The Bank of Italy has published a research paper in its “Markets, infrastructures, payment systems” series examining whether changing the processing order of payments in gross-settlement high-value payment systems can reduce the liquidity institutions must hold to complete payments. Applying a hybrid quantum approach to payments between Italian institutions in TARGET2, the paper uses a Constrained Quadratic Model solver to optimize payment batches and estimates average daily liquidity savings of between EUR 23 million and EUR 38 million over a 35-day sample. Machine learning techniques are used to identify batch characteristics associated with larger savings, and results are benchmarked against a Simulated Annealing Algorithm, which delivers comparable savings. The simulated annealing approach is also extended to handle larger batch sizes that remain difficult for current quantum hardware, with reported liquidity savings rising more than proportionally as batch size increases.