Robust quantum gates for singlet-triplet spin qubits using composite pulses

Abstract

We present a comprehensive theoretical treatment of SUPCODE, a method for\ngenerating dynamically corrected quantum gate operations, which are immune to\nrandom noise in the environment, by using carefully designed sequences of soft\npulses. SUPCODE enables dynamical error suppression even when the control field\nis constrained to be positive and uniaxial, making it particularly suited to\ncounteracting the effects of noise in systems subject to these constraints such\nas singlet-triplet qubits. We describe and explain in detail how to generate\nSUPCODE pulse sequences for arbitrary single-qubit gates and provide several\nexplicit examples of sequences that implement commonly used gates, including\nthe single-qubit Clifford gates. We develop sequences for noise-resistant\ntwo-qubit gates for two exchanged-coupled singlet-triplet qubits by cascading\nrobust single-qubit gates, leading to a 35% reduction in gate time compared to\nprevious works. This cascade approach can be scaled up to produce gates for an\narbitrary-length spin qubit array, and is thus relevant to scalable quantum\ncomputing architectures. To more accurately describe real spin qubit\nexperiments, we show how to design sequences that incorporate additional\nfeatures and practical constraints such as sample-specific charge noise models\nand finite pulse rise times. We provide a detailed analysis based on randomized\nbenchmarking to show how SUPCODE gates perform under realistic $1/f^\\alpha$\nnoise and find a strong dependence of gate fidelity on the exponent $\\alpha$,\nwith best performance for $\\alpha>1$. Our SUPCODE sequences can therefore be\nused to implement robust universal quantum computation while accommodating the\nfundamental constraints and experimental realities of singlet-triplet qubits.\n