Certain algorithms for quantumcomputers are able to outperform their classical counterparts.
In 1994, Peter Shor came up with a quantum algorithm that calculates the prime factors
of a large number vastly more efficiently than a classical computer. For general scalability of
such algorithms, hardware, quantum error correction, and the algorithmic realization itself
need to be extensible.Herewe present the realization of a scalable Shor algorithm, as proposed
by Kitaev.We factor the number 15 by effectively employing and controlling seven qubits
and four “cache qubits” and by implementing generalized arithmetic operations, known as
modular multipliers.This algorithm has been realized scalably within an ion-trap quantum
computer and returns the correct factors with a confidence level exceeding 99%.