Rachel Yun Zhang

The development of quantum codes with good error correction parameters and useful sets of transversal gates is an area of major interest in quantum error correction. Abundant prior works have studied transversal gates which are restricted to acting on all logical qubits simultaneously. In this work, we study codes that support transversal gates which induce addressable logical gates, i.e., the logical gates act only on logical qubits of our choice. As we consider scaling from low-rate to high-rate codes, the study and design of low-overhead, addressable logical operations presents an important problem for both theoretical and practical purposes. In this work, we construct the first quantum codes to support transversally addressable non-Clifford gates. Concretely, given any three logical qubits across one or multiple codeblocks, one can execute the logical CCZ on those qubits via a depth-one physical circuit of CCZ gates. We present a simple, explicit construction based on Reed-Solomon codes that is nearly asymptotically good, and a more involved, asymptotically good construction based on transitive, iso-orthogonal algebraic geometry codes. We go on to develop a powerful theory of quantum codes supporting a rich class of transversally addressable gates in the Clifford hierarchy, going far beyond just the CCZ gate. We call this framework addressable orthogonality, and show that it can be used to construct asymptotically good quantum codes supporting an arbitrary product of multiply-controlled Z gates transversally and addressably, enabling major adaptivity to particular algorithms. Our constructions mark the first quantum codes to support any multi-qubit gate transversally and addressably. Accordingly, our results have major implications for the general addressabilitiy problem in error correction. This is a merged submission based on arXiv:2502.01864 and arXiv:2507.05392.