We present a rigorous derivation and numerical validation of a universal projection-law factorization for quartic nonlinear coupling rates across physically distinct platforms. The central result is that observable Kerr-type interactions -- self-Kerr, cross-Kerr, and cross-phase modulation -- factorize into a dimensionless projection coefficient and an intrinsic quartic energy scale. This structure follows from canonical quantization of a quartic interaction projected onto a finite normal-mode basis. We state this result as a formal proposition with clearly enumerated assumptions, provide a proof sketch based on second quantization of the anharmonic potential, and enumerate the domain of validity. We then implement the scaling law as a lightweight computational toolkit (UEFT-Designer) with platform-specific kernels for superconducting circuits, photonic microcavities, and epsilon-near-zero (ENZ) structures. A complete, step-by-step worked example for a superconducting quarton device -- with full uncertainty propagation -- predicts a cross-Kerr rate $χ/2π= 361\pm 13\,\mathrm{MHz}$, agreeing with the independently measured value of $366\pm 0.5\,\mathrm{MHz}$ \cite{Ye2025} to within 1.4\%. A formal error-propagation analysis establishes that the dominant uncertainty is the Josephson-energy extraction uncertainty ($\sim\!2\%$), not the geometric projection factor. Cross-platform validation against five independent experiments spanning eight orders of magnitude in coupling strength confirms the universality of the factorization to within reported experimental uncertainties. The ghost-sector spectral correction introduced in earlier versions is reframed as an optional phenomenological self-energy model with no mandatory role in the validated scaling law.
We present a rigorous derivation and numerical validation of a universal projection-law factorization for quartic nonlinear coupling rates across physically distinct platforms. The central result is that observable Kerr-type interactions -- self-Kerr, cross-Kerr, and cross-phase modulation -- factorize into a dimensionless projection coefficient and an intrinsic quartic energy scale. This structure follows from canonical quantization of a quartic interaction projected onto a finite normal-mode basis. We state this result as a formal proposition with clearly enumerated assumptions, provide a proof sketch based on second quantization of the anharmonic potential, and enumerate the domain of validity. We then implement the scaling law as a lightweight computational toolkit (UEFT-Designer) with platform-specific kernels for superconducting circuits, photonic microcavities, and epsilon-near-zero (ENZ) structures. A complete, step-by-step worked example for a superconducting quarton device -- with full uncertainty propagation -- predicts a cross-Kerr rate χ/2π=361±13MHz, agreeing with the independently measured value of 366±0.5MHz \cite{Ye2025} to within 1.4%. A formal error-propagation analysis establishes that the dominant uncertainty is the Josephson-energy extraction uncertainty (∼2%), not the geometric projection factor. Cross-platform validation against five independent experiments spanning eight orders of magnitude in coupling strength confirms the universality of the factorization to within reported experimental uncertainties. The ghost-sector spectral correction introduced in earlier versions is reframed as an optional phenomenological self-energy model with no mandatory role in the validated scaling law.
Strong nonlinear coupling of superconducting qubits and/or photons is a critical building block for quantum information processing. Because of the perturbative nature of the Josephson nonlinearity, linear coupling is often used in the dispersive regime to approximate nonlinear coupling. However, this dispersive coupling is weak and the underlying linear coupling mixes the local modes, which, for example, distributes unwanted self-Kerr nonlinearity to photon modes. Here, we use the quarton to yield purely nonlinear coupling between two linearly decoupled transmon qubits. The quarton's zero ϕ^{2} potential enables an ultrastrong gigahertz-level cross-Kerr coupling, which is an order of magnitude stronger compared to existing schemes, and the quarton's positive ϕ^{4} potential can cancel the negative self-Kerr nonlinearity of qubits to linearize them into resonators. This ultrastrong cross-Kerr coupling between bare modes of qubit-qubit, qubit-photon, and even photon-photon is ideal for applications such as single microwave photon detection, ultrafast two-qubit gates, and readout.
The engineering of Kerr interactions is of great interest for processing quantum information in multipartite quantum systems and for investigating many-body physics in a complex cavity-qubit network. We study how coupling multiple different types of superconducting qubits to the same cavity modes can be used to modify the self- and cross-Kerr effects acting on the cavities and demonstrate that this type of architecture could be of significant benefit for quantum technologies. Using both analytical perturbation theory results and numerical simulations, we first show that coupling two superconducting qubits with opposite anharmonicities to a single cavity enables the effective self-Kerr interaction to be diminished, while retaining the number splitting effect that enables control and measurement of the cavity field. We demonstrate that this reduction of the self-Kerr effect can maintain the fidelity of coherent states and generalised Schrödinger cat states for much longer than typical coherence times in realistic devices. Next, we find that the cross-Kerr interaction between two cavities can be modified by coupling them both to the same pair of qubit devices. When one of the qubits is tunable in frequency, the strength of entangling interactions between the cavities can be varied on demand, forming the basis for logic operations on the two modes. Finally, we discuss the feasibility of producing an array of cavities and qubits where intermediary and on-site qubits can tune the strength of self- and cross-Kerr interactions across the whole system. This architecture could provide a way to engineer interesting many-body Hamiltonians and be a useful platform for quantum simulation in circuit quantum electrodynamics.
