  In usual restriction terms of the Quadratic Unconstrained Binary Optimization
(QUBO) hamiltonians, a integer number of logical qubits R, called the Integer
Restriction Coefficient (IRC), are forced to stay active. In this paper we
gather the well-known methods of implementing these restrictions, as well as
some novel methods that show to be more efficient in some frequently
implemented cases. Moreover, it is mathematically allowed to ask for fractional
values of $R$. For these Fractionary Restriction Coefficients (FRC) we show how
they can reduce the number of qubits needed to implement the restriction
hamiltonian even further. Lastly, we characterize the response of DWave's
Advantage$\_$system4.1 Quantum Annealer (QA) when faced with the implementation
of FRCs, and offer a summary guide of the presented methods and the situations
each of them is to be used.
