Geometry, Zenodo, December 2025, DOI: 10.5281/zenodo.18000641) and its first algorithmic application (Coherence-Regulated Variational Quantum Eigensolver: An Exploratory H₄ Benchmark, Zenodo, December 2025, DOI: 10.5281/zenodo.18049302), this work explores the impact of a fixed decoherence regulation law on variational quantum algorithms applied to a graphene-inspired system. An effective six-site graphene hexagon is modeled using a Fermi–Hubbard Hamiltonian with periodic boundary conditions. Variational Quantum Eigensolver (VQE) simulations are performed for both the neutral (N = 6) and hole-doped (N = 5) cases over a range of interaction strengths U/t. A controlled A/B methodology is employed: identical VQE simulations are executed using standard noise parameters (control) and RCD-regulated noise parameters (treatment), where the dephasing time is scaled according to the previously published law T2→T2/αT_2 \rightarrow T_2/\sqrt{\alpha}T2→T2/α with fixed α≈1.3×10−4\alpha \approx 1.3 \times 10^{-4}α≈1.3×10−4. No additional parameters are introduced. This work does not claim ab initio graphene results. The “exact” reference corresponds to the ground state of the effective Hubbard model used here. The benchmark is intended solely to assess whether a previously established decoherence suppression law produces consistent effects when transferred, without tuning, to multi-qubit variational algorithms. All code, data, and figures are provided for independent evaluation by the scientific community.

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Coherence-Regulated Variational Quantum Eigensolver: An Exploratory H₄ Benchmark Based on a Published Decoherence Law

Arturo Cerezo, IA Collaborative Panel — Claude (Anthropic) • ChatGPT (OpenAI) • Gemini (Google) • Grok (xAI)

Exploratory Benchmark — Applied Quantum Computing Track This record presents the first applied benchmark in the quantum computing track of the Radial Coherential Dynamics (RCD) research program. Building upon the previously published decoherence suppression model (Topological Decoherence Suppression via Coherential Geometry, Zenodo, December 2025, DOI: 10.5281/zenodo.18000641), which predicts a √α reduction of effective dephasing rates (α ≈ 1.3×10⁻⁴), this work explores the implications of that fixed decoherence law for variational quantum algorithms operating under noisy conditions. As an exploratory benchmark, the RCD noise suppression law (γ₍RCD₎ = γ₀√α) is applied to a Variational Quantum Eigensolver (VQE) simulation targeting the H₄ molecule in rectangular geometry. A controlled A/B methodology is employed: identical VQE simulations are performed using standard noise parameters (control) and RCD-regulated noise parameters (treatment), with all Hamiltonian, ansatz, optimizer, and geometry settings held fixed. This work does not claim molecular validation of RCD. Rather, it investigates whether a decoherence suppression law—previously established for single-qubit dynamics—produces observable effects when transferred, without additional tuning, to multi-qubit variational algorithms. All code, data, and figures are provided for independent evaluation by the scientific community. Guiding principle: “We do not use quantum computing as an oracle, but as a controlled laboratory of coherence.”

