Quantum computation for optimization in exchange systems

A system comprising:

• a classical processor;
• a quantum computing device in data communication with the classical processor;
• wherein the classical processor and quantum computing device are configured to perform operations comprising:
• receiving data representing an exchange problem;
• determining, from the received data, an integer programming formulation of the exchange problem, the integer programming formulation of the exchange problem comprising:
• i) an objective function to be maximized, and ii) one or more constraints comprising equality and inequality constraints;
• mapping the integer programming formulation of the exchange problem to a quadratic unconstrained binary optimization (QUBO) formulation of the exchange problem, comprising:
• mapping the objective function to be maximized to a QUBO objective function to be minimized;
• determining a penalty term, comprising, for each equality constraint:
• representing the constraint as an equation equaling zero when the constraint is satisfied and equaling a strictly positive value when the constraint is not satisfied;
• multiplying the equation by a weight to generate a corresponding partial-penalty term;
• and
• including the generated partial-penalty terms in the penalty term;
• and
• adding the penalty term to the QUBO objective function to be minimized;
• 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.