Composite pulses for quantum computation with trapped electrons

In a scalable quantum computer, based on trapped electrons in vacuum, qubits are encoded in the external (cyclotron motion) and internal (spin) degrees of freedom. We show how to extend the technique of composite pulses to manipulate the cyclotron oscillator without leaving the computational subspace. In particular, we describe and discuss how to implement the explicit pulse sequence which operates the conditional phase shift between the cyclotron and the spin qubits.