Lorentzian threads and nonlocal computation in holography

TL;DR

This paper investigates how holographic complexity, specifically the CV proposal reformulated with Lorentzian threads, can support nonlocal