Solving Differential Equations Using Continuous-Variable Quantum Annealing

• URL: http://arxiv.org/abs/2608.04601v1
• Date: Wed, 05 Aug 2026 09:06:29 GMT
• Title: Solving Differential Equations Using Continuous-Variable Quantum Annealing
• Abstract summary: We develop a continuous-variable quantum annealing formulation for solving linear differential equations.<n>The proposed formulation reproduces the corresponding analytical solutions.<n>These results establish a potential route toward solving differential equations without the discretization overhead inherent in qubit-based implementations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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