DVQE: Discrete variational quantum eigensolver for memory allocation in continual learning

Continual learning systems encounter the persistent challenge of catastrophic forgetting, wherein acquiring new knowledge degrades performance on previously learned tasks. Experience replay maintains a memory buffer of historical samples to mitigate this issue, yet optimally allocating finite memory across multiple domains remains an open combinatorial optimization problem. We introduce DVQE (Discrete Variational Quantum Eigensolver), a quantum-classical hybrid framework designed for memory allocation optimization in continual learning scenarios. The proposed approach employs parameterized quantum circuits with five distinct ansatz architectures, integrated with a discretization mechanism to address integer constraints inherent to the allocation problem. Comprehensive experiments across CIFAR-10, CIFAR-100, and Tiny ImageNet benchmarks demonstrate that DVQE attains performance comparable to state-of-the-art classical optimization techniques, including Bayesian Optimization and CMA-ES, while utilizing only 5 qubits and shallow circuits amenable to near-term quantum devices. Statistical analysis across five random seeds confirms that DVQE attains comparable or superior performance to BO and CMA-ES while requiring fewer function evaluations. This work represents, to our knowledge, the first application of variational quantum optimization to memory allocation in continual learning, thereby demonstrating the feasibility of quantum approaches for machine learning resource optimization on near-term quantum hardware.