Qubit decoherence in a nuclear magnetic resonance-like quantum processor with trapped particles

We present an in-depth analysis of a potentially significant source of decoherence for a quantum processor, we proposed in our previous paper.1 The processor consists of an array of charged particles confined in planar micro-Penning traps. Qubits are encoded in the particle spins, that are mutually coupled as nuclear spins in a nuclear magnetic resonance-molecule. In this paper, we study in detail the de-phasing effect on the qubit dynamics produced by thermal excitations in the cyclotron motion of the particles.