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A ring resonator involves a scattering process where a part of the output isfed again into the input. The same formal structure is encountered in theproblem of time travel in a neighborhood of a closed timelike curve (CTC). Weknow how to describe quantum optics of ring resonators, and the resultingdescription agrees with experiment. We can apply the same formal strategy toany looped quantum evolution, in particular to the time travel. The argument isin its essence a topological one and thus does not refer to any concretegeometry. It is shown that the resulting paradigm automatically removes logicalinconsistencies associated with chronology protection, provided allinput-output relations are given by unitary maps. Examples of elementary loopsand a two-loop time machine illustrate the construction. In order to apply theformalism to quantum computation one has to describe multi-qubit systemsinteracting via CTC-based quantum gates. This is achieved by secondquantization of loops. An example of a multiparticle system, with oscillatorsinteracting via a time machine, is explicitly calculated. However, theresulting treatment of CTCs is not equivalent to the one proposed by Deutsch inhis classic paper.

Time travel without paradoxes: Ring resonator as a universal paradigm for looped quantum evolutions