Successful Shor's Factorization of N=1031167 using the IBM Quantum Systems

So far, the highest number factorized on a quantum computer using Shor’s algorithm was 35. This poster shows that much larger numbers can be factorized using this algorithm on current quantum computers. The factorization of number 1031167, along with the quantum circuits used and results from the IBM quantum systems ibm_brisbane and ibm_kyoto, is shown. Shor’s algorithm was proposed in 1994, but only now has quantum technology evolved to such a level that its realization has become possible. The bottleneck of this algorithm is the implementation of the modular exponentiation function (MEF), which is also the subject of this poster. Thanks to the appropriately chosen parameter "a", this implementation was quite simple. Therefore, it was not a problem to use the Qiskit framework to program and run the necessary quantum circuits on the IBM quantum systems. The measured results of the whole circuit were then accurate enough to determine both factors. Since they were correct, it can be stated that the highest number factorized by a quantum computer using Shor's algorithm is now 1031167.