In my thesis I work on several layers of the quantum error correction stack, from physical encodings to fault-tolerant implementations of logical gates. This talk focuses on implementing non-Clifford gates fault-tolerantly, one of the most expensive parts of a quantum computation.  I will first discuss codes that implement diagonal non-Clifford gates, such as the T gate, transversally at the logical level. Combined with code switching, these codes provide a path towards universal fault-tolerant quantum computation. We construct such codes with high distance and low qubit overhead, together with the corresponding codes with transversal Clifford gates that can be code-switched into them, which gives a full universal gate set. Another way to achieve universality is magic-state injection. Here, a separate architectural module, a magic-state factory, produces encoded magic states that are injected into the computing unit when the computation needs them. The difficulty of performing a non-Clifford gate is thus outsourced to a separate unit, which prepares magic states by postselection. We describe the structure behind these factory circuits, uncover the symmetry requirements for such constructions and introduce an approach to search problems of this kind based on an AI agent loop, in which agents propose where to search and exact tools verify their claims. Using these methods, we construct hundreds of new circuits, many of them pushing the known frontier, in the parameter regime where exhaustive searches become intractable.

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