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    Quantum algorithms (e.g., Shor's algorithm) solve problem... — Carmelics
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    Challenges→Exponential time complexity is a sufficient condition for classifying a decidable problem as intractable.

    Quantum algorithms (e.g., Shor's algorithm) solve problems in polynomial time that classical models require exponential time for.

    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    1 reason against

    Reasons For

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    Reason for
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    • 1.Shor's algorithm empirically demonstrates superpolynomial speedup by exploiting quantum superposition to test multiple factorizations simultaneously.
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    • 2.Quantum complexity theory proves BQP problems exist outside classical P, establishing theoretical separation between quantum and classical capabilities.
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    • 3.Quantum advantage has been experimentally validated on small instances, confirming the speedup mechanism works in physical systems, not just theory.
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    Reasons Against

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    • 1.No large-scale quantum computer yet exists; speedup claims rest on untested scalability assumptions that may fail due to decoherence or engineering limits.
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    • 2.Classical algorithms like GNFS may achieve subexponential (not full exponential) factorization, reducing the gap between quantum and classical time complexity.
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    • 3.Quantum measurement collapses superposition, requiring repeated trials; total wall-clock time including setup and error correction may exceed classical methods practically.
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    Related

    Classical algorithms like GNFS may achieve subexponential (not full exponential)...Exponential time complexity is a sufficient condition for classifying a decidabl...No large-scale quantum computer yet exists; speedup claims rest on untested scal...Quantum advantage has been experimentally validated on small instances, confirmi...
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    Quantum complexity theory proves BQP problems exist outside classical P, establi...Quantum measurement collapses superposition, requiring repeated trials; total wa...Shor's algorithm empirically demonstrates superpolynomial speedup by exploiting ...

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    2 (1 for, 1 against)
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