Notch filtering the nuclear environment of a spin qubit

Nuclear spins in gallium arsenide produce noise at discrete frequencies, which can be notch-filtered efficiently to extend coherence times of electron spin qubits to nearly 1 ms. Electron spins in gate-defined quantum dots provide a promising platform for quantum computation 1 , 2 , 3 , 4 , 5 , 6 , 7 . In particular, spin-based quantum computing in gallium arsenide takes advantage of the high quality of semiconducting materials, reliability in fabricating arrays of quantum dots and accurate qubit operations 5 , 6 , 7 , 8 , 9 , 10 . However, the effective magnetic noise arising from the hyperfine interaction with uncontrolled nuclear spins in the host lattice constitutes a major source of decoherence 4 , 5 , 10 , 11 . Low-frequency nuclear noise, responsible for fast (10 ns) inhomogeneous dephasing 5 , can be removed by echo techniques 4 , 5 , 11 , 12 , 13 , 14 . High-frequency nuclear noise, recently studied via echo revivals 4 , 11 , occurs in narrow-frequency bands related to differences in Larmor precession of the three isotopes 69 Ga, 71 Ga and 75 As (refs 15 , 16 , 17 ). Here, we show that both low- and high-frequency nuclear noise can be filtered by appropriate dynamical decoupling sequences, resulting in a substantial enhancement of spin qubit coherence times. Using nuclear notch filtering, we demonstrate a spin coherence time ( T 2 ) of 0.87 ms, five orders of magnitude longer than typical exchange gate times, and exceeding the longest coherence times reported to date in Si/SiGe gate-defined quantum dots 18 , 19 .