Sparse Quantum State Preparation with Sublinear T-Count

Quantum Physics arXiv:2608.00414 (quant-ph) [Submitted on 1 Aug 2026] Title:Sparse Quantum State Preparation with Sublinear T-Count Authors:Jingquan Luo, Lvzhou Li View a PDF of the paper titled Sparse Quantum State Preparation with Sublinear T-Count, by Jingquan Luo and Lvzhou Li View PDF Abstract:We study the fault-tolerant cost of preparing sparse quantum states, measured by $T$-count in the Clifford+$T$ model. Here an $n$-qubit state is called $s$-sparse if it is supported on at most $s$ computational-basis states. For arbitrary $n$-qubit states, the optimal $T$-count is $\Theta(\sqrt{2^n\log(1/\epsilon)}+\log(1/\epsilon))$, but for $s$-sparse states the best previous upper bounds remained linear in $s$. We show that any $n$-qubit $s$-sparse state can be prepared up to error $\epsilon$ using $\widetilde{O}(\min\{s,\ n^{3/4}\sqrt{s}\}+\sqrt{s\log(1/\epsilon)}+\log(1/\epsilon))$ $T$ gates, giving the first sublinear dependence on $s$ once the support is sufficiently large. Our approach is based on a support-aware synthesis theorem for sparse Boolean functions, which may be of independent interest. We also prove that, for every $0 new | recent | 2026-08 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?)