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We investigate prime factorization from two perspectives: quantum annealing and computational algebraic geometry, specifically Grobner bases. We present a novel scalable algorithm which combines the two approaches and leads to the factorization of all bi-primes up to just over $200 , 000$, the largest number factored to date using a quantum processor.
We have developed a framework to convert an arbitrary integer factorization problem to an executable Ising model by first writing it as an optimization function and then transforming the k-bit coupling ($kgeq 3$) terms to quadratic terms using ancill
The road to computing on quantum devices has been accelerated by the promises that come from using Shors algorithm to reduce the complexity of prime factorization. However, this promise hast not yet been realized due to noisy qubits and lack of robus
We propose a prime factorizer operated in a framework of quantum annealing (QA). The idea is inverse operation of a multiplier implemented with QA-based Boolean logic circuits. We designed the QA machine on an application-specific-annealing-computing
In this paper we consider the use of certain classical analogues to quantum tunneling behavior to improve the performance of simulated annealing on a discrete spin system of the general Ising form. Specifically, we consider the use of multiple simult
Gaussian boson sampling exploits squeezed states to provide a highly efficient way to demonstrate quantum computational advantage. We perform experiments with 50 input single-mode squeezed states with high indistinguishability and squeezing parameter