Proposal of realizing superadiabatic geometric quantum computation in decoherence-free subspaces

We propose a practical scheme to implement universal superadiabatic geometric quantum gates in decoherence-free subspaces in the trapped-ions system. The logical qubit is only encoded by two neighboring physical qubits, which is the minimal resource for the decoherence-free subspace encoding. Different from the nonadiabatic control in decoherence-free subspace (Liang et al. in Phys Rev A 89:062312, 2014), a new Hamiltonian to implement universal effective interaction between logical qubits is proposed in the scheme. The proposed gates are numerically demonstrated to be robust against both systematic errors and collective dephasing noises, which combine the advantages of superadiabatic geometric quantum control and decoherence-free subspace. Since the Hamiltonian we use relies solely on two-body interactions, our scheme would be promising to be realized experimentally in trapped-ions systems.