Universal quantum computation in a decoherence-free subspace for collective relaxation with transmon qubits

Abstract

For the transmon, its dephasing has experimentally been suppressed to an extent that dephasing time is mainly limited by the relaxation process [Schreier et al., Phys. Rev. B 77, 180502(R) (2008)]. In the Hilbert space of two transmons, there exists a two-dimensional subspace immune to the collective relaxation. In this paper, by encoding a logical qubit in this subspace, we demonstrate how to realize universal quantum computation in the decoherence-free subspace. In our scheme, the transmons are coupled through a one-dimensional superconducting transmission-line resonator. With the help of some classical driving fields, two noncommutable single-logical-qubit rotation operators and a controlled-phase gate between two logical qubits are obtained. We always work in the detuning regime, which largely decreases relaxation induced by the Purcell effect.