Primality Test Via Quantum Factorization
H. F. Chau, H. -K. Lo
Abstract
We consider a probabilistic quantum implementation of a variable of the Pocklington-Lehmer N-1 primality test using Shor's algorithm. O(3 N N N) elementary q-bit operations are required to determine the primality of a number N, making it (asymptotically) the fastest known primality test. Thus, the potential power of quantum mechanical computers is once again revealed.
Create a lesson
Related papers
Parallel quantum channel discrimination and numerical ranges in tensor product subspaces
Adam Bílek, Paulina Lewandowska, Ryszard Kukulski
Asymptotically Good Quantum Locally Testable Codes
William Gay, Fernando Granha Jeronimo
All causally separable quantum processes are quantum circuits with classical control of causal order
Julian Wechs, Alastair A. Abbott, Cyril Branciard
Analytic leakage suppression with a single control field: fast two-qubit gates with tunable couplers
Lukas Heunisch, Michael J. Hartmann, Aashish A. Clerk
Procrastinating einselection in non-Markovian quantum dynamics
Michael J. Moody, Tara Kalsi, Agung Budiyono et al.
Quantum Entropy Contraction and Factorization from Hypercontractivity
Li Gao, Lijun Wang