Optimization methods boost fidelity in quantum factorization up to 8 bits

Alan C. Santos has developed a new approach to quantum factorization, achieving results for integers up to 8 bits. This work introduces a digitized adiabatic algorithm that encodes solutions within the kernel subspace of the problem Hamiltonian, a departure from standard methods proposed by Peng et al. The resulting Quadratic Unconstrained Binary Optimization (QUBO) formulation demonstrates a substantial improvement over previous Polynomial Unconstrained Binary Optimization (PUBO) methods, reducing circuit complexity and increasing the fidelity of identifying the correct solution. This advance uses the flexibility of digitized quantum computers to lower the computational costs of factorization. The implementation of a new Quadratic Unconstrained Binary Optimization (QUBO) formulation has enabled the factorization of integers with improved efficiency, a benchmark demonstrating the practical scope of this digitized adiabatic quantum factorization method. The shift in encoding strategy directly addresses limitations in circuit complexity and solution fidelity, key hurdles in scaling quantum factorization algorithms. This new method harnesses the capabilities of digitized quantum computers to decompose analog…