Coherence across many-body degrees of freedom is governed by a simple empirical law. Defining a global order parameter C from phase samples, we observe three robust behaviors: (1) Gaussian dephasing, where C(σ) behaves approximately like exp(−ασ²); (2) return-to-attractor dynamics, where C relaxes back toward a fixed point C* with rate κ; and (3) finite-size scaling, where C(N) behaves approximately like C₀ − β/N and converges toward a stable limit C* ≈ 1. These relations appear consistently across simulations and hardware-stress surrogates over wide sweeps of disorder and system size. Together, they define a minimal phenomenological framework for “coherent computing,” where architectures are judged by how they shape, rather than suppress, phase noise.
Coherence across many-body degrees of freedom is governed by a simple empirical law. Defining a global order parameter C from phase samples, we observe three robust behaviors: (1) Gaussian dephasing, where C(σ) behaves approximately like exp(−ασ²); (2) return-to-attractor dynamics, where C relaxes back toward a fixed point C* with rate κ; and (3) finite-size scaling, where C(N) behaves approximately like C₀ − β/N and converges toward a stable limit C* ≈ 1. These relations appear consistently across simulations and hardware-stress surrogates over wide sweeps of disorder and system size. Together, they define a minimal phenomenological framework for “coherent computing,” where architectures are judged by how they shape, rather than suppress, phase noise.
We investigate the competition between system size and decoherence in open quantum systems using a minimal spin-chain model. The system is an N-qubit one-dimensional XY chain evolving under local amplitude-damping and dephasing Lindblad operators whose rates are scaled uniformly by a tunable stabilizer parameter, s, over the range 0.3 to 1.0. Simulations cover system sizes N = 4, 6, 8, and 10, together with static on-site disorder strengths sigma = 0.0, 0.15, and 0.40. Across the full parameter sweep, the global purity half-life decreases monotonically with increasing N for every fixed stabilizer and disorder level, following a power-law relation in which t1/2 is proportional to N raised to alpha, with alpha about -1.04. Lowering the stabilizer factor extends coherence lifetime by roughly a factor of three and allows modest genuine nearest-neighbor entanglement to appear. Static disorder up to 40% has essentially no effect on half-life or final purity. Explicit falsification tests show no evidence of collective protection under strictly local-noise conditions. Taken together, the results indicate that proliferation acts as a testable liability in local-noise models unless per-site decoherence is actively suppressed. The study offers a quantitative baseline for quantum-biological models of ordered lattices. In particular, fluorescence lifetime and quantum-yield measurements on stabilized versus unstabilized microtubule preparations could directly test the predicted scaling behavior
We provide a brief survey of quantum statistical characterisations of order, disorder and coherence in systems of many degrees of freedom. Here, order and coherence are described in terms of symmetry breakdown, while disorder is described in terms of entropy and algorithmic complexity, whose interconnection has been recently extended from the classical to the quantum domain. We see that, in the present physical context, the concepts of order and disorder are not mutually antithetical, but bear an interrelationship similar to that between signals and noise.
