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## Section: New Results

### Fast and virtually exact quantum gate generation in $U\left(n\right)$ via Iterative Lyapunov Methods

Participants: Pierre Rouchon

This work presents an iterative algorithm published in [20] and named RIGA for Reference Input Generation Algorithm. This algorithm constructs smooth control pulses for quantum gate preparations of closed quantum systems. It combines right translation invariance and Lyapunov trajectory tracking. It exhibits exponential convergence when the system is controllable. It can be seen as a closed-loop version of the widely used GRAPE algorithm. Two numerical case-studies borrowed from the recent literature are addressed. The first one is relative to a system of 10 coupled qubits with local controls. The second one considers a C-NOT gate generation involving the lower levels of two coupled nonlinear cavities (transmon-qubits).