Constant-optimized quantum circuits for modular multiplication and exponentiation

@article{Markov2012ConstantoptimizedQC,
  title={Constant-optimized quantum circuits for modular multiplication and exponentiation},
  author={Igor L. Markov and Mehdi Saeedi},
  journal={Quantum Inf. Comput.},
  year={2012},
  volume={12},
  pages={361-394}
}
Reversible circuits for modular multiplication Cx%M with x < M arise as components of modular exponentiation in Shor's quantum number-factoring algorithm. However, existing generic constructions focus on asymptotic gate count and circuit depth rather than actual values, producing fairly large circuits not optimized for specific C and M values. In this work, we develop such optimizations in a bottom-up fashion, starting with most convenient C values. When zero-initialized ancilla registers are… 

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