24.3 20k-spin Ising chip for combinational optimization problem with CMOS annealing

In the near future, the performance growth of Neumann-architecture computers will slow down due to the end of semiconductor scaling. Presently a new computing paradigm, so-called natural computing, which maps problems to physical models and solves the problem by its own convergence property, is expected. The analog computer using superconductivity from D-Wave [1] is one of those computers. A neuron chip [2] is also one of them. We proposed a CMOS-type Ising computer [3]. The Ising computer maps problems to an Ising model, a model to express the behavior of magnetic spins (the upper left diagram in Fig. 24.3.1), and solves the problems by ground-state search operations. The energy of the system is expressed by the formula in the diagram. Computing flows are expressed in the lower flow chart in Fig. 24.3.1. In the conventional Neumann architecture, the problem is sequentially and repeatedly calculated, and therefore, the number of computing steps drastically increases as the problem size grows. In the Ising computer, in the first step, the problem is mapped to the Ising model. In the next steps, an annealing operation, the ground-state search by interactions between spins, are activated and the state transitions to the ground state where the energy of the system is minimized. The interacting operation between spins is decided by the interaction coefficients, which are set to each connection. Here, the configuration of the interaction coefficients is decided by the problem, and therefore, the interaction coefficients are equivalent to the programming in the conventional computing paradigm. The ground state corresponds to the solution of the original problem, and the solution is acquired by observing the ground state. The interactions for the annealing are performed in parallel, and the necessary steps for the annealing are smaller than that used by a sequential computing, Neumann architecture. As the table in Fig. 24.3.1, our Ising computer uses CMOS circuits to expre- s the Ising model, and acquires the scalability and operation at room temperature.