•Dec 24, 2025•0 citations

Decoherence in e.m. vacuum

Vladimir B. Braginsky, F. Y. Khalili, Mikhail Vasil'evich Sazhin

Physics Letters A•Nov 1, 1995•8 citations
A companion paper predicted a two-step quantum–classical threshold at 13.1–22.6 μg from a close-packed vacuum lattice, resting on a stated hypothesis (P3): the lattice sustains a coherent mass excitation only while it can resolve the excitation's Compton wavelength. Here we derive as much of that structure as the lattice's own error-correcting code permits, working exactly on the [[3L_s^3, 2L_s^3+2, 3]] CSS family. Results: (1) an exact dephasing law — the vacuum code's own syndrome extraction dephases center-of-mass superpositions of edge-supported excitations at a rate set by the weight variance of the stabilizer group on the excitation's support; (2) a revival dichotomy theorem — at clock phase π per cycle, coherence is exactly 1 or exactly 0, decided by a one-line kernel criterion; (3) exact locality and composite laws — the composite clock runs at total mass because rest energies add, and dephasing is exactly additive beyond contact range, with a subadditive co-monitoring correction at contact; (4) a tracking band, conditional on one isolated dynamical assumption: if passive verification gives way to active checking at phase aliasing, the crossover spans m_alias = h/(8Lc) = 10.3 μg to m_wrap = h/(4Lc) = 20.5 μg — a cadence-derived band that the geometric window 13.1–22.6 μg overlaps without coinciding, so two independently constructed mechanisms select the same narrow microgram regime; and (5) the calibration foundation — the vacuum's entanglement obeys an exact area law on flat cuts, and for ball regions the exactly derived staircase factor of 3/2 is numerically compensated by inter-facet correlations to 10–15% at the tested sizes, with exactness of the compensation conjectured. What is not derived is stated with equal care: the existence of the passive-to-active transition is postulated, not derived, and the precise geometric endpoints and their √3 ratio remain inputs. Every claim carries a status tag.
Exploratory Benchmark — Applied Quantum Computing Track This record presents an exploratory benchmark in the applied quantum computing track of the Radial Coherential Dynamics (RCD) research program. Building upon the previously published decoherence suppression model (Topological Decoherence Suppression via Coherential Geometry, Zenodo, December 2025, DOI: 10.5281/zenodo.18000641) and its first algorithmic application (Coherence-Regulated Variational Quantum Eigensolver: An Exploratory H₄ Benchmark, Zenodo, December 2025, DOI: 10.5281/zenodo.18049302), this work explores the impact of a fixed decoherence regulation law on variational quantum algorithms applied to a graphene-inspired system. An effective six-site graphene hexagon is modeled using a Fermi–Hubbard Hamiltonian with periodic boundary conditions. Variational Quantum Eigensolver (VQE) simulations are performed for both the neutral (N = 6) and hole-doped (N = 5) cases over a range of interaction strengths U/t. A controlled A/B methodology is employed: identical VQE simulations are executed using standard noise parameters (control) and RCD-regulated noise parameters (treatment), where the dephasing time is scaled according to the previously published law T2→T2/αT_2 \rightarrow T_2/\sqrt{\alpha}T2→T2/α with fixed α≈1.3×10−4\alpha \approx 1.3 \times 10^{-4}α≈1.3×10−4. No additional parameters are introduced. This work does not claim ab initio graphene results. The “exact” reference corresponds to the ground state of the effective Hubbard model used here. The benchmark is intended solely to assess whether a previously established decoherence suppression law produces consistent effects when transferred, without tuning, to multi-qubit variational algorithms. All code, data, and figures are provided for independent evaluation by the scientific community.
Exploratory Benchmark — Applied Quantum Computing Track This record presents the first applied benchmark in the quantum computing track of the Radial Coherential Dynamics (RCD) research program. Building upon the previously published decoherence suppression model (Topological Decoherence Suppression via Coherential Geometry, Zenodo, December 2025, DOI: 10.5281/zenodo.18000641), which predicts a √α reduction of effective dephasing rates (α ≈ 1.3×10⁻⁴), this work explores the implications of that fixed decoherence law for variational quantum algorithms operating under noisy conditions. As an exploratory benchmark, the RCD noise suppression law (γ₍RCD₎ = γ₀√α) is applied to a Variational Quantum Eigensolver (VQE) simulation targeting the H₄ molecule in rectangular geometry. A controlled A/B methodology is employed: identical VQE simulations are performed using standard noise parameters (control) and RCD-regulated noise parameters (treatment), with all Hamiltonian, ansatz, optimizer, and geometry settings held fixed. This work does not claim molecular validation of RCD. Rather, it investigates whether a decoherence suppression law—previously established for single-qubit dynamics—produces observable effects when transferred, without additional tuning, to multi-qubit variational algorithms. All code, data, and figures are provided for independent evaluation by the scientific community. Guiding principle: “We do not use quantum computing as an oracle, but as a controlled laboratory of coherence.”