A reduction framework from sample complexity yields matching time lower bounds for purity estimation, high-order functionals, productness testing, and related quantum protocols.
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Presents a concrete quantum oracle for bilinear Diophantine equations enabling factoring of n-bit biprimes with 2n-5 qubits or fewer and near-100% simulated success for numbers up to 35 bits.
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Quantum Time Lower Bounds by Permutation Invariance
A reduction framework from sample complexity yields matching time lower bounds for purity estimation, high-order functionals, productness testing, and related quantum protocols.
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Efficient Quantum Oracle for Solving Bilinear Diophantine Equations on Digital Quantum Computers
Presents a concrete quantum oracle for bilinear Diophantine equations enabling factoring of n-bit biprimes with 2n-5 qubits or fewer and near-100% simulated success for numbers up to 35 bits.