Abstract
The standard Hilbert space formulation of quantum mechanics assumes instantaneous superposition across an exponentially large state space. Physical systems, however, operate under strict resource limits: finite coherence, finite bandwidth, finite energy, and finite operational age. We present a finite state, stochastic exploration model that quantifies these limits through a factorial bounded numerical experiment. Random permutations drawn from a finite alphabet are sampled until all n! unique configurations are discovered, producing a saturation curve that directly measures the cost of state space traversal. This experiment reveals a finite, measurable boundary between physically accessible states and the unphysical tail implied by Hilbert space completeness. The results provide an operational metric for state space accessibility and demonstrate that real quantum systems behave as finite age combinatorial oscillators rather than idealized infinite dimensional vectors. This framework offers a new tool for evaluating the physical feasibility of quantum computation and aligns with recent mathematical results identifying the unphysicality of infinite dimensional Hilbert spaces.
Recommended Citation
Sobczynski, Radek M.
(2026)
"STOCHASTIC FACTORIAL EXPLORATION OF QUANTUM STATE SPACE,"
International Journal of Computer and Systems Engineering: Vol. 5:
Iss.
1, Article 2.
Available at:
https://digitalcommons.fairfield.edu/ijcase/vol5/iss1/2