Jan Michálek | Search arXiv

arXiv2026

On Relationship Between Circuit Depth and Trainability of VQAs

The training efficiency of Variational Quantum Algorithms (VQAs) is dictated by the geometry of their loss landscapes, which can be formally analysed by mapping these functions to random fields on manifolds. Instead of VQAs, we can then directly study the corresponding random fields, in our case, the Wishart Hypertoroidal Random Fields (WHRFs). We are mostly interested in the distribution of critical points (especially local minima) of WHRFs. For this purpose, the Kac-Rice formula is presented, reformulated, and simulated. The findings identify a phase transition in the distribution of local minima. Beyond a specific threshold, local minima concentrate near the global minimum in function value, meaning that even local minima are good approximators of the global one. The threshold is governed by the ratio between the problem Hamiltonian degrees of freedom and by the number of independent parameters in the VQA. Since the degrees of freedom parameter scales exponentially, we propose symmetry reduction operations to lower the degrees of freedom. This mathematically reduces the dimension, scaling down the required parameter threshold and enabling to solve bigger problems.

quant-ph↗

arXiv2022

Federated Learning Enables Big Data for Rare Cancer Boundary Detection

Although machine learning (ML) has shown promise in numerous domains, there are concerns about generalizability to out-of-sample data. This is currently addressed by centrally sharing ample, and importantly diverse, data from multiple sites. However, such centralization is challenging to scale (or even not feasible) due to various limitations. Federated ML (FL) provides an alternative to train accurate and generalizable ML models, by only sharing numerical model updates. Here we present findings from the largest FL study to-date, involving data from 71 healthcare institutions across 6 continents, to generate an automatic tumor boundary detector for the rare disease of glioblastoma, utilizing the largest dataset of such patients ever used in the literature (25,256 MRI scans from 6,314 patients). We demonstrate a 33% improvement over a publicly trained model to delineate the surgically targetable tumor, and 23% improvement over the tumor's entire extent. We anticipate our study to: 1) enable more studies in healthcare informed by large and diverse data, ensuring meaningful results for rare diseases and underrepresented populations, 2) facilitate further quantitative analyses for glioblastoma via performance optimization of our consensus model for eventual public release, and 3) demonstrate the effectiveness of FL at such scale and task complexity as a paradigm shift for multi-site collaborations, alleviating the need for data sharing.

cs.LG↗