Quantum annealing distributed integer decomposition study of local field coefficient <italic>h</italic> and coupling coefficient <italic>J</italic> with stability Ising model

Deciphering a Million-Plus RSA Integer with Ultralow Local Field Coefficient h and Coupling Coefficient J of the Ising Model by D-Wave 2000Q

“…The current study analyze the influence of column width on integer factorization and find the optimal column width through traversal experiments. The local coefficient h and the coupling term coefficient J (hereinafter referred to as h and J) of the Ising model were improved by 75%-93% compared with those in the study of Wang et al [23] by adopting the optimal block division method. Notably, a 21-bit large number, 1 245 407, is factored on the real D-Wave machine, indicating that the proposed scheme and D-Wave work well.…”

“…This framework differs from traditional algorithms in that it transforms the integer factorization problem into an optimization problem and maps it to D-Wave 2000Q for quantum annealing to conduct prime factorization. Under the above framework, the distributed integer factorization algorithm proposed by Wang et al [23] uses distributed ideas to construct cost functions independently for each block of the multiplication table and perform independent annealing. Each block is independent.…”

“…However, as stated in the article, "unless we know in advance that the factors will differ at two bits, this reduction will not allow us to crack big RSA codes." Hegade et al [22] proposed a digitized AQC paradigm for factorization enhanced by shortcuts to adiabaticity techniques, which decreased the required circuit depth in quantum computers, and factored 235 with 4 qubits in an IBM quantum computer with up to 6 qubits. In March 2020, Wang et al [23] proposed a distributed quantum annealing integer factorization scheme.…”

“…Hegade et al [22] proposed a digitized AQC paradigm for factorization enhanced by shortcuts to adiabaticity techniques, which decreased the required circuit depth in quantum computers, and factored 235 with 4 qubits in an IBM quantum computer with up to 6 qubits. In March 2020, Wang et al [23] proposed a distributed quantum annealing integer factorization scheme. Compared to Ref.…”

“…Compared to Ref. [18], the range of the local field coefficient and the coupling term coefficient was further reduced, and a 20-bit integer 1 001 677 was factored [23,24] .…”