[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86189-en":3,"doc-seo-86189-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},86189,13056703019662,"Evangeline","https://ap-avatar.wpscdn.com/avatar/be000253a8e92610077?_k=1778726343310543188",8,"Research & Report","Fixed-Protocol Amortized MPS Tomography with Conformalized Predictive Uncertainty","Quantum state tomography faces severe sample complexity because full n-qubit reconstruction needs exponentially many measurements. This work targets “high fidelity at few measurements” by leveraging that prepared states occupy a learnable, structured manifold. It studies shared matrix-product-state (MPS) core parameterizations with two routes: a measurement-guided generative prior and, mainly, a fixed-protocol amortized MPS estimator with gauge-invariant fidelity training. Informative local Pauli measurement design drives large gains, yielding ~0.95 fidelity and ~90% conformal coverage, validated against prior-only and shuffled-measurement integrity controls, including IBM hardware tests.","arXiv :2607 . 11273v1 [ quant-ph] 13 Jul 2026  \nFIXED-PROTOCOL AMORTIZED MPS TOMOGRAPHY WITH CONFORMALIZED PREDICTIVE UNCERTAINTY  \nJian Xu 1 ,2 , Delu Zeng3 , John Paisley4 , Qibin Zhao2  \n1RIKEN iTHEMS 2RIKEN AIP 3 South China University of Technology 4 Columbia University [jian.xu@riken.jp](jian.xu@riken.jp)  \nABSTRACT  \nQuantum state tomography is sample-starved, and the states one prepares live  \non a narrow, learnable manifold. A k=0 prior-only control shows that on con  \ncentrated families a prior estimate is already near-optimal, so “high fidelity at  \nfew measurements” can be family memorization rather than tomography; genuine  \nmeasurement-efficiency needs a model that conditions on the measurements and  \ndemonstrably uses them. On a shared matrix-product-state (MPS) core parameter  \nization we study two routes. Approach A learns a generative prior over MPS cores  \nwith measurement-guided posterior inference (gold-standard-validated, but whose  \nfew-measurement accuracy the control shows is largely the prior) . Approach B,  \nour main proposal, is a fixed-protocol amortized MPS estimator trained once with  \na gauge-invariant fidelity loss; we deliberately do not rest it on a permutation  \ninvariant set encoder (a plain MLP matches it) . The decisive lever is the measure  \nment design: motivated by the fact that local reduced density matrices determine a  \nχ-MPS, conditioning on an informative local Pauli set rather than random strings  \nturns a modest, memorization-prone estimator into a high-fidelity one (≈ 0.95,  \nup to +0 .59 over prior-only, decisively passing a shuffled-measurement control) .  \nA dropout ensemble, conformally recalibrated, gives ≈ 90%-coverage intervals—  \nincluding for observables never measured, where a shot-based interval does not  \nexist. Quality holds as the system grows (fidelity 0.90 at n=10, gain growing  \nin n ; 0.88 at bond dimension χ=4), the parameterization is polynomial (native  \ncontraction to 20 qubits), and we close the loop on IBM hardware (5 states at  \n0.97 from hardware-measured Paulis) . Our prior-only and shuffled controls are a necessary integrity check we argue learned-QST work should adopt.  \n1 INTRODUCTION  \nQuantum state tomography (QST)—estimating an unknown quantum state ρ from measurement data—is a cornerstone primitive for benchmarking and debugging quantum hardware. Its central difficulty is sample complexity: full tomography of an n-qubit state requires a number of measurements that scales exponentially in n, and each measurement (state preparation plus readout) is expensive. Reducing the measurement budget needed to reach a target fidelity is therefore the practically important axis.  \nTwo broad families reduce this cost. Structural methods restrict the model class: compressedsensing QST exploits low rank (Gross et al., 2010), and matrix-product-state (MPS) tomography exploits low entanglement (Cramer et al., 2010; Lanyon et al., 2017), both recovering poly-parameter states from poly-many measurements. Bayesian methods (Blume-Kohout, 2010; Granade et al., 2016; Lukens et al., 2020) return a posterior—and hence uncertainty—but rely on hand-chosen priors on the dense state and do not learn from the distribution of states a device actually produces. Neither family uses the key empirical fact that the states prepared in a given experiment are not arbitrary: they lie on a narrow, structured manifold (e.g. ground states of a Hamiltonian family, orthe output states of a parameterized circuit) .  \nA learned prior alone is not enough—and a control that shows it. The tempting recipe is to learn a generative prior over the family and invert by posterior sampling (Chung et al., 2022) .  \nWe build this (Approach A: a flow-matching prior over MPS cores with a measurement-guided proximal/Doob-h-transform sampler)—a genuine, gold-standard-validated Bayesian posterior—and it produces high fidelity at few measurements. But a simple control deflates the interpretation. On a concen","cbCainnnQaUVhhE3","https://ap.wps.com/l/cbCainnnQaUVhhE3","pdf",600658,1,23,"English","en",105,"# Abstract\n# Introduction\n## Sample complexity and cost of QST\n## Structural and Bayesian reduction methods\n## Learned priors: necessity of controls\n## Measurement-conditioned amortized estimation\n## Why local informative measurements matter\n## MPS core parameterization","[{\"question\":\"What problem does the paper address in quantum state tomography?\",\"answer\":\"Quantum state tomography is sample-starved: achieving a target fidelity with limited measurements becomes difficult because full tomography scales exponentially with the number of qubits.\"},{\"question\":\"Why do prior-only baselines and shuffled-measurement controls matter?\",\"answer\":\"The paper argues learned-QST must be benchmarked against a k=0 prior-only baseline and must demonstrate that the algorithm truly uses measurement data; shuffling measurements provides an integrity check that learned performance is not mere family memorization.\"},{\"question\":\"How does the proposed method achieve high fidelity and uncertainty quantification?\",\"answer\":\"It trains a fixed-protocol amortized MPS estimator using a gauge-invariant fidelity loss, then uses informative local Pauli measurement sets rather than random strings. A dropout ensemble with conformal recalibration provides ~90% coverage intervals, including for observables not directly measured.\"}]",1784209253,58,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"fixed-protocol-amortized-mps-tomography-with-conformalized-predictive-uncertainty","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/fixed-protocol-amortized-mps-tomography-with-conformalized-predictive-uncertainty/86189/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the paper address in quantum state tomography?","Question",{"text":75,"@type":76},"Quantum state tomography is sample-starved: achieving a target fidelity with limited measurements becomes difficult because full tomography scales exponentially with the number of qubits.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why do prior-only baselines and shuffled-measurement controls matter?",{"text":80,"@type":76},"The paper argues learned-QST must be benchmarked against a k=0 prior-only baseline and must demonstrate that the algorithm truly uses measurement data; shuffling measurements provides an integrity check that learned performance is not mere family memorization.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the proposed method achieve high fidelity and uncertainty quantification?",{"text":84,"@type":76},"It trains a fixed-protocol amortized MPS estimator using a gauge-invariant fidelity loss, then uses informative local Pauli measurement sets rather than random strings. A dropout ensemble with conformal recalibration provides ~90% coverage intervals, including for observables not directly measured.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":45,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":45,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":45,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":45,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":45,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]