Quantum

Adaptive Qubit Encoding for Continuous-Variable Quantum Optimization

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Briefings

A new framework for continuous-variable quantum optimization combines adaptive discretization with iterative local mapping to an effective spin-glass Hamiltonian. The method was tested on the n-dimensional Gramacy-Lee benchmark and an IMRT inverse-planning problem, producing competitive solutions for both constrained and unconstrained instances.

Key points

• The framework uses adaptive discretization to represent the search space and iterative local mapping to construct an effective spin-glass Hamiltonian for objective functions.
• Performance was evaluated on the n-dimensional Gramacy-Lee benchmark and an inverse-planning problem in intensity-modulated radiotherapy (IMRT) for cancer treatment.

Context

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 restrict the search to a predefined range and resolution, while constructing a compact Hamiltonian for a general continuous-variable objective can be impractical. This new approach addresses these limitations.

Limitations

The framework was assessed on specific benchmark instances and a proof-of-concept IMRT problem. Results are limited to these test cases, and the approach's performance on larger-scale or different problem types remains unverified.

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