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Chaotic-Amplitude-Controlled Coherent Ising Machines: Extensions to Quadratic Unconstrained Binary Optimisation and Simplified Models

Mastiyage Don Sudeera Hasaranga Gunathilaka, Sudeera Hasaranga Gunathilaka Mastiyage Don

Published Mar 1, 2025• 0 citations
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Chaotic-Amplitude-Controlled Coherent Ising Machines: Extensions to Quadratic Unconstrained Binary Optimisation and Simplified Models

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In this paper, a methodology for finding the optimal solution by building a QUBO (Quadratic Unconstrained Binary Optimisation) model and using a combination of the Simulated Annealing algorithm and the CIM (Coherent Equivalent Machine) simulator in the Open Matter SDK will be presented. Firstly, the QUBO model was chosen because of its significant advantages in dealing with logical inference and combinatorial optimisation problems. The QUBO model provides an efficient solution method by transforming the problem into a quadratic unconstrained binary optimisation problem. In solving this problem, the first step is to define the objective and constraints of the problem, where the objective is to satisfy the relevant requirements and make the best of them, and the constraints are the relevant parameters provided by the data, and to build a mathematical model that matches the QUBO model. Next, a simulated annealing algorithm and a CIM simulator were used to solve this QUBO problem. By combining the QUBO model with these two algorithms, the optimal solution can be searched efficiently. Finally, the optimal solution is derived from the solution results. These scenarios not only satisfy the constraints but also achieve the given objective by optimising the combination of decision variables.

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Advances in artificial intelligence (AI) and deep learning have raised concerns about its increasing energy consumption, while demand for deploying AI in mobile devices and machines at the edge is growing. Binary neural networks (BNNs) have recently gained attention as energy and memory efficient models suitable for resource constrained environments; however, training BNNs exactly is computationally challenging because of its discrete characteristics. Recent work proposing a framework for training BNNs based on quadratic unconstrained binary optimisation (QUBO) and progress in the design of Ising machines for solving QUBO problems suggest a potential path to efficiently optimising discrete neural networks. In this work, we extend existing QUBO models for training BNNs to accommodate arbitrary network topologies and propose two novel methods for regularisation. The first method maximises neuron margins biasing the training process toward parameter configurations that yield larger pre-activation magnitudes. The second method employs a dropout-inspired iterative scheme in which reduced subnetworks are trained and used to adjust linear penalties on network parameters. We apply the proposed QUBO formulation to a small binary image classification problem and conduct computational experiments on a GPU-based Ising machine. The numerical results indicate that the proposed regularisation terms modify training behaviour and yield improvements in classification accuracy on data not present in the training set.

arXiv:2601.00449•Jan 1, 2026•0 citations
In this paper, a methodology for finding the optimal solution by building a QUBO (Quadratic Unconstrained Binary Optimisation) model and using a combination of the Simulated Annealing algorithm and the CIM (Coherent Equivalent Machine) simulator in the Open Matter SDK will be presented. Firstly, the QUBO model was chosen because of its significant advantages in dealing with logical inference and combinatorial optimisation problems. The QUBO model provides an efficient solution method by transforming the problem into a quadratic unconstrained binary optimisation problem. In solving this problem, the first step is to define the objective and constraints of the problem, where the objective is to satisfy the relevant requirements and make the best of them, and the constraints are the relevant parameters provided by the data, and to build a mathematical model that matches the QUBO model. Next, a simulated annealing algorithm and a CIM simulator were used to solve this QUBO problem. By combining the QUBO model with these two algorithms, the optimal solution can be searched efficiently. Finally, the optimal solution is derived from the solution results. These scenarios not only satisfy the constraints but also achieve the given objective by optimising the combination of decision variables.
Quantum computing poses a threat to contemporary cryptosystems, with advances to a state in which it will cause problems predicted for the next few decades. Many of the proposed cryptosystems designed to be quantum-secure are based on the Shortest Vector Problem and related problems. In this paper we use the Quadratic Unconstrained Binary Optimisation formulation of the Shortest Vector Problem implemented as a quantum Ising model on a simulated Coherent Ising Machine, showing progress towards solving SVP for three variants of the algorithm.
Advances in artificial intelligence (AI) and deep learning have raised concerns about its increasing energy consumption, while demand for deploying AI in mobile devices and machines at the edge is growing. Binary neural networks (BNNs) have recently gained attention as energy and memory efficient models suitable for resource constrained environments; however, training BNNs exactly is computationally challenging because of its discrete characteristics. Recent work proposing a framework for training BNNs based on quadratic unconstrained binary optimisation (QUBO) and progress in the design of Ising machines for solving QUBO problems suggest a potential path to efficiently optimising discrete neural networks. In this work, we extend existing QUBO models for training BNNs to accommodate arbitrary network topologies and propose two novel methods for regularisation. The first method maximises neuron margins biasing the training process toward parameter configurations that yield larger pre-activation magnitudes. The second method employs a dropout-inspired iterative scheme in which reduced subnetworks are trained and used to adjust linear penalties on network parameters. We apply the proposed QUBO formulation to a small binary image classification problem and conduct computational experiments on a GPU-based Ising machine. The numerical results indicate that the proposed regularisation terms modify training behaviour and yield improvements in classification accuracy on data not present in the training set.