Entanglement and its Role in Shor's Algorithm

Entanglement has been termed a critical resource for quantum information processing and is thought to be the reason that certain quantum algorithms, such as Shor's factoring algorithm, can achieve exponentially better performance than their classical counterparts. The nature of this resource is still not fully understood: here we use numerical simulation to investigate how entanglement between register qubits varies as Shor's algorithm is run on a quantum computer. The shifting patterns in the entanglement are found to relate to the choice of basis for the quantum Fourier transform.Comment: 15 pages, 4 eps figures, v1-3 were for conference proceedings (not included in the end); v4 is improved following referee comments, expanded explanations and added reference