**8. Results of simulation and verification of quantum circuits**

The proposed quantum circuits for squaring and multiplying floating-point numbers as part of the computational-basis representation, were systematically verified by gate-level simulation of the circuits for a wide range of cases with and without sub-normal numbers as well as cases with overflow results. The C++ quantum computer simulator detailed in previous work [4] was used for this purpose. To illustrate the process, the quantum algorithm used to square numbers with *NM* ¼ 3 and *NE* ¼ 3 is considered, with the following 19-qubit register (algorithm demonstrated accounts for sub-normal numbers as well as underflow/overflow protection, see Eq. (8) for reference):
