Protected gates for superconducting qubits
Peter Brooks, Alexei Kitaev, John P. Preskill · Physical Review A · 2013
We analyze the accuracy of quantum phase gates acting on ``0-$\ensuremath{\pi}$ qubits'' in superconducting circuits, where the gates are protected against thermal and Hamiltonian noise by continuous-variable quantum error-correcting codes. The gates are executed by turning on and off a tunable Josephson coupling between an $LC$ oscillator and a qubit or pair of qubits; assuming perfect qubits, we show that the gate errors are exponentially small when the oscillator's impedance $\sqrt{L/C}$ is large compared to $\ensuremath{\hbar}/4{e}^{2}\ensuremath{\approx}1\phantom{\rule{4pt}{0ex}}\mathrm{k}\ensuremath{\Omega}$. The protected gates are not computationally universal by themselves, but a scheme for universal fault-tolerant quantum computation can be constructed by combining them with unprotected noisy operations. We validate our analytic arguments with numerical simulations.