Block Encoding Linear Combinations of Pauli Strings Using the Stabilizer Formalism

Quantum Physics arXiv:2601.05740 (quant-ph) [Submitted on 9 Jan 2026] Title:Block Encoding Linear Combinations of Pauli Strings Using the Stabilizer Formalism Authors:Niclas Schillo, Andreas Sturm, Rüdiger Quay View a PDF of the paper titled Block Encoding Linear Combinations of Pauli Strings Using the Stabilizer Formalism, by Niclas Schillo and 2 other authors View PDF Abstract:The Quantum Singular Value Transformation (QSVT) provides a powerful framework with the potential for quantum speedups across a wide range of applications. Its core input model is the block encoding framework, in which non-unitary matrices are embedded into larger unitary matrices. Because the gate complexity of the block-encoding subroutine largely determines the overall cost of QSVT-based algorithms, developing new and more efficient block encodings is crucial for achieving practical quantum advantage. In this paper, we introduce a novel method for constructing quantum circuits that block encode linear combinations of Pauli strings. Our approach relies on two key components. First, we apply a transformation that converts the Pauli strings into pairwise anti-commuting ones, making the transformed linear combination unitary and thus directly implementable as a quantum circuit. Second, we employ a correction transformation based on the stabilizer formalism which uses an ancilla register to restore the original Pauli strings. Our method can be implemented with an ancilla register whose size scales logarithmically with the number of system qubits. It can also be extended to larger ancilla registers, which can substantially reduce the overall quantum circuit complexity. We present four concrete examples and use numerical simulations to compare our method's circuit complexity with that of the Linear Combination of Unitaries (LCU) approach. We find that our method achieves circuit complexities comparable to or better than LCU, with possible advantages when the structure of the target operators can be exploited. These results suggest that our approach could enable more efficient block encodings for a range of relevant problems extending beyond the examples analyzed in this work. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.05740 [quant-ph] (or arXiv:2601.05740v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.05740 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Niclas Schillo [view email] [v1] Fri, 9 Jan 2026 11:41:46 UTC (45 KB) Full-text links: Access Paper: View a PDF of the paper titled Block Encoding Linear Combinations of Pauli Strings Using the Stabilizer Formalism, by Niclas Schillo and 2 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-01 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)