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[0912.4807] Quantum Algorithms for many-to-one Functions to Solve the Regulator and the Principal Ideal Problem
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Quantum Physics
arXiv:0912.4807 (quant-ph)
[Submitted on 24 Dec 2009]
Title:Quantum Algorithms for many-to-one Functions to Solve the Regulator and the Principal Ideal Problem
Authors:Arthur Schmidt
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Abstract: 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.
| Comments: | 11 pages |
| Subjects: | Quantum Physics (quant-ph); Computational Complexity (cs.CC) |
| Cite as: | arXiv:0912.4807 [quant-ph] |
| (or arXiv:0912.4807v1 [quant-ph] for this version) | |
| https://doi.org/10.48550/arXiv.0912.4807
arXiv-issued DOI via DataCite
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View a PDF of the paper titled Quantum Algorithms for many-to-one Functions to Solve the Regulator and the Principal Ideal Problem, by Arthur Schmidt
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