High-fidelity two-qubit gates via dynamical decoupling of local 1/f noise at optimal point

Abstract: We investigate the possibility to achieve high-fidelity universal two-qubit gates by supplementing optimal tuning of individual qubits with dynamical decoupling (DD) of local 1/f noise. We consider simultaneous local pulse sequences applied during the gate operation and compare the efficiencies of periodic, Carr-Purcell and Uhrig DD with hard $\pi$-pulses along two directions ($\pi_{z/y}$ pulses). We present analytical perturbative results (Magnus expansion) in the quasi-static noise approximation combined with numerical simulations for realistic 1/f noise spectra. The gate efficiency is studied as a function of the gate duration, of the number $n$ of pulses, and of the high-frequency roll-off. We find that the gate error is non-monotonic in $n$, decreasing as $n^{-\alpha}$ in the asymptotic limit, $\alpha \geq 2$ depending on the DD sequence. In this limit $\pi_z$-Urhig is the most efficient scheme for quasi-static 1/f noise, but it is highly sensitive to the soft UV-cutoff. For small number of pulses, $\pi_z$ control yields anti-Zeno behavior, whereas $\pi_y$ pulses minimize the error for a finite $n$. For the current noise figures in superconducting qubits, two-qubit gate errors $\sim 10^{-6}$, meeting the requirements for fault-tolerant quantum computation, can be achieved. The Carr-Purcell-Meiboom-Gill sequence is the most efficient procedure, stable for $1/f$ noise with UV-cutoff up to gigahertz.