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Computer Science Research Notes

Bayesian Update Step Using Adiabatic Quantum Computing

Rheinische Friedrich- Wilhelms-Universität, Norman Bunk, Felix Govaers, Fraunhofer FKIE

Published Jan 1, 2025• 1 citation
Publisher

Abstract

We propose a quantum algorithm for the filtering step in Bayesian state estimation, based on adiabatic quantum computing (AQC).The approach embeds the likelihood function into the energy landscape of an Ising Hamiltonian, enabling the posterior distribution to emerge through quantum annealing.Unlike existing gate-based methods, our formulation avoids complex conditional operations and scales more naturally with the size of the state space.Numerical simulations confirm that the resulting distributions closely match the correct posterior, even with approximate parameter settings.This demonstrates the feasibility of AQC as a tool for probabilistic inference in high-dimensional filtering problems.

DOI
10.24132/csrn.2025-a23

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We propose a quantum algorithm for the filtering step in Bayesian state estimation, based on adiabatic quantum computing (AQC).The approach embeds the likelihood function into the energy landscape of an Ising Hamiltonian, enabling the posterior distribution to emerge through quantum annealing.Unlike existing gate-based methods, our formulation avoids complex conditional operations and scales more naturally with the size of the state space.Numerical simulations confirm that the resulting distributions closely match the correct posterior, even with approximate parameter settings.This demonstrates the feasibility of AQC as a tool for probabilistic inference in high-dimensional filtering problems.
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This paper explores the application of quantum computing to accelerate Bayesian inference. Traditional Bayesian inference suffers from significant computational bottlenecks, particularly in complex models with large datasets. We propose a novel approach leveraging the inherent parallelism of quantum computers to drastically reduce the time required for inference. Specifically, we design a quantum algorithm based on a parameterized quantum circuit (PQC) to perform Bayesian updating. This approach utilizes quantum superposition and interference to perform computations on multiple possibilities simultaneously. The core claim is that this method can significantly speed up Bayesian inference. We detail the mathematical formulation of the algorithm, including the quantum circuit representation and the key operations involved. The potential of this approach to overcome the limitations of classical Bayesian inference is discussed, highlighting the transformative impact of quantum computing on probabilistic reasoning and data analysis. The efficiency gains are expected to be particularly pronounced for problems where the prior distributions and the likelihood functions are highly correlated, allowing for efficient quantum interference.
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