Even a proof that P is a strict subset of BQP would not b... — Carmelics

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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

Modality & Possibility Skepticism

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2 reasons against

Reasons For

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Reason for

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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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Reasons Against

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Reason against 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 against 2 of 2

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