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

Abstract

We investigate the possibility of achieving 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 $\ensuremath{\pi}$ pulses along two directions (${\ensuremath{\pi}}_{z/y}$ pulses). We present analytical perturbative results (Magnus expansion) in the quasistatic 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 nonmonotonic in $n$, decreasing as ${n}^{\ensuremath{-}\ensuremath{\alpha}}$ in the asymptotic limit, $\ensuremath{\alpha}\ensuremath{\ge}2$, depending on the DD sequence. In this limit ${\ensuremath{\pi}}_{z}$-Urhig is the most efficient scheme for quasistatic $1/f$ noise, but it is highly sensitive to the soft UV cutoff. For small number of pulses, ${\ensuremath{\pi}}_{z}$ control yields anti-Zeno behavior, whereas ${\ensuremath{\pi}}_{y}$ pulses minimize the error for a finite $n$. For the current noise figures in superconducting qubits, two-qubit gate errors $\ensuremath{\sim}{10}^{\ensuremath{-}6}$, 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.