Compressed Sensing Shadow Tomography
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Quantum Physics arXiv:2602.12518 (quant-ph) [Submitted on 13 Feb 2026] Title:Compressed Sensing Shadow Tomography Authors:Joseph Barreto, Daniel Lidar View a PDF of the paper titled Compressed Sensing Shadow Tomography, by Joseph Barreto and Daniel Lidar View PDF HTML (experimental) Abstract:Estimating many local expectation values over time is a central measurement bottleneck in quantum simulation and device characterization. We study the task of reconstructing the Pauli-signal matrix $S_{ij}=\text{Tr}(O_i \rho(t_j))$ for a collection of $M$ low-weight Pauli observables $\{O_i\}_{i=1}^M$ over $N$ timesteps $\{t_j\}_{j=1}^N$, while minimizing the total number of device shots. We propose a Compressed Sensing Shadow Tomography (CSST) protocol that combines two complementary reductions. First, local classical shadows reduce the observable dimension by enabling many Pauli expectation values to be estimated from the same randomized snapshots at a fixed time. Second, compressed sensing reduces the time dimension by exploiting the fact that many expectation-value traces are spectrally sparse or compressible in a unitary (e.g., Fourier) transform basis. Operationally, CSST samples $m\ll N$ timesteps uniformly at random, collects shadows only at those times, and then reconstructs each length-$N$ signal via standard $\ell_1$-based recovery in the unitary transform domain. We provide end-to-end guarantees that explicitly combine shadow estimation error with compressed sensing recovery bounds. For exactly $s$-sparse signals in a unitary transform basis, we show that $m=O \left(s\log^2 s \log N\right)$ random timesteps suffice (with high probability), leading to total-shot savings scaling as $\widetilde{\Theta}(N/s)$ (i.e., up to polylogarithmic factors) relative to collecting shadows at all $N$ timesteps. For approximately sparse signals, the reconstruction error decomposes into a compressibility (tail) term plus a noise term. We present numerical experiments on noisy many-qubit dynamics that support strong Fourier compressibility of Pauli traces and demonstrate substantial shot reductions with accurate reconstruction. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2602.12518 [quant-ph] (or arXiv:2602.12518v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.12518 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Joseph Barreto [view email] [v1] Fri, 13 Feb 2026 01:50:02 UTC (8,739 KB) Full-text links: Access Paper: View a PDF of the paper titled Compressed Sensing Shadow Tomography, by Joseph Barreto and Daniel LidarView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 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?)