Adaptive Qubit Encoding for Continuous-Variable Quantum Optimization

Abstract

Optimizing continuous-variable functions on qubit-based quantum hardware requires a finite representation of the search space and a solver-compatible representation of the objective function. Fixed-grid discretizations provide a direct encoding, but restrict the search to a predefined range and resolution; at the same time, constructing a compact Hamiltonian for a general continuous-variable objective can be impractical. Here, we introduce a framework for continuous-variable optimization tailored to qubit-based quantum architectures. The method combines an adaptive discretization with an iterative local mapping of the objective function onto an effective spin-glass Hamiltonian. We assess the approach on unconstrained and constrained instances of the $n$-dimensional Gramacy-Lee benchmark, and on a proof-of-concept inverse-planning problem in intensity-modulated radiotherapy (IMRT) for cancer treatment. The results show that this framework can produce competitive solutions, supporting its use as a flexible mapping strategy for continuous-variable optimization in qubit-based quantum and quantum-inspired pipelines.