Logical Compilation for Multi-Qubit Iceberg Patches

Quantum Physics [Submitted on 10 Apr 2026] Logical Compilation for Multi-Qubit Iceberg Patches Cordell Mazzetti, Sayam Sethi, Rich Rines, Pranav Gokhale, Jonathan Mark Baker Recent advancements in quantum computing have enabled practical use of quantum error detecting and correcting codes. However, current architectures and future proposals of quantum computer design suffer from limited qubit counts, necessitating the use of high-rate codes. Such codes, with their code parameters denoted as [[n, k, d]], have more than 1 logical qubit per code (i.e., k > 1). This leads to reduced error tolerance of the code, since \lceil (d-1)/2\rceil errors on any of the n physical qubits can affect the logical state of all k logical qubits. Therefore, it becomes critical to optimally map the input qubits of a quantum circuit to these codes, in such a way that the circuit fidelity is maximized. \par However, the problem of mapping program qubits to logical qubits for high-rate codes has not been studied in prior work. A brute force search to find the optimal mapping is super exponential (scaling as O(n!), where n is the number of input qubits), making exhaustive search infeasible past a small number of qubits. We propose a framework that addresses this problem on two fronts: (1) for any given mapping, it performs logical-to-physical compilation that translates input gates into efficiently encoded implementations utilizing Hadamard commutation and gate merging; and (2) it quickly searches the space of possible mappings through a merge-optimizing, noise-biased packing heuristic that identifies high-performing qubit assignments without exhaustive enumeration. To the best of our knowledge, our compiler is the first work to explore mapping and compilation for high-rate codes. Across 71 benchmark circuits, we reduce circuit depth by 34\%, gate counts by up to 31\% and 17\% for one-qubit and two-qubit gates, and improve total variation distance by 1.75\times, with logical selection rate improvements averaging 86\% relative to naive compilation. Comments: 15 pages, 17 figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.09956 [quant-ph]   (or arXiv:2604.09956v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.09956 Focus to learn more Submission history From: Cordell Mazzetti [view email] [v1] Fri, 10 Apr 2026 23:31:03 UTC (1,972 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)