Improving the efficiency of payments systems using quantum computing

High-value payment systems (HVPSs) are typically liquidity-intensive because the payment requests are indivisible and settled on a gross basis. Finding the right order in which payments should be processed to maximize the liquidity efficiency of these systems is an NP-hard combinatorial optimization problem, which quantum algorithms may be able to tackle at meaningful scales. We develop an algorithm and run it on a hybrid quantum annealing solver to find an ordering of payments that reduces the amount of system liquidity necessary without substantially increasing payment delays. Despite the limitations in size and speed of today's quantum computers, our algorithm provides quantifiable efficiency improvements when applied to the Canadian HVPS using a 30-day sample of transaction data. By reordering each batch of 70 payments as they enter the queue, we achieve an average of Can $ 240 million in daily liquidity savings, with a settlement delay of approximately 90 seconds. For a few days in the sample, the liquidity savings exceed Can $ 1 billion. This algorithm could be incorporated as a centralized preprocessor into existing HVPSs without entailing a fundamental change to their risk management models.