Dynamic Phases and Robust Quantum Gates

We are interested in composite pulses widely employed in Nuclear Magnetic Resonance (NMR) and geometric phase gates (GQGs) with vanishing dynamic phases in Quantum Information Processing (QIP). A composite pulse in NMR is constructed with poor quality pulses but becomes more reliable than its components. We found: a composite pulse robust against pulse length error in NMR is always a GQG [1]. We then extended this observation to two-qubit operations. Let us consider the interaction $e^{-i \theta \sigma_z \otimes \sigma_z}$ and assume that there is a systematic error in $\theta$. When we construct a ``composite pulse'' robust against this error, we obtain a two-qubit GQG [2]. We clarified that geometric phase gates are really useful in QIT. \\[4pt] [1]Y.\ Kondo \& M.\ Bando, {\it J. Phys. Soc. Jpn.} {\bf 80}, 054002.\\[0pt] [2] T.\ Ichikawa, M.\ Bando, Y.\ Kondo \& M.\ Nakahara, submitted to {\it philosophical transaction} A.