Universal Holonomic Quantum Gates in Decoherence-free Subspace on Superconducting Circuits

To implement a universal set of quantum logic gates based on non-Abelian geometric phases, one needs quantum systems that are beyond two levels. However, this is extremely difficult for superconducting qubits, and thus the recent experiment has only realized single qubit gates [A. A. Abdumalikov Jr et al., Nature 496, 482 (2013)]. Here, we propose to implement non-adiabatic holonomic quantum computation in decoherence-free subspace on circuit QED, where we only use two levels in transmon qubits, and require minimal resources for the decoherence-free subspace encoding. In this way, our scheme avoids difficulties in previous works while still can achieve considerable large effective coupling strength and thus leads to high fidelity quantum gates. Therefore, our scheme presents a promising way for robust quantum computation on superconducting circuits.