On Maximum Complexity in Holography

Abstract

In a quantum circuit, it is believed that complexity itself reaches a maximum of order exponential in the number of q-bits or equivalently exponential in entropy of the black hole. However, the current holographic proposals do not meet this criterion. The holographic proposals find the complexity of the very late times to be linear in the entropy, while in the quantum circuit, it is expected that complexity meets within a finite time its maximum value in an exponential in the entropy. These points are required to be altered in holographic proposals of complexity. This paper introduces a new holographic proposal that meets this criterion and consolidates the Lloyd bound.

arXiv comment13 pages, 5 figures. v2: 16 pages, 7 figures, section 4 improved, refs added. v3: 18 pages, 7 figures, improved version

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