Faster Quantum Number Factoring via Circuit Synthesis

@article{Markov2013FasterQN,
  title={Faster Quantum Number Factoring via Circuit Synthesis},
  author={Igor L. Markov and Mehdi Saeedi},
  journal={ArXiv},
  year={2013},
  volume={abs/1301.3210}
}
A major obstacle to implementing Shor's quantum number-factoring algorithm is the large size of modular-exponentiation circuits. We reduce this bottleneck by customizing reversible circuits for modular multiplication to individual runs of Shor's algorithm. Our circuit-synthesis procedure exploits spectral properties of multiplication operators and constructs optimized circuits from the traces of the execution of an appropriate GCD algorithm. Empirically, gate counts are reduced by 4-5 times… 

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