Entanglement and its Role in Shor's Algorithm

TL;DR

This paper investigates how entanglement evolves during Shor's algorithm using numerical simulations, revealing its dependence on the basis choice in the quantum Fourier transform and its role as a key resource.

Contribution

It provides new insights into the dynamics of entanglement in Shor's algorithm and how it relates to the basis selection in the quantum Fourier transform.

Findings

Entanglement patterns vary with the basis in the quantum Fourier transform.

Entanglement dynamics are linked to the algorithm's performance.

Numerical simulations reveal the role of entanglement in quantum speedup.

Abstract

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.