Fast and robust quantum computation with ionic Wigner crystals

Abstract

We present a detailed analysis of the modulated-carrier quantum phase gate implemented with Wigner crystals of ions confined in Penning traps. We elaborate on a recent scheme, proposed by two of the authors, to engineer two-body interactions between ions in such crystals. We analyze the situation in which the cyclotron (${\ensuremath{\omega}}_{c}$) and the crystal rotation (${\ensuremath{\omega}}_{r}$) frequencies do not fulfill the condition ${\ensuremath{\omega}}_{c}=2{\ensuremath{\omega}}_{r}$. It is shown that even in the presence of the magnetic field in the rotating frame the many-body (classical) Hamiltonian describing small oscillations from the ion equilibrium positions can be recast in canonical form. As a consequence, we are able to demonstrate that fast and robust two-qubit gates are achievable within the current experimental limitations. Moreover, we describe a realization of the state-dependent sign-changing dipole forces needed to realize the investigated quantum computing scheme.