Comment on “Adiabatic quantum computation with a one-dimensional projector Hamiltonian”

Abstract

The partial adiabatic search algorithm was introduced in Tulsi's paper [Phys. Rev. A 80, 052328 (2009)] as a modification of the usual adiabatic algorithm for a quantum search with the idea that most of the interesting computation only happens over a very short range of the adiabatic path. By focusing on that restricted range, one can potentially gain an advantage by reducing the control requirements on the system, enabling a uniform rate of evolution. In this Comment, we point out an oversight in Tulsi's paper [Phys. Rev. A 80, 052328 (2009)] that invalidates its proof. However, the argument can be corrected, and the calculations in Tulsi's paper [Phys. Rev. A 80, 052328 (2009)] are then sufficient to show that the scheme still works. Nevertheless, subsequent works [Phys. Rev. A 82, 034304 (2010), Chin. Phys. B 20, 040309 (2011), Chin. Phys. B 21, 010306 (2012), AASRI Procedia 1, 5862 (2012), and Quantum Inf. Process. 12, 2689 (2013)] cannot all be recovered in the same way.