Methods, systems, and apparatus for improving exchange systems. In one aspect, a method includes receiving data representing an exchange problem; determining, from the received data, an integer programming formulation of the exchange problem; mapping the integer programming formulation of the exchange problem to a quadratic unconstrained binary optimization (QUBO) formulation of the exchange problem; obtaining data representing a solution to the exchange problem from a quantum computing resource; and initiating an action based on the obtained data representing a solution to the exchange problem.