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arXiv:0906.1714 · AIP conference proceedings

Priors in Quantum Bayesian Inference

Christopher A. Fuchs, Rüdiger Schack, Luigi Accardi, Guillaume Adenier, Christopher A. Fuchs, Gregg S. Jaeger, Andrei Yu. Khrennikov, Jan-Åke Larsson, Stig Stenholm

Published Jan 1, 2009• 18 citations
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Abstract

In quantum Bayesian inference problems, any conclusions drawn from a finite number of measurements depend not only on the outcomes of the measurements but also on a prior. Here we show that, in general, the prior remains important even in the limit of an infinite number of measurements. We illustrate this point with several examples where two priors lead to very different conclusions given the same measurement data.

DOI
10.1063/1.3109948

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Bayesian inference, a cornerstone of statistical modeling, often struggles with the complexities of high-dimensional data and non-Gaussian distributions commonly encountered in complex systems. This paper proposes a novel approach termed Quantum-Inspired Bayesian Inference (QIBI), leveraging concepts from quantum mechanics – specifically superposition and entanglement – to enhance the efficiency and accuracy of Bayesian inference. QIBI represents prior distributions as superposition states and employs entangled quantum-like circuits to perform marginalization and posterior calculation, effectively addressing the computational bottlenecks associated with traditional methods. We demonstrate the potential of this approach to significantly improve inference performance in scenarios where classical Bayesian methods face limitations. The core of this work lies in the conceptual mapping of Bayesian calculations onto a quantum-inspired framework, providing a new perspective on statistical inference. We define key mathematical formulations to illustrate the proposed methodology, including the superposition state representation of prior distributions and the entanglement-based circuit design for posterior calculation. This exploration aims to bridge the gap between statistical inference and quantum computing, opening avenues for tackling previously intractable problems.