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Probabilistic computing has been introduced to operate functional networksusing a probabilistic bit (p-bit), generating 0 or 1 probabilistically from itselectrical input. In contrast to quantum computers, probabilistic computingenables the operation of adiabatic algorithms even at room temperature, and isexpected to broaden computational abilities in non-deterministic polynomialsearching and learning problems. However, previous developments ofprobabilistic machines have focused on emulating the operation of quantumcomputers similarly, implementing every p-bit with large weight-sum matrixmultiplication blocks or requiring tens of times more p-bits than semiprimebits. Furthermore, previous probabilistic machines adopted the graph model ofquantum computers for updating the hardware connections, which furtherincreased the number of sampling operations. Here we introduce a digitallyaccelerated prime factorization machine with a virtually connected Boltzmannmachine and probabilistic annealing method, designed to reduce the complexityand number of sampling operations to below those of previous probabilisticfactorization machines. In 10-bit to 64-bit factorizations were performed toassess the effectiveness of the machine, and the machine offers 1.2 X 10^8times improvement in the number of sampling operations compared with previousfactorization machines, with a 22-fold smaller hardware resource. This workshows that probabilistic machines can be implemented in a cost-effective mannerusing a field-programmable gate array, and hence we suggest that probabilisticcomputers can be employed for solving various large NP searching problems inthe near future.

Probabilistic Prime Factorization based on Virtually Connected Boltzmann Machine and Probabilistic Annealing