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Scientific Reports

Multi-level probabilistic computing: application to the multiway number partitioning problems

Ki-Hyuk Han, G.S. Park, Jeong Ung Ahn, YongJin Kim, Deok Hyun Yun, Seung-Hun Jang, Young-Jun Nah, Min Gu Kang, Hyun Cheol Koo, OukJae Lee

Published Aug 7, 2025• 0 citations
Publisher

Abstract

Probabilistic computing, a class of physics-based computing, bridges the gap between quantum computing and the classical von Neumann architecture. This approach provides more efficient means of addressing NP problems, which are challenging for classical computers. In this work, we analyze the core concept of probabilistic computing which is based on the Ising model framework-including bit fluctuations and energy trends. In addition, we extend the traditional binary (two-level) system into a multi-level probabilistic framework, i.e. number partitioning problem to multiway number partitioning problem, as a case study.

DOI
10.1038/s41598-025-14531-w

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Quantum entanglement, a cornerstone of quantum mechanics, presents a unique opportunity for revolutionary computational and communication paradigms. However, harnessing this phenomenon effectively requires sophisticated optimization techniques. This paper explores the application of probabilistic modeling to optimize complex quantum systems, particularly those involving multi-particle entanglement. We propose a novel framework that transforms the inherent evolution of quantum states into a probabilistic process, leveraging the properties of entanglement to control and optimize the behavior of these systems. The core mechanism centers around the design of a probabilistic computation method, offering a potential pathway to enhance quantum computing and quantum communication efficiency. This work addresses a critical gap in our understanding of optimizing complex quantum systems, offering a promising approach to tackling challenges in these rapidly evolving fields.
A bit-quantum map relates probabilistic information for Ising spins or classical bits to quantum spins or qubits. Quantum systems are subsystems of classical statistical systems. The Ising spins can represent macroscopic two-level observables, and the quantum subsystem employs suitable expectation values and correlations. We discuss static memory materials based on Ising spins for which boundary information can be transported through the bulk in a generalized equilibrium state. They can realize quantum operations as the Hadamard or CNOT-gate for the quantum subsystem. Classical probabilistic systems can account for the entanglement of quantum spins. An arbitrary unitary evolution for an arbitrary number of quantum spins can be described by static memory materials for an infinite number of Ising spins which may, in turn, correspond to continuous variables or fields. We discuss discrete subsets of unitary operations realized by a finite number of Ising spins. They may be useful for new computational structures. We suggest that features of quantum computation or more general probabilistic computation may be realized by neural networks, neuromorphic computing or perhaps even the brain. This does neither require small isolated entities nor very low temperature. In these systems the processing of probabilistic information can be more general than for static memory materials. We propose a general formalism for probabilistic computing for which deterministic computing and quantum computing are special limiting cases.
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