Arithmetic Summary

• Basic exponentiation algorithms O(n^3)

• Constant factors are critical!!!!

• Architecture impacts constant factors and asymptotic performance

  • Can reach O(log^3 n) w/ unlimited space on some architectures
  • Other archs O(n^2 log n)
  • Communications, concurrency important

• full paper at quant-ph/0408006

• JJAP letter in progress

• see also Fowler 0402196 & Devitt 0408081