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Journal Article

Spacetime as a quantum circuit


Heller,  Michal P.
Gravity, Quantum Fields and Information, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Chandra, A. R., de Boer, J., Flory, M., Heller, M. P., Hörtner, S., & Rolph, A. (2021). Spacetime as a quantum circuit. Journal of High Energy Physics, 2021(04): 207. doi:10.1007/JHEP04(2021)207.

Cite as: http://hdl.handle.net/21.11116/0000-0007-CB88-B
We propose that finite cutoff regions of holographic spacetimes represent quantum circuits that map between boundary states at different times and Wilsonian cutoffs, and that the complexity of those quantum circuits is given by the gravitational action. The optimal circuit minimizes the gravitational action. This is a generalization of both the "complexity equals volume" conjecture to unoptimized circuits, and path integral optimization to finite cutoffs. Using tools from holographic $T\bar T$, we find that surfaces of constant scalar curvature play a special role in optimizing quantum circuits. We also find an interesting connection of our proposal to kinematic space, and discuss possible circuit representations and gate counting interpretations of the gravitational action.