A Leakage-Resilient Approach to Fault-Tolerant Quantum Computing with Superconducting Elements

Joydip Ghosh, Austin G. Fowler

Published 2014-06-10, updated 2014-12-02Version 2

Superconducting qubits, while promising for scalability and long coherence times, 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 the existing quantum error-correcting schemes from protecting the encoded quantum information, and therefore, are considered to be a prominent roadblock towards Fault-Tolerant Quantum Computing (FTQC) with superconducting qubits. FTQC using topological codes is based on sequential measurements of multi-qubit stabilizer operators. Here, we first propose a leakage-resilient procedure to perform repetitive measurements of multi-qubit stabilizer operators, and then use this scheme as an ingredient to develop a leakage-resilient approach for surface code quantum error correction with superconducting circuits. Our protocol is based on SWAP operations between data and ancilla qubits at the end of every cycle, requiring read-out and reset operations on every physical qubit in the system, and thereby preventing persistent leakage errors from occurring.