Back to News
quantum-computing

The Feedback Hamiltonian is the Score Function: A Diffusion-Model Framework for Quantum Trajectory Reversal

arXiv Quantum Physics
Loading...
2 min read
0 likes
⚡ Quantum Brief
Researchers Sagar Dubey and Alan John revealed that the García-Pintos feedback Hamiltonian ($H_{\mathrm{meas}} = rA/\tau$) functions as the score of quantum trajectory distributions, mathematically proving its role in time-reversal via diffusion-model frameworks. The study bridges quantum physics and machine learning by showing this Hamiltonian aligns with Anderson’s reverse-time diffusion theorem, enabling trajectory reversal when feedback gain $X < -2$—a mechanism previously unexplained. Using Girsanov’s theorem and Fréchet differentiation, they derived the score function directly in density-matrix space, linking measurement records to Kähler geometry on pure-state manifolds for rigorous proof. Unlike classical diffusion (binary reversal), quantum systems exhibit a continuous family of path measures under feedback, with $X = -2$ recovering time-reversed dynamics—a novel quantum-classical distinction. The framework extends to multi-qubit systems, where the score becomes a sum of local operators, offering scalable control for complex quantum trajectories.
The Feedback Hamiltonian is the Score Function: A Diffusion-Model Framework for Quantum Trajectory Reversal

Summarize this article with:

Quantum Physics arXiv:2604.21210 (quant-ph) [Submitted on 23 Apr 2026] Title:The Feedback Hamiltonian is the Score Function: A Diffusion-Model Framework for Quantum Trajectory Reversal Authors:Sagar Dubey, Alan John View a PDF of the paper titled The Feedback Hamiltonian is the Score Function: A Diffusion-Model Framework for Quantum Trajectory Reversal, by Sagar Dubey and 1 other authors View PDF HTML (experimental) Abstract:In continuously monitored quantum systems, the feedback protocol of García-Pintos, Liu, and Gorshkov reshapes the arrow of time: a Hamiltonian $H_{\mathrm{meas}} = r A / \tau$ applied with gain $X$ tilts the distribution of measurement trajectories, with $X new | recent | 2026-04 Change to browse by: cs cs.LG 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?)

Read Original

Tags

quantum-investment
quantum-hardware

Source Information

Source: arXiv Quantum Physics