Fault-tolerant quantum computing with superconducting circuits: Prospects and Challenges

Quantum computing with superconducting elements promises scalability and long coherence time, and is widely regarded as a viable approach to developing a fault-tolerant architecture of a quantum computer. In this talk, I first give a brief overview on quantum computing, and discuss how the universal quantum gates can be performed with Josephson-junction-based superconducting devices. Next, I talk about the surface code, a state-of-the-art scheme for topological quantum error correction, and describe how superconducting components can be coupled together to design a surface-code-based quantum computer. Superconducting qubits, however, contain more than two energy levels, and therefore are susceptible to errors generated by the leakage of population outside of the computational subspace. Such leakage errors preclude even the sophisticated topological error-correcting schemes from protecting the encoded quantum information, thereby posing a serious threat to fault-tolerant quantum computing. I conclude with our recent proposal of SWAP-based topological scheme that enables the existing topological codes resilient against the notorious leakage errors as well as the decoherence.