# Quantum Computers Can Find Quadratic Nonresidues in Deterministic Polynomial Time

@article{Draper2021QuantumCC, title={Quantum Computers Can Find Quadratic Nonresidues in Deterministic Polynomial Time}, author={Thomas G. Draper}, journal={ArXiv}, year={2021}, volume={abs/2106.03991} }

An integer a is a quadratic nonresidue for a prime p if x2 ≡ a mod p has no solution. Quadratic nonresidues may be found by probabilistic methods in polynomial time. However, without assuming the Generalized Riemann Hypothesis, no deterministic polynomial-time algorithm is known. We present a quantum algorithm which generates a random quadratic nonresidue in deterministic polynomial time.

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