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It is not the case that Deutsch and Penrose both argue quantum computation's theoretical model is itself a physical thesis about what nature permits, not merely mathematical.
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Reasons For
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Reason for
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1.
All computation models (Turing machines, lambda calculus, circuits) are ultimately abstract formalisms independent of physical substrate.
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2.
Quantum computation's theoretical model can be formulated in purely mathematical terms without reference to physical realizability.
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3.
Calling a model a 'physical thesis' conflates what nature *permits* with claims about computational complexity or algorithmic power.
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Reasons Against
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Reason against
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1.
Quantum computers exploit superposition and entanglement, which are physical phenomena, not abstract mathematical constructs.
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2.
The Church-Turing thesis is a mathematical claim about computability; quantum computation's advantage requires physical realizability constraints.
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3.
Deutsch's many-worlds interpretation explicitly grounds quantum computation in physical branch structure, not mere mathematical formalism.
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