Comment on Nongeometric Conditional Phase Shift via Adiabatic Evolution of Dark Eigenstate

TL;DR

This paper critically examines claims of a new quantum phase for phase gates, arguing that the so-called new phase is actually a known geometric phase with no new physical meaning.

Contribution

The paper refutes previous claims of a novel phase in quantum computation, clarifying that the phase is actually a well-known geometric phase and not a new physical phenomenon.

Findings

The claimed new phase is actually a known geometric phase.

The phase has no new physical meaning or observability.

Previous claims are incorrect and based on misinterpretation.

Abstract

In a recent letter [Phy. Rev. Lett. 95, 080502 (2005)], it is claimed that based on a new kind of quantum mechanical phase of wave function which is neither dynamical nor geometrical a new kind of phase gate for quantum computation is discovered. The origin of this phase is the adiabatic evolution of a dark state. I would like to point out that these claims are questionable. The so called new phase gate was based on a phase which was nothing new but has been known for decades. It is something which has no physical meaning and is not observable. It was also pointed out by [quant-ph/0509150v1] that [Phy. Rev. Lett. 95, 080502 (2005)] was incorrect and the phase is the known geometric phase. Here we present a totally different argument.