Abstract
We present a detailed analysis of the impact on quantum modular exponentiation of architectural features and possible concurrent gate execution. Various arithmetic algorithms are evaluated for execution time, potential concurrency, and space trade-offs. We find that to exponentiate an number, for storage space (20 times the minimum ), we can execute modular exponentiation 200–700 times faster than optimized versions of the basic algorithms, depending on architecture, for . Addition on a neighbor-only architecture is limited to time, whereas non-neighbor architectures can reach , 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.
5 More- Received 28 July 2004
DOI:https://doi.org/10.1103/PhysRevA.71.052320
©2005 American Physical Society