6533b7defe1ef96bd127662a

RESEARCH PRODUCT

Arbitrary qudit gates by adiabatic passage

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We derive an adiabatic technique that implements the most general SU($d$) transformation in a quantum system of $d$ degenerate states, featuring a qudit. This technique is based on the factorization of the SU($d$) transformation into $d$ generalized quantum Householder reflections, each of which is implemented by a two-shot stimulated Raman adiabatic passage with appropriate static phases. The energy of the lasers needed to synthesize a single Householder reflection is shown to be remarkably constant as a function of $d$. This technique is directly applicable to a linear trapped ion system with $d+1$ ions. We implement the quantum Fourier transform numerically in a qudit with $d=4$ (defined as a quartit) as an example.