The Physical and Contextual Limits of Quantum Speedup

• URL: http://arxiv.org/abs/2605.12675v2
• Date: Tue, 19 May 2026 16:27:11 GMT
• Title: The Physical and Contextual Limits of Quantum Speedup
• Abstract summary: Quantum computation is frequently mischaracterized as the simultaneous execution of exponentially many classical computations.<n>This article offers a conceptual clarification, demonstrating that the components of a quantum superposition cannot be treated as independently readable classical branches.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum computation is frequently mischaracterized as the simultaneous execution of exponentially many classical computations. This article offers a conceptual clarification of why this ``branchwise parallelism'' picture is misleading, demonstrating that the components of a quantum superposition cannot be treated as independently readable classical branches. Quantum speedups arise instead from reversible embeddings of algebraic structure made accessible through engineered interference patterns; more precisely, many speedups identify a class in a partition of possible instances rather than reconstructing the full instance. We review this mechanism through several constraints: unitary garbage erasure is impossible, copying and deletion are context-dependent, and contextuality obstructs a single global classical history. We also distinguish circuit or unitary universality from Turing universality: dense generation of unitaries is not the same as symbolic computation over unbounded inputs with recursion, uniformity, and self-reference. In closed unitary dynamics there is no nontrivial absorbing halting state of the classical many-to-one kind; operational termination requires clocks, flags, measurements, open-system records, or external control. Exponential Hilbert-space dimension supplies a geometry for interference and high-dimensional embedding, not unlimited classical readout.

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