Abstract
Factoring integers is considered as a computationally hard problem for classical methods, whereas there exists polynomial-time Shor’s quantum algorithm for solving this task. However, requirements for running Shor’s algorithm for realistic tasks, which are beyond the capabilities of existing and upcoming generations of quantum computing devices, motivate to search for alternative approaches. In this work, we experimentally demonstrate factoring of the integer with a trapped ion quantum processor using the Schnorr approach and a modified version of the quantum approximate optimization algorithm (QAOA). The key difference of our approach in comparison with the recently proposed QAOA-based factoring method is the use of the fixed-point feature, which relies on the use of universal parameters. We present experimental results on factoring 1591 = 37 × 43 using 6 qubits as well as simulation results for 74425657 = 9521 × 7817 with 10 qubits and 35183361263263 = 4194191 × 8388593 with 15 qubits. Although we present all the necessary details for reproducing our results and analysis of the performance of the factoring method, the scalability of this approach in both the classical and quantum domains still requires further studies.