III. Quantum Bayesianism

Christopher G. Timpson

Syed Muntasir Mamun

The pursuit of massive foundation models is hindered by the limitations of Maximum Likelihood Estimation (MLE), which struggles with uncertainty quantification and out-of-distribution generalization. The Bayesian framework resolves these deficiencies but is crippled by the "marginalisation bottleneck"—the computational intractability of integrating over high-dimensional parameter spaces. Classical approximations like MCMC and Variational Inference (VI) are fundamentally limited by slow mixing times or sub-optimal local minima. Quantum computing offers a paradigm-shifting resolution, leveraging superposition and entanglement to execute high-dimensional integrals with theoretical exponential speedups by mapping statistical probabilities to quantum amplitude vectors. This review systematically details foundational quantum mapping and state-of-the-art Mamun, SM (2026) ………………………………….1 Quantum Computing for Bayesian Inference: Algorithms, Speedups, Challenges, and Synergies with Scalable Machine Learning (Vol-III) K S C algorithms, including Quantum Bayesian Computation (QBC), Quantum Annealing Variational Bayes (QAVB), and Quantum Gaussian Processes (Q-GPs). A key insight is the deep synergy where inherent quantum noise (decoherence) functionally serves as a native Bayesian regularizer, analogous to classical dropout. Also available on Academia.edu: https://www.academia.edu/attachments/132601227/download_file?s=portfolio

Enrico Zardini, Massimo Rizzoli, Sebastiano Dissegna +2 more

Bayesian networks are widely used probabilistic graphical models, whose structure is hard to learn starting from the generated data. O'Gorman et al. have proposed an algorithm to encode this task, i.e., the Bayesian network structure learning (BNSL), into a form that can be solved through quantum annealing, but they have not provided an experimental evaluation of it. In this paper, we present (i) an implementation in Python of O'Gorman's algorithm, (ii) a divide et impera approach that allows addressing BNSL problems of larger sizes in order to overcome the limitations imposed by the current architectures, and (iii) their empirical evaluation. Specifically, several problems with an increasing number of variables have been used in the experiments. The results have shown the effectiveness of O'Gorman's formulation for BNSL instances of small sizes, and the superiority of the divide et impera approach on the direct execution of O'Gorman's algorithm.

Jon Frost, Carlos Madeira, Harald Uhlig

S. Sýkora

Jacob Benestad, Jan A. Krzywda, Evert van Nieuwenburg +1 more

Slow fluctuations of Overhauser fields are an important source for decoherence in spin qubits hosted in III-V semiconductor quantum dots. Focusing on the effect of the field gradient on double-dot singlet-triplet qubits, we present two adaptive Bayesian schemes to estimate the magnitude of the gradient by a series of free induction decay experiments. We concentrate on reducing the computational overhead, with a real-time implementation of the schemes in mind. We show how it is possible to achieve a significant improvement of estimation accuracy compared to more traditional estimation methods. We include an analysis of the effects of dephasing and the drift of the gradient itself.