Fast Quantum Modular Exponentiation

Details Fast Quantum Modular Exponentiation Fast Quantum Modular Exponentiation

2004-08-01

arxiv.org/abs/quant-ph/0408006v2

Phys. Rev. A 71, 052320 (2005)

Physics

Quantum Physics

to appear in PRA 71(5); RevTeX, 12 pages, 12 figures; v2 revision is substantial, with new algorithmic variants, much shorter

Scientific paper

10.1103/PhysRevA.71.052320

We present a detailed analysis of the impact on modular exponentiation of architectural features and possible concurrent gate execution. Various arithmetic algorithms are evaluated for execution time, potential concurrency, and space tradeoffs. We find that, to exponentiate an n-bit number, for storage space 100n (twenty times the minimum 5n), we can execute modular exponentiation two hundred to seven hundred times faster than optimized versions of the basic algorithms, depending on architecture, for n=128. Addition on a neighbor-only architecture is limited to O(n) time when non-neighbor architectures can reach O(log n), demonstrating that physical characteristics of a computing device have an important impact on both real-world running time and asymptotic behavior. Our results will help guide experimental implementations of quantum algorithms and devices.

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