Qubits are the minimum unit of information in quantum computing. As current quantum devices have a very limited number of available qubits, finding circuits that optimize their use is crucial for this computing paradigm. Optimizing the qubits needed to implement a quantum circuit is not trivial, as these circuits have important restrictions such as the impossibility of copying values or the requirement that the computation done in them must always be reversible. This paper presents a framework for optimizing circuits for quantum computing. The framework is able to obtain, given a quantum circuit, an equivalent one that is more efficient in terms of number of qubits. In particular, the framework has applicability in quantum circuits dedicated to arithmetic operations such as addition or multiplication. As a representative case study, it is applied to a reversible comparator circuit, obtaining a design that reduces the number of qubits and controlled gates compared to other reversible comparators reported in the recent literature. As part of the work, a public repository is included with the necessary code to simplify any other circuit.