Entanglement of periodic states, the quantum Fourier transform, and Shor's factoring algorithm
- Racah Institute of Physics, Hebrew University, Jerusalem IL-91904 (Israel)
The preprocessing stage of Shor's algorithm generates a class of quantum states referred to as periodic states, on which the quantum Fourier transform is applied. Such states also play an important role in other quantum algorithms that rely on the quantum Fourier transform. Since entanglement is believed to be a necessary resource for quantum computational speedup, we analyze the entanglement of periodic states and the way it is affected by the quantum Fourier transform. To this end, we derive a formula that evaluates the Groverian entanglement measure for periodic states. Using this formula, we explain the surprising result that the Groverian entanglement of the periodic states built up during the preprocessing stage is only slightly affected by the quantum Fourier transform.
- OSTI ID:
- 21413365
- Journal Information:
- Physical Review. A, Vol. 81, Issue 5; Other Information: DOI: 10.1103/PhysRevA.81.052306; (c) 2010 The American Physical Society; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
Similar Records
Tree tensor network approach to simulating Shor's algorithm
Collective decoherence of the superpositional entangled states in the quantum Shor algorithm