Q-Flex (United States)

Prime Numbers as Universal Optimization Primitives

The scholarly understanding of prime numbers is structured around four paradigms: quantum chaos, classical optimization, algorithmic information theory, and deterministic law. However, these paradigms are marked by unresolved tensions—dynamical, hierarchical, and methodological—t...

Reassessing the Foundations of Quantum Computation: From Theoretical Artifacts to Physical Realities

Abstract: This analysis argues that Shor’s algorithm, while mathematically elegant, functions as a theoretical artifact defined under physically unrealizable conditions—perfect coherence, infinite precision, and unbounded resources—rendering it a mathematical trap that has misdir...

Number Theory as Physics: The Prime-Coded Universe: How Scaling Ratios, Not Numbers, Generate Continuous Reality from Discrete Foundations

Human perception of continuous space and time is not a window onto fundamental reality but an evolutionary adaptation. Mammalian sensory systems—particularly vision, touch, and proprioception—evolved to represent the world as continuous because this representation conferred survi...

HYDRODYNAMIC-TOPOLOGICAL CONTINUUM: AN INTEGRATED ONTOLOGY OF EMERGENT STABILITY

The reconciliation of general relativity with quantum field theory remains the premier open problem in theoretical physics, exemplified by the "vacuum catastrophe"—the 120-order-of-magnitude discrepancy between the calculated vacuum energy density and the observed cosmological co...

Quantum Laws of Form: Consolidation, Open Questions, and Extensions

George Spencer-Brown's Laws of Form (1969) proposed that the act of drawing a distinction is the primitive operation from which logic, mathematics, and physics can be constructed. This consolidation paper (v2.0) synthesizes the known quantum-Laws-of-Form correspondences — includi...

Quantum Laws of Form: A Syntactic Foundation for Physics

A synthesis of Spencer-Brown's Laws of Form with quantum foundations, exploring the re-entrant form as minimal observer and the calculus of indications as a native language for quantum measurement.

CRYOGENICALLY STABILIZED SYNTHETIC LATTICE ARCHITECTURE FOR FAULT-TOLERANT QUANTUM COMPUTING

We present the design and physical operating principles of a rack-mountable photonic hardware platform designed to instantiate a synthetic vacuum capable of passive quantum error rejection. Unlike conventional quantum processors that rely on algorithmic error correction, this arc...

Thermodynamic and Quantum Constraints on Scalable Quantum Computing: A Consilience of Modeling, Experiment, and Theory

The central tension in scalable quantum computing lies between the exponential growth of quantum information density and the polynomial limits of cryogenic heat extraction. This thermodynamic bottleneck motivates an architectural inversion, where high-power control and readout el...

Locale Framework Applied to Quantum Computing Innovations & Practical Applications

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 amplitu...

The Continuum is Real: Quantization as the Binning of a Continuous Reality

For over a century, physics has been defined by an ontological schism. The continuous, deterministic, and local reality described by classical mechanics and general relativity stands in direct opposition to the discrete, probabilistic, and non-local phenomena of quantum mechanics...

Programming the Vacuum: A Unified Hamiltonian Engineering Framework for Optimization and Spectral Synthesis

The exponential growth of Hilbert space dimensions presents a fundamental barrier to the classical simulation of quantum systems, necessitating a paradigm shift from algorithmic simulation to physical instantiation. This study validates the “Inverted Church-Turing-Deutsch” (CTD)...

Quantum Laws of Form: A Syntactic Foundation for Physics: From The Calculus of Distinction to Ultrametric Cosmology

Quantum information is not intrinsically fragile; we have been measuring it incorrectly. This monograph presents a radical re‑foundation of physics based on George Spencer‑Brown’s Laws of Form, strictly adhered to and extended into a Syntactic Token Calculus (STC). The framework...

Hamiltonian Dynamics as the Engine of Biological Computation: Linking Gamma Oscillations to Scale-Inseparable Memory

This study investigates the physical basis of biological computation, focusing on the tension between static structuralism and dynamic evolution. Utilizing a Hamiltonian formulation of the Kuramoto model, we simulate a biological reservoir to rigorously evaluate the relationship...

Escaping the Millikelvin Death Spiral: A Systems Architecture for High-Tc Topological Processing

Standard quantum architectures rely on dilution refrigeration to suppress thermal noise, tethering the industry to a non-scalable 20 mK thermal floor. The cooling power at millikelvin temperatures scales poorly, creating a “mainframe constraint” that limits widespread deployment....

A Computational Toy Model of Non-Local Information Storage in a Quantum Cellular Automaton

The holographic principle, which posits that the physics of a volume of space can be encoded on its boundary, has been profoundly reinterpreted as a form of quantum error correction. Separately, Quantum Cellular Automata (QCAs) offer a bottom-up model for the emergence of complex...

PRIME NUMBERS AS SPECTRAL ARTIFACTS OF QUANTUM GEOMETRIC SYSTEMS

This establishes a mathematical framework demonstrating that prime numbers emerge as spectral artifacts from a continuous quantum geometric substrate, rather than representing fundamental discrete entities. Through formal deduction from five established mathematical facts—base-in...

Configuration-Space Topology and the Distinction Calculus: The Exchange Scalar, Its +/-1 Shadow, and a Pre-Registered Derivation Program

Configuration-space topology (CST) derives exchange statistics from the fundamental group of the configuration space of indistinguishable particles: the symmetric group S_N in d>=3 (only boson +1 and fermion -1 exchange phases) and the braid group B_N in d=2 (anyons). This paper...

Configuration-Space Topology and the Distinction Calculus: The Exchange Scalar, Its +/-1 Shadow, and a Pre-Registered Derivation Program

Configuration-space topology (CST) derives exchange statistics from the fundamental group of the configuration space of indistinguishable particles: the symmetric group S_N in d>=3 (only boson +1 and fermion -1 exchange phases) and the braid group B_N in d=2 (anyons). This paper...