Year: 2025
Type: article
Abstract: With the advent of physical qubits exhibiting strong noise bias, it becomes increasingly relevant to identify which quantum gates can be efficiently implemented on error-correcting s designed to address a single dominant error type. Here, we consider [n,k,d]-classical stabilizer s addressing bit-flip errors where n, k, and d are the numbers of physical and logical qubits, and the code distance, respectively. We prove that operations essential for achieving a universal logical gate set necessarily require complex unitary circuits to be implemented. Specifically, these implementation circuits either consists of h layers of r-transversal operations on c code blocks such that c^{h-1}r^{h}≥d or of h gates, each operating on at most r physical qubits on the same code block, such that hr≥d. Similar constraints apply not only to classical codes designed to correct phase-flip errors, but also to quantum stabilizer codes tailored to biased noise. This motivates a closer examination of alternative logical gate constructions using, e.g., magic state distillation and cultivation within the framework of biased-noise stabilizer codes.
Source: Physical Review Letters
DOI: 10.1103/h741-4678
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W7117120994