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In usual restriction terms of the Quadratic Unconstrained Binary Optimization(QUBO) hamiltonians, a integer number of logical qubits R, called the IntegerRestriction Coefficient (IRC), are forced to stay active. In this paper wegather the well-known methods of implementing these restrictions, as well assome novel methods that show to be more efficient in some frequentlyimplemented cases. Moreover, it is mathematically allowed to ask for fractionalvalues of $R$. For these Fractionary Restriction Coefficients (FRC) we show howthey can reduce the number of qubits needed to implement the restrictionhamiltonian even further. Lastly, we characterize the response of DWave'sAdvantage$\_$system4.1 Quantum Annealer (QA) when faced with the implementationof FRCs, and offer a summary guide of the presented methods and the situationseach of them is to be used.

Qubit Number Optimization for Restriction Terms of QUBO Hamiltonians