  High-value payment systems (HVPSs) are typically liquidity-intensive as 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
developed an algorithm and ran it on a hybrid quantum annealing solver to find
an ordering of payments that reduced 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 provided
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 entered the queue, we achieved an average of C\$240 million in daily
liquidity savings, with a settlement delay of approximately 90 seconds. For a
few days in the sample, the liquidity savings exceeded C\$1 billion. This
algorithm could be incorporated as a centralized preprocessor into existing
HVPS without entailing a fundamental change to their risk management models.
