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    Shor's quantum algorithm solves integer factorization in ... — Carmelics
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    Challenges→Factorization is not efficient, even though an effective procedure for it exists

    Shor's quantum algorithm solves integer factorization in polynomial time, demonstrating that efficiency is model-dependent, not inherent to the problem's logical structure.

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    Reasons For

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    Reason for
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    • 1.Classical and quantum models have fundamentally different computational primitives, making algorithmic complexity relative to the model chosen.
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    • 2.Shor's algorithm exploits quantum superposition and interference—unavailable classically—proving the same problem has different inherent difficulty across models.
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    • 3.No known classical polynomial algorithm for factorization exists despite decades of effort, suggesting efficiency emerges from computational substrate, not problem structure.
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    Reasons Against

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    Reason against
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    • 1.The problem's logical structure *includes* the constraint that quantum operations exist in nature; efficiency relative to physical reality is inherent, not model-dependent.
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    • 2.Polynomial vs. exponential complexity reflects objective mathematical properties (group structure, periodicity); Shor's algorithm reveals these properties, not their absence.
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    • 3.Different models may have different speeds, but this reflects the models' power, not proof that logical difficulty is independent of problem structure.
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    Related

    Classical and quantum models have fundamentally different computational primitiv...Different models may have different speeds, but this reflects the models' power,...Factorization is not efficient, even though an effective procedure for it existsNo known classical polynomial algorithm for factorization exists despite decades...
    +3 moreShow less
    Polynomial vs. exponential complexity reflects objective mathematical properties...Shor's algorithm exploits quantum superposition and interference—unavailable cla...The problem's logical structure *includes* the constraint that quantum operation...

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    2 (1 for, 1 against)
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