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    It is not the case that Even a proof that P is a strict subset of BQP would not by itself settle the bearing of quantum computation on feasible computation or the Cobham-Edmonds thesis

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.A formal proof that P ⊊ BQP would establish that quantum computation transcends classical polynomial-time bounds as a matter of mathematical necessity.
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    • 2.The Cobham-Edmonds thesis equates feasibility with polynomial-time computability, so any provably larger class of feasible computation directly revises the thesis.
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    • 3.Mathematical proof, not empirical implementation, is the appropriate arbiter of what the Cobham-Edmonds thesis entails about computational boundaries.
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    Reason for 2 of 2
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    • 1.Church-Turing thesis revisions historically follow from theoretical separations, not from physical realizability—as Deutsch's 1985 argument itself demonstrates.
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    • 2.If P ⊊ BQP were proven, the burden of proof shifts to defenders of classical feasibility bounds to justify retaining a thesis known to exclude realizable quantum speedups.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The relationship between BQP and NP is currently not well understood
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    • 2.No polynomial-time quantum algorithms have been found for NP-complete problems on widely accepted quantum computation models
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    • 3.Whether physically robust realizations of quantum computation models sufficient to solve classically intractable problems can be constructed remains an open empirical question
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