Abstract
We constructed a virtual quantum computer by running a complete, scaling, quantum-gate\char21{}by\char21{}quantum-gate implementation of Shor's algorithm on a 128-core classical cluster computer. In mode A [quantum period finding (PF) only, supplied with classical results for the modular exponentiation (ME) part of Shor's algorithm], factoring semiprimes up to $N=557\phantom{\rule{0.16em}{0ex}}993$ with up to $n=39$ qubits, we confirm earlier, smaller-$n$ results concerning the performance scaling of Shor's algorithm equipped with a truncated (banded) quantum Fourier transform. Running our virtual quantum computer in mode B (full quantum implementation of ME and PF), we find that a large number of gates may be discarded in a scalable way in both the ME and PF parts of Shor's algorithm in exchange for only a small reduction in performance. We explicitly state the associated scaling laws. Implying significant savings in quantum gates, we suggest that these results are of importance for future experimental and technical large-$n$ implementations of quantum computers.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
