Quantum Computers Can Find Quadratic Nonresidues in Deterministic Polynomial Time
Abstract
An integer $a$ is a quadratic nonresidue for a prime $p$ if $x^2 \equiv a \bmod p$ has no solution. Quadratic nonresidues may be found by probabilistic methods in polynomial time. However, without assuming the Generalized Riemann Hypothesis, no deterministic polynomialtime algorithm is known. We present a quantum algorithm which generates a random quadratic nonresidue in deterministic polynomial time.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.03991
 Bibcode:
 2021arXiv210603991D
 Keywords:

 Quantum Physics;
 Computer Science  Emerging Technologies
 EPrint:
 7 pages, 6 figures