2009/12/24 by Arthur Schmidt, Schmidt, Arthur
Computer Science · Physics and Astronomy · #Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Physical sciences #Quantum Physics (quant-ph) #cs.CC #quant-ph
paper · pdf · doi:10.48550/arxiv.0912.4807
11 pages
arxiv created 2009/12/24 · arxiv updated 2010/01/14
We propose new quantum algorithms to solve the regulator and the principal ideal problem in a real-quadratic number field. We improve the algorithms proposed by Hallgren by using two different techniques. The first improvement is the usage of a period function which is not one-to-one on its period. We show that even in this case Shor's algorithm computes the period with constant probability. The second improvement is the usage of reduced forms (a, b, c) of discriminant D with a>0 instead of reduced ideals of the same discriminant. These improvements reduce the number of required qubits by at least 2 log D.