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High-distance codes with transversal Clifford and T-gates

Abstract

The non-local interactions in several quantum devices allow for the realization of more compact quantum encodings while retaining the same degree of protection against noise. Anticipating that short to medium-length codes will soon be realizable, it is important to construct stabilizer codes that, for a given code distance, admit fault-tolerant implementations of logical gates with the fewest number of physical qubits. We extract high-distance doubly even codes from the quantum quadratic-residue code family that admit a transversal implementation of the single-qubit Clifford group. Applying a doubling procedure [arXiv:1509.03239] to such codes yields a family of high-distance triply even codes which admit a transversal implementation of the logical T-gate. To our knowledge, both code families require a lower qubit overhead than any other qubit stabilizer code of the same distance which can realize their respective gates.

Publication Details

Authors
Publication Type
Journal Article
Year of Publication
2024
Journal
arXiv
Date Published
08/2024