Grover Adaptive Search for Constrained Polynomial Binary Optimization

In this paper we discuss Grover Adaptive Search (GAS) for Constrained Polynomial Binary Optimization (CPBO) problems, and in particular, Quadratic Unconstrained (QUBO) as a special case. GAS can provide quadratic speed-up combinatorial optimization problems compared to brute force search. However, requires the development of efficient oracles represent flag states that satisfy certain search criteria. general, be achieved using quantum arithmetic, however, is expensive terms Toffoli gates well required ancilla qubits, which prohibitive near-term. Within work, develop way construct solve CPBO algorithms. We demonstrate approach potential portfolio problem, i.e. QUBO, simulation experimental results obtained on real hardware. our applies higher-degree polynomial objective functions constrained problems.