Locale Framework Applied to Quantum Computing Innovations & Practical Applications

Abstract

Quantum computing is often presented through a small set of recurring claims: continuous-variable systems are naturally advantaged, more modes means more power, quantum advantage has been demonstrated at device level, statistics could in principle be non-standard, complex amplitudes are essential, approximation-based gate synthesis is the only approach, a transmon is a qubit, and fault tolerance is a matter of years. This paper argues that each of these claims is true only within a restricted domain of applicability, and that the boundaries at which they fail are not defects of the claims but the places where the physics relevant to practitioners actually lives. Drawing on the locale framework introduced in a companion record, the paper states eight of the most widely repeated claims, makes the domain of each explicit, and pairs each boundary with work presented at the 23rd International Conference on Quantum Physics and Logic (QPL 2026), including new results on the energy cost of continuous-variable computation, classical simulation of Clifford+T circuits, invariance under quantum permutations, real-valued quantum theory, and the arithmetic structure of gate synthesis. A review of the practitioner-oriented contributions at QPL 2026 follows, and five challenges raised at the conference are answered. The paper closes with the observation that the quantity which survives every boundary examined is energy per solution. Why a reader should care: this paper turns every quantum-computing innovation and practical-application claim into a conditional truth with an explicit locale, then pairs each claim with the exact QPL 2026 paper that documents where it breaks. The seams catalog T1-T8 replaces a year of vendor roadmaps: claims are conditional truths, the seams are public, and the energy exchange rate between paradigms is the currency. Premise-depth: the framework's primitives 'locale' and 'interface' are imported (UMP.011); OSR is a named input; the energy theorems are imported external results; the catalog is retrodictive; no dynamical theory of seams is claimed.