A Quantum Adiabatic Algorithm for Factorization and Its Experimental   Implementation
  We propose an adiabatic quantum algorithm capable of factorizing numbers, using fewer qubits than Shor's algorithm. We implement the algorithm in an NMR quantum information processor and experimentally factorize the number 21. Numerical simulations indicate that the running time grows only quadratically with the number of qubits. 
Xinhua Peng, Zeyang Liao, Nanyang Xu, Gan Qin, Xianyi Zhou, Dieter   Suter, and Jiangfeng Du