Hadamard Random Forest: Reconstructing real-valued quantum states with exponential reduction in measurement settings

Hadamard Random Forest: Reconstructing real-valued quantum states with exponential reduction in measurement settings | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Hadamard Random Forest: Reconstructing real-valued quantum states with exponential reduction in measurement settings Zhixin song, Hang Ren, Melody Lee, Bryan Gard, Nicolas Renaud, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7545275/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Quantum tomography is a crucial tool for characterizing quantum states and devices and estimating nonlinear properties of the systems. Performing full quantum state tomography on an N qubit system requires an exponentially increasing overhead with O(3^N) distinct Pauli measurement settings to resolve all complex phases and reconstruct the density matrix. However, many potential quantum computing applications, such as linear system solves, require only real-valued amplitudes. We introduce a readout method for real-valued quantum states that reduces measurement settings required for state vector reconstruction to O(N); the post-processing cost remains exponential Ω(2^N). This approach offers a substantial speedup over conventional tomography. We experimentally validate our method up to 10 qubits on the latest available IBM quantum processor and demonstrate that it accurately extracts key properties such as entanglement and magic. Our method also outperforms the standard SWAP test for state overlap estimation. This calculation resembles a numerical integration in certain cases and can be applied to extract nonlinear properties, which are important in application fields. We further implement the method to readout the solution from a quantum linear solver. Physical sciences/Mathematics and computing/Computational science Physical sciences/Physics/Quantum physics/Quantum information Full Text Additional Declarations There is NO Competing Interest. Supplementary Files HRFsupplemental.pdf Supplemental Material Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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