Fig. 2: Memory/space requirements for quantum methods quantum branch-and-bound (QBnB) and QTG-based search (QTG) in comparison with standard classical solvers (COMBO, GUROBI, and CP-SAT).

The subfigures (from left to right) show the measured average requirements for different groups g = 2, 3 ≤ g ≤ 6 and 7 ≤ g ≤ 10, respectively. See Section “Results” for a description of the instance set. The time limit for GUROBI and CP-SAT was set to COMBO's execution time. As a result, these solvers were unable to find an optimal solution for all benchmark instances. The blue line shows the number of qubits required for executing QTG-based search for the given instances. Its main qubit contribution is due to the augmented quantum amplitude amplification; all the ancilla qubits for gate decompositions etc. are accounted for. Assuming for the moment comparability of bits and qubits, the initial requirement for COMBO is four orders of magnitude higher than for QTG-based search. In the regime of hard instances, i.e., 7 ≤ g ≤ 10, the memory demands of COMBO quickly rise to 10 GB, while QTG-based search as well as QBnB retain their moderate qubit requirements. Note that this is a feature of quantum algorithms, so methods such as Grover search have a similar advantage over classical RAM-based algorithms.