Relative Computational Power of Integrable and Nonintegrable Soliton Systems∗

The present document is devoted to the question of whether effective computation can be performed by the interaction of solitons [24, 34] in a bulk medium. The resulting computational system would fulfill the promise of Toffoli’s “programmable matter” [42] — offering computation that is very close to the underlying physics, and therefore potentially providing ultra-scale parallel processing. The most immediate physical realization of such computation may be provided by solitons in an optical fiber [41, 20, 15]. Other media are also possible, including Josephson junctions [35] and electrical transmission lines [31, 21]. We should emphasize that using optical solitons in this way is quite different from what is commonly termed “optical computing” [19, 20], which uses optical solitons to construct gates that replace electronic gates, but which remains within the “lithographic” paradigm of laying out gates and wires. The idea here uses a completely homogeneous medium for computation — the entire computation is determined by an input stream of particles. A general version of the structure proposed is shown in Fig. 1.