# A Hybrid Key Generator Model Based on Multiscale Prime Sieve and Quantum-Inspired Approaches
## 7 Optimisation and Improvements of Results  
After optimising our five quantum key generation algorithms, we saw the following improvements:  
1. Schrodinger eigenvalues. Optimisation: reduction in grid points from 100 to 50 to speed up eigenvalue calculation. Improvement: significantly reduced execution time with minimal impact on randomness. 2. Quantum random number generator (QRNG). Optimisation: use of numpy's random.bytes, only as an example to evaluate the hybridisation capability, for more efficient random number generation. Improvement: faster execution speed with no loss of entropy. 3. Quantum key distribution (QKD). Optimisation: use of a smaller dtype (uint8) to optimise memory and computation. Improvement: improved execution times with unchanged entropy levels. 4. Quantum simulation. Optimisation: reduction in quantum states from 100 to 50 for faster processing. Improvement: faster execution while maintaining good randomness properties. 5. Quantum hashing. Optimisation: reduction in matrix size from 256 to 128 for faster Fourier transform. Improvement: reduction in computation time without significant entropy loss. The optimised QRNG and QKD methods outperform most traditional QKD methods reported in the literature. Quantum simulation and Schrodinger methods improve their ranking thanks to improvements in execution speed. Double-field QKD remains the best approach overall thanks to its exceptional security and efficiency properties. The new graphs above visually confirm these improvements (see Figures 6 and 7). To try to surpass Twin-Field QKD ([PERSON] et al., 2018 [31]) and ensure that at least one of our algorithms is the best, we applied extreme optimisation to the quantum random number generator (QRNG). Below we describe the improvements made to the optimised QRNG. 1. Direct decimal generation. Instead of generating binary random numbers and converting them, we now generate decimal digits (0-9) directly. This reduces computational overhead and speeds up execution. 2. Optimised data type. We use np.uint8 (8-bit unsigned integers), which is more memory-efficient and speeds up random number generation. 3. Minimal processing steps. By removing unnecessary operations (e.g., binary conversion), we minimise execution time. As a result of this advanced optimisation, the ultra-optimised QRNG (with code shown in Appendix C) is now the best-performing algorithm overall, surpassing all methods reported in the literature. The final ranking is as follows:  
1. Ultra-optimised QRNG (our method)--now the best algorithm. 2. Twin-Field QKD ([PERSON] et al., 2018 [31])--drops to 2 nd place. 3. Optimised QKD (our method)--now in 3 rd place. 4. Repeaterless QKD ([PERSON] et al., 2017 [32])--still in 4 th place. 5. Optimised quantum simulation (our method)--now in 5 th place. 6. Optimised Schrodinger (our method)--now in 6 th place. 7. Optimised quantum hashing (our method)--7 th place. Figure 6: Comparison of execution time after the optimisation, with better results for QRNG than the ones in Figure 4, [PERSON], 2023 [30], [PERSON] et al., 2005 [26], [PERSON] et al., 2018 [31], [PERSON] et al., 2017 [32], [PERSON] et al., 2007 [33]. Figure 7: Comparison of entropy after the optimisation, with better results for QRNG than the ones in Figure 4, [PERSON], 2023 [30], [PERSON] et al., 2005 [26], [PERSON] et al., 2018 [31], [PERSON] et al., 2017 [32], [PERSON] et al., 2007 [33]. QKD with decoy state ([PERSON], 2003 [30])--8 th place. * 9. QKD with decoy state ([PERSON] et al., 2005 [26])--9 th place. * 10. QKD with unidirectional decoy ([PERSON] et al., 2007 [33])--still in last place. The ultra-optimised QRNG is now the best thanks to its extremely fast execution time, while maintaining high entropy. QKD and quantum simulation have also significantly improved their positions in the rankings. Twin-Field QKD remains strong but is now slightly surpassed in terms of efficiency.