2025/10/22 by Virgile Guémard, Guemard, Virgile · 1 citation
Computer Science · #Complexity and Algorithms in Graphs #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2510.19809
openalex publication_date 2025/10/22 · openalex created_date 2025/10/24 · openalex updated_date 2026/08/02
In this work, we prove that for any m>1, there exists a family of good qudit quantum codes supporting transversal logical Cm-1Z gates that can address specified logical qudits and be largely executed in parallel. Building on the family of good quantum error-correcting codes presented in He et al. (2025), which support addressable and transversal logical CCZ gates, we extend their framework and show how to perform large sets of gates in parallel. The construction relies on the classical algebraic geometry codes of Stichtenoth (IEEE Trans. Inf. Theory, 2006). Our results lead to a substantial reduction in the depth overhead of multi-control-Z circuits. In particular, we show that the minimal depth of any logical Cm-1Z circuit involving qudits from m distinct code blocks is upper bounded by O(km-1), where k is the code dimension. While this overhead is optimal for dense Cm-1Z circuits, for sparse circuits we discuss how the depth overhead can be significantly reduced by exploiting the structure of the quantum code.