{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/faster-stochastic-first-order-method-for","title":"Faster Stochastic First-Order Method for Maximum-Likelihood Quantum State Tomography","arxiv_id":"2211.12880","date":"2022-11-23","proceeding":null,"authors":["Chung-En Tsai","Hao-Chung Cheng","Yen-Huan Li"],"abstract":"In maximum-likelihood quantum state tomography, both the sample size and dimension grow exponentially with the number of qubits. It is therefore desirable to develop a stochastic first-order method, just like stochastic gradient descent for modern machine learning, to compute the maximum-likelihood estimate. To this end, we propose an algorithm called stochastic mirror descent with the Burg entropy. Its expected optimization error vanishes at a $O ( \\sqrt{ ( 1 / t ) d \\log t } )$ rate, where $d$ and $t$ denote the dimension and number of iterations, respectively. Its per-iteration time complexity is $O ( d^3 )$, independent of the sample size. To the best of our knowledge, this is currently the computationally fastest stochastic first-order method for maximum-likelihood quantum state tomography.","url_abs":"https://arxiv.org/abs/2211.12880v1","url_pdf":"https://arxiv.org/pdf/2211.12880v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"faster-stochastic-first-order-method-for","repo_url":"https://github.com/chungentsai/pip","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"quantum-state-tomography","task_name":"Quantum State Tomography"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}