Chapter 3
Quadratic Unconstrained Binary Optimisation
Undoubtedly, Quadratic Unconstrained Binary Optimisation (QUBO) is a flagship use case of quantum annealing. We only need to have a closer look at the name of this class of optimisation problems to see why:
- Quantum annealers operate on binary spin variables. It is straightforward to perform mapping between binary decision variables (represented by the logical qubits) and spin variables.
- The objective functions of quadratic optimisation problems have only linear and quadratic terms. This significantly simplifies the models and allows their embedding on existing quantum annealing hardware.
- Unconstrained optimisation means that although QUBO allows us to specify conditions that must be satisfied, they are not hard constraints. The violation of constraints is penalised through the additional terms in the QUBO objective function, but it is still possible to find solutions that violate specified constraints.
All these features make...
