Arbitrary qudit gates by adiabatic passage

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. DOI: 10.1103/PhysRevA.87.032328