I present a mathematically consistent framework in which a single light scalar field Φ generatescorrelated signatures across quantum tunneling, spin-dependent interactions, and decoherence. Alleffects are derived from a single effective Lagrangian without ad hoc insertions. The frameworkuses a dimensionless coupling g to a density operator OˆS (mass dimension 3), ensuring dimensionalconsistency across all three regimes. The effective 1D tunneling potential is obtained by explicittransverse projection of the 3D interaction, eliminating phenomenological reduction factors. Mean-field validity is justified in the high-density regime where quantum fluctuations are suppressed by1/√nmV . In tunneling systems, the force is derived from the potential gradient F = −R|ψ|2∂xV dx,independent of stress-tensor ambiguities. To leading order in g and in the absence of operator mixing,both ∆P/P0 and the decoherence rate γ scale as g2, establishing ∆γ/γ = ∆(P/I)/(P/I) as a directtest of the shared coupling structure. Renormalization group flow connects the couplings throughδg/g = β0 δc/c with β0 = 2/3 in a minimal UV completion and β0 = O(1) generically. Eliminatingparameters yields the falsifiable prediction ∆(P/I)/(P/I) = β0 · ∆(c2/Λ2)/(c2/Λ2) = ∆γ/γ. Ipresent a multi-platform protocol with NEMS, spin sensors, and superconducting qubits, usingnuclear spin polarization as the common modulation. The key experimental observable is notthe absolute signal magnitude but the cross-regime correlation structure, which is robust againstindependent backgrounds. A deviation from the predicted scaling would directly falsify the unifiedframework.
Abstract Cross-platform comparison of superconducting quantum devices requires statistical care because heterogeneous architectures implement qualitatively different transport mechanisms, couple to distinct microscopic loss channels, and typically operate in different temperature regimes. We present a methodological case study showing how aggregation of data across platforms can mask qualitatively different within-architecture temperature dependencies when platform identity is confounded with operating temperature. To enable controlled comparison, we introduce two scaling parameters: a dimensionless normalized temperature T∗=kBT/(hf) and a resistance-like decoherence parameter A=(hf/eIc)(lnQ/2π). We develop a detailed physical argument for why the baseline value of A is expected to be architecture-dependent, focusing on the distinct roles of Cooper-pair tunneling in SIS junctions, Andreev bound states in SNS junctions, ferromagnetic layer effects in SIsFS devices, and confinement effects in nanowire junctions. Applying this framework to published data from five distinct junction architectures (Transmon SIS, conventional SIS, SIsFS, planar SNS, and nanowire SNS; N=23 points from five independent studies), we find that the pooled dataset exhibits a weak positive correlation between A and T∗ (r=0.085, p=0.70). However, when stratified by architecture, within-group correlations reveal qualitatively different temperature dependencies: SIsFS shows strong positive dependence (308.4±22.6Ω, p=0.047), planar SNS shows strong positive dependence (205.6±11.6Ω, p=0.036), while transmons show near-zero dependence (−7.2±17.3Ω, p=0.688). Two architectures show positive slopes that reach statistical significance despite small samples (n=3 each), though these results are sensitive to individual data points (see Appendix C). Analysis of variance confirms that architecture explains the dominant share of variance (ANOVA F4,18=670.7, p<0.0001; ICC ≈0.98). Decomposition of A reveals that the 1/Ic term accounts for the factor-of-6.6 variation across architectures (r=−0.94 with logIc), while the lnQ term varies by only 30\%. We argue that these observations are physically expected from architecture-specific transport and loss mechanisms, and we outline experimental designs with overlapping temperature sweeps that could disentangle temperature dependence from platform identity in future benchmarking efforts. All data, extraction uncertainties, and analysis code are provided in the appendices to ensure reproducibility.
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.
We study correlation properties of polaritons at zero temperature in a multiconnected Jaynes--Cummings (MCJC) lattice on a superconducting circuit quantum electrodynamics platform with engineered cross-Kerr nonlinearity that mimics attractive nearest-neighbour interaction. A multi-connected Jaynes--Cummings lattice is a one-dimensional lattice constructed from alternating qubits and resonators with different left and right couplings. The nearest-neighbour interaction or cross-Kerr coupling is implemented dispersively through ladder-type qutrits between each nearest neighboring pair of resonator modes. Projecting onto the lower-polaritonic manifold, we derive an extended two-mode (bipartite) Bose--Hubbard-like model featuring on-site and attractive nearest-neighbor interactions. Employing a continuum bosonization approach, we express the Hamiltonian in terms of symmetric (+) and antisymmetric (−) collective modes. In the regime where the (−) sector acquires a finite gap, one can reduce the system to an effective single-component Luttinger liquid model for the + sector. The cross-Kerr term reduces the compressibility of the (+) mode, thereby enhancing the corresponding Luttinger parameter K+, resulting in the slower algebraic decay of single-particle correlations, G(x)∝∣x∣−1/(4K+).