Liquidity Optimization in Gross Settlement Systems with Quantum Reordering: Application to TARGET2∗

In McMahon et al. (2024) the authors demonstrated the effectiveness of a hybrid quantum solver in improving the liquidity efficiency of Canada’s high-value payments system (HVPS), altering the payment queue in order to minimize liquidity requirements. In this work, we apply a similar technique to the Italian segment of TARGET2, the Eurosystem’s HVPS, using the Constrained Quadratic Model (CQM) solver provided by D-Wave. This application achieves improvements in optimizing payment batches of size 70 and 140, showing daily average liquidity savings of respectively EUR 23 million and EUR 38 million over a 35 days sample. In addition we clarify the causes and possible extent of the liquidity savings realized. Introducing a machine learning framework to identify batch features that enhance liquidity savings, we find that batch optimizability increases with the number of participants acting as both senders and receivers, as well as the number of unique receivers within the batch. Finally we benchmark the CQM solver results against those obtained using a simulated annealing algorithm (SAA) under the same time constraints, finding comparable liquidity savings for batch sizes of 70 and 140 payments. The SAA is extended to handle batch sizes of up to 700 payments, a scale that is challenging for current quantum hardware, demonstrating a more than tenfold increase in liquidity savings.