The Physical and Contextual Limits of Quantum Speedup

Abstract

Quantum computation is not many classical computations running in parallel, but controlled interference in Hilbert space. Amplitude is spread, problem structure is folded into phases, and measurement detects the invariant made visible by recombination. What is exposed is usually not a branchwise table of values, but a structure-matched statistic such as a parity, period, symmetry class, or marked subspace. Quantum advantage comes from matching the relevant structure to an efficient interference pattern, under the constraints of measurement contexts, thermodynamic irreversibility, and contextuality.