TL;DR
This paper addresses a conceptual puzzle in the AdS/CFT correspondence related to quantum circuit complexity and wormhole volume, proposing a resolution that preserves the Extended Church-Turing thesis by highlighting gravitational backreaction effects.
Contribution
It introduces a resolution to the complexity puzzle by emphasizing gravitational backreaction, and discusses a strengthened firewall puzzle from a computational complexity viewpoint.
Findings
No computational shortcut exists in measuring wormhole volume due to backreaction.
The proposed resolution preserves the quantum Extended Church-Turing thesis.
A new perspective on the firewall puzzle from a complexity standpoint.
Abstract
Recently a certain conceptual puzzle in the AdS/CFT correspondence, concerning the growth of quantum circuit complexity and the wormhole volume, has been identified by Bouland-Fefferman-Vazirani and Susskind. In this note, we propose a resolution of the puzzle and save the quantum Extended Church-Turing thesis by arguing that there is no computational shortcut in measuring the volume due to gravitational backreaction from bulk observers. A certain strengthening of the firewall puzzle from the computational complexity perspective, as well as its potential resolution, is also presented.
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