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We present a comprehensive theoretical treatment of SUPCODE, a method forgenerating dynamically corrected quantum gate operations, which are immune torandom noise in the environment, by using carefully designed sequences of softpulses. SUPCODE enables dynamical error suppression even when the control fieldis constrained to be positive and uniaxial, making it particularly suited tocounteracting the effects of noise in systems subject to these constraints suchas singlet-triplet qubits. We describe and explain in detail how to generateSUPCODE pulse sequences for arbitrary single-qubit gates and provide severalexplicit examples of sequences that implement commonly used gates, includingthe single-qubit Clifford gates. We develop sequences for noise-resistanttwo-qubit gates for two exchanged-coupled singlet-triplet qubits by cascadingrobust single-qubit gates, leading to a 35% reduction in gate time compared toprevious works. This cascade approach can be scaled up to produce gates for anarbitrary-length spin qubit array, and is thus relevant to scalable quantumcomputing architectures. To more accurately describe real spin qubitexperiments, we show how to design sequences that incorporate additionalfeatures and practical constraints such as sample-specific charge noise modelsand finite pulse rise times. We provide a detailed analysis based on randomizedbenchmarking to show how SUPCODE gates perform under realistic $1/f^\alpha$noise and find a strong dependence of gate fidelity on the exponent $\alpha$,with best performance for $\alpha>1$. Our SUPCODE sequences can therefore beused to implement robust universal quantum computation while accommodating thefundamental constraints and experimental realities of singlet-triplet qubits.

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