# Quantum control at the nanoscale – Arbitrary qudit gates by adiabatic passage

## Benjamin Rousseaux

### (Université de Bourgogne)

Time: Thu Dec 12 13:30:00 2013

Location: Building 4, Room 123

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 OFD. 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.