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In this talk, I will introduce our recent work on the variations of complexity for two nearby target states. Based on Nielsen’s geometric approach, we find the variation only depends on the endpoint of the optimal trajectory, a result which we designate the first law of complexity. As an example, we examine the complexity=action conjecture when the AdS vacuum is perturbed by a scalar field excitation, which corresponds to a coherent state. Remarkably the gravitational contributions to the variation completely cancel, leaving the final variation to come entirely from the scalar field action on the boundary. From the simple result, we are led to speculate that the boundary of the WDW patch (null surface) may correspond to the ‘end of the quantum circuit”. Reference: “ The First Law of Complexity ”, arXiv: 1903.04511 |