Update Notice (v2) 2026/2/13 This preprint has been superseded by a significantly revised version, which has been uploaded as a separate submission. In the original version (v1), the relation between internal dissipation power and the energy relaxation rate was introduced in a phenomenological manner. However, a rigorous first-principles derivation has now been completed in a companion paper [Guo (2026), Exact Relation between Internal Dissipation Power and Energy Relaxation Rate——A Rigorous Derivation in Markovian Quantum Systems]. Using this exact relation Rinternal=ℏωqΓ1⟨σ+σ−⟩Rinternal=ℏωqΓ1⟨σ+σ−⟩, the previously phenomenological "energy competition" framework has been reformulated from the ground up. As a result: The parameter ff (energy allocation fraction) is now rigorously defined in terms of experimentally accessible quantities, rather than introduced as a phenomenological fit parameter. The previous phenomenological arguments and associated experimental discussions in v1 are no longer valid and should be disregarded. The new version provides a complete microscopic foundation for the theory of energy competition in superconducting qubit decoherence. Readers are strongly encouraged to consult the latest version (available at [10.5281/zenodo.18624328) for a comprehensive and self-contained treatment. Version 2 The decoherence time of superconducting qubits is commonly believed to be dominatedby dielectric loss (loss tangent tan 𝛿). Multiple experimental studies have found an empiricalscaling relationship approximately Γ ∝ (tan 𝛿)0.7 between the decoherence rate Γ = 1/𝑇2and tan 𝛿. Based on the ”Interface Projection Realism” framework, this paper proposes apossible new physical picture for decoherence. By analyzing 25 superconducting quantumdevices covering single-qubit, multi-qubit, hybrid systems, and 3D integration, we observethe dispersion of this scaling relationship in optimized interface samples. Experimentaldata show that unoptimized samples indeed follow Γ ∝ (tan 𝛿)0.7, while optimized samplesexhibit significant dispersion in the scaling exponent.To explain this phenomenon, we propose a decoherence theoretical framework basedon the ”Energy Competition” picture. This framework reinterprets decoherence as the re-sult of competitive allocation of the input microwave energy between the ”internal dissipa-tion channel generating noise” and the ”net channel maintaining coherence.” This physicalpicture is a concrete implementation of Interface Projection Realism in the decoherenceproblem. By introducing the energy allocation ratio 𝑓 and the interface intrinsic competi-tion coefficient 𝜒, the theoretical framework predicts that the pure dephasing rate satisfiesΓ𝜙 = 𝜒 · 𝑓 /(1 − 𝑓 ) in the strong suppression limit. This framework provides a possibleexplanation for the dispersion of scaling behavior. Furthermore, the analysis of paired sam-ples (with the same tan 𝛿 but 𝑇2 differing by a factor of 16.7) provides indirect evidence forthe possibility of 𝑓 being an independent parameter.Moreover, the theoretical framework can unify the explanation of decoherence data fromsingle qubits to complex systems and proposes unique predictions that can be directly veri-fied experimentally, such as power independence and noise spectrum evolution. This workprovides a new perspective based on Interface Projection Realism for understanding quan-tum decoherence and deepens the goal of interface engineering from simply reducing lossto possibly regulating the energy allocation ratio 𝑓 . Important Update (Updated January 28, 2026) The square-root decoherence scaling law (Γ∝κeff) with scaling exponent α=0.5 reported in this work was derived via empirical fitting against superconducting qubit experimental datasets, based on the "resource competition theory at dynamic projection interfaces." This exponent was established under the framework of phenomenological analysis, leveraging established physical heuristics for intrinsic material loss and the loss angle tanδ, and exhibited high fitting goodness for low-noise, weak-coupling quantum systems. Subsequent research has advanced this framework to a comprehensive mathematical-physical theory—Interface Projection Realism (IPR)—grounded in quantum information first principles. A key innovation of IPR is the introduction of the transmissivity field Ξ(x,t) (as the fundamental order parameter describing the quantum-classical interface) and the rigorous derivation of its quantum information dynamics equation. By analyzing an expanded set of superconducting qubit decoherence data through weighted least-squares fitting (yielding R2=0.9987, an extremely significant F-statistic of 2856.3), the universal decoherence scaling exponent is refined to α=0.792±0.008. This revised exponent corresponds to a synergy index m=4.81±0.15, which originates from the cooperative effect of five major noise channels (dielectric loss, quasiparticle tunneling, flux noise, charge noise, and radiation loss) embedded in quantum channel dynamics. IPR further makes two independent testable predictions—equivalence principle violation (Δa/aˉ∼2.3×10−9) and a first-principles calculation of dark energy density (ρΛ≈4.2×10−47GeV4, consistent with Planck 2018 observations)—demonstrating its explanatory power across quantum decoherence, quantum gravity, and cosmology. A complete account of the theoretical derivation, microphysical mechanism, and experimental corroboration is provided in our latest work: Interface Projection Realism: A Multiscale Unified Theory Based on Quantum Information Dynamics (Zenodo, Version v3, DOI: 10.5281/zenodo.18400122, January 28, 2026). This preprint serves as a foundational stage-specific contribution to the evolutionary trajectory of the IPR framework. The α=0.5 square-root scaling relation remains a valid limiting case for low-noise, weak-coupling material systems, while the refined α=0.792 exponent offers a universal description across broader material and noise conditions. Version 1 We report a universal square-root scaling law between the decoherence rate Γ of a quantum system and its effective intrinsic dissipation κeff, i.e., Γ ∝ √ κeff. This empirical law, observed across platforms like superconducting qubits, finds its mechanistic explanation within a new theoretical framework of resource com petition at a dynamic projection interface. The framework posits that our (3+1)-dimensional classical spacetime emerges from a higher-dimensional realm of potentialities (L1) through a filtering process governed by the interface perme ability field Ξ(x, t). Finite information-energy flux from L1 is contested between systems’ tendency to maintain quantum coherence and their intrinsic demand to dissipate noise for classical stability, quantified by κeff. From this competition dy namics, we derive the square-root scaling law. The model further provides unified, objective descriptions of quantum measurement as channel locking and of grav ity as emergence from Ξ-field distortion. Several concrete, testable predictions are proposed, including nonlinear jumps in coherence at phase transitions and a novel testable correlation for equivalence principle experiments.
The study and control of coherence in quantum systems is one of the most exciting recent developments in physics. Quantum coherence plays a crucial role in emerging quantum technologies as well as fundamental experiments. A major obstacle to the utilization of quantum effects is decoherence, primarily in the form of dephasing that destroys quantum coherence, and leads to effective classical behavior. We show that there are universal relationships governing dephasing that constrain the relative rates at which quantum correlations can disappear. These lead effectively to speed limits which become especially important in multipartite systems.
This Theorem establishes that the coherence decay rate is the unique globally attracting fixed point of a self-consistent kernel-induced dynamical map. The exponential saturation law of T51 emerges as the asymptotic reduction of this fixed-point structure in the strong-suppression regime, rather than being postulated. The kernel-induced map is F(Γ_coh) := Γ_max[1 − exp(−M(Γ_coh)/M₀)], where the composite hazard variable M(Γ_coh) := P_inst(1 − exp[−β/(γ + Γ_coh)]) is self-referential, stronger decoherence suppresses revival, increasing M, increasing decoherence further. Four steps prove the unique attractor: (1) Monotonicity F'(Γ_coh) < 0 by explicit sign chain; (2) Existence and uniqueness via IVT on G = F − id with G' < −1; (3) Global convergence via even/odd subsequence monotone convergence; (4) Asymptotic reduction, in the regime β/γ ≫ 1, M(Γ_coh) ≈ P_inst and the fixed-point equation reduces to the exponential saturation law Γ_coh ≈ Γ_max(1 − e^{−P_inst/M₀}). Three corollaries: mechanism separation (β = 0 forces Γ_coh* = 0, phase instability alone is insufficient); universality across Q5 parameter families; saturation bound Γ_coh* ≤ Γ_max. The Grumpy Bear Principle provides an informal interpretation of three dynamical regimes: sleeping bear (M ≈ 0, coherent), grumpy bear (instability present but strong revival), and bear claws (M large, fixed point near Γ_max, self-referential lock-in). Status: Fixed-point monotonicity, G' < −1, existence and uniqueness, global convergence, mechanism separation, and saturation bound are all solid by explicit algebraic argument. Asymptotic reduction solid in β/γ ≫ 1 regime, regime validity not yet verified from T17 kernel. Local stability is solid in the perturbative regime. Primary open step: explicit derivation of β from [M_n,D_n]Y geometry from T17 kernel generators. All results inherit T17, T29, T33, T35, T50, T51 conditionality. Dependencies: T8, T11, T29, T33, T35, T50, T51.