Asuka Koura | Searcharxiv

arXiv2026

Solving Differential Equations Using Continuous-Variable Quantum Annealing

Most existing quantum annealing approaches are formulated for qubit-based architectures. Consequently, applying them to continuous-variable optimization problems requires discretizing the variables, which can incur substantial qubit overhead. Continuous-variable quantum annealing based on bosonic systems has recently been proposed as an alternative framework, in which each optimization variable is directly encoded in a bosonic mode, such as a cavity mode. In this work, we develop a continuous-variable quantum annealing formulation for solving linear differential equations. By recasting the determination of the solution as a continuous-variable optimization problem, the differential equation can be mapped onto an objective function compatible with bosonic quantum annealing. Numerical simulations of second-order linear differential equations demonstrate that, under the conditions considered, the proposed formulation reproduces the corresponding analytical solutions. These results establish a potential route toward solving differential equations without the discretization overhead inherent in qubit-based implementations.

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arXiv2024

Linear Regression Using Quantum Annealing with Continuous Variables

Linear regression is a data analysis technique, which is categorized as supervised learning. By utilizing known data, we can predict unknown data. Recently, researchers have explored the use of quantum annealing (QA) to perform linear regression where parameters are approximated to discrete values using binary numbers. However, this approach has a limitation: we need to increase the number of qubits to improve the accuracy. Here, we propose a novel linear regression method using QA that leverages continuous variables. In particular, the boson system facilitates the optimization of linear regression without resorting to discrete approximations, as it directly manages continuous variables while engaging in QA. The major benefit of our new approach is that it can ensure accuracy without increasing the number of qubits as long as the adiabatic condition is satisfied.

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