Comment on "Phase Change during a Cyclic Quantum Evolution"

Arun Kumar Pati

M. G. Benedict, Wolfgang P. Schleich

Ravi Baijulal Bhandari

Ognyan Oreshkov, John Calsamiglia

In [Phys. Rev. Lett. 95, 080502 (2005)], Zheng proposed a scheme for implementing a conditional phase shift via adiabatic passages. The author claims that the gate is "neither of dynamical nor geometric origin" on the grounds that the Hamiltonian does not follow a cyclic change. He further argues that "in comparison with the adiabatic geometric gates, the nontrivial cyclic loop is unnecessary, and thus the errors in obtaining the required solid angle are avoided, which makes this new kind of phase gates superior to the geometric gates." In this Comment, we point out that geometric operations, including adiabatic holonomies, can be induced by noncyclic Hamiltonians, and show that Zheng's gate is geometric. We also argue that the nontrivial loop responsible for the phase shift is there, and it requires the same precision as in any adiabatic geometric gate.

L-B Fu, J-L Chen

We show that the geometric phase for mixed state during a cyclic evolution suggested in 2004 J. Phys. A 37 3699 is U(1) invariant and can be observed by nowaday techniques.

Erik Sjöqvist

It is shown that a recently suggested concept of mixed state geometric phase in cyclic evolutions (Fu L-B and Chen J-L 2004 J. Phys. A: Math. Gen. 37 3699 ) is gauge dependent.