Duration: 37:30

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We introduce a unified framework that implements one round of magic state distillation and multi-qubit gate synthesis in a single step. Typically, our method uses the same number of T-gates as conventional gate synthesis, but with the added benefit of quadratic error suppression. Because of this, one less round of magic state distillation needs to be performed, leading to significant resource savings. We also present several new efficient algorithms for synthesizing multi-qubit circuits