Figure 3

Demonstration of probabilistic annealing. (a), Conceptual diagram of state transitions during annealing processes. In general, sequential updating makes it difficult for the system to escape from a local minimum. Quantum annealer employs the quantum annealing method to tunnel the energy barriers, targeting to reach the minimum energy state during the annealing process. However, sampling operation by the readout circuit is required to analyze the system energy of the final state. The probabilistic annealing of the current work was designed to accelerate the system convergence to a minimum with parallel updating and dynamic SSPB control. Upon completion of 8 sampling operations (in which the number 8 is constant for every factorization operation in this work), the system restarts a searching iteration from a higher energy state with high probability, until achieving the solution to the problem. (b), High-level concept diagram of the probabilistic annealing process. The number of fixed p-bits and random p-bits are not always equivalent as shown in the figure, since the p-bits change stochastically by their current energy state. c, Flowchart and operating sequence of the factorization machine. This machine is designed to employ a decision block (X and Y modulo operators) for determining the completion of factorization when N mod X or N mod Y becomes 0. The operation of the candidate sieve is conducted after the p-bit update (omitted in the flowchart for simplicity).