Need One Bell-pair Only (NOBOL) for Low-Overhead Fault-Tolerant Quantum Computing

Quantum Physics arXiv:2609.01901 (quant-ph) [Submitted on 1 Sep 2026] Title:Need One Bell-pair Only (NOBOL) for Low-Overhead Fault-Tolerant Quantum Computing Authors:Sean Grzenda, Shahram Babaie, Chunming Qiao View a PDF of the paper titled Need One Bell-pair Only (NOBOL) for Low-Overhead Fault-Tolerant Quantum Computing, by Sean Grzenda and 2 other authors View PDF HTML (experimental) Abstract:Fault-tolerant quantum computation fundamentally relies on encoding a logical qubit into a structured block of physical qubits, typically in the tens to hundreds. As a trade-off for improved fault-tolerance, logical gate operations will incur a linear overhead in terms of both the amount of time and quantum resources than before. For example, in monolithic quantum computing, performing a gate operation on two distant logical qubits will first require using a linear number of SWAP operations in order to move the logical qubits next to each other; while in distributed quantum computing, doing so will first require a linear number of ancilla qubits in order to form entanglement connections (or a logical Bell pair). In this paper, we focus on significantly reducing the overhead involved in logical CNOT operations, a fundamental primitive. We propose NOBOL, a novel approach that requires only one Bell pair to perform a logical CNOT operation on two distant qubits encoded in arbitrary CSS codes. More importantly, NOBOL only requires performing gate operations on the logical X or Z operator subsets of the logical qubits. For many CSS codes, such as the surface code, these subsets are significantly smaller than the size of the code itself. In this paper, we describe various circuit realizations of NOBOL, including a depth-optimal circuit with logarithmic depth in terms of the size of the logical operators. Finally, we propose effective methods to contain error propagation without incurring much additional overhead. Since NOBOL can be effectively applied to a wide range of quantum error-correcting (QEC) codes and, in addition, is agnostic to qubit modalities and effective for various architectures, including those based on either a monolithic QPU or distributed QPUs. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.01901 [quant-ph] (or arXiv:2609.01901v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.01901 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Shahram Babaie [view email] [v1] Tue, 1 Sep 2026 22:02:03 UTC (421 KB) Full-text links: Access Paper: View a PDF of the paper titled Need One Bell-pair Only (NOBOL) for Low-Overhead Fault-Tolerant Quantum Computing, by Sean Grzenda and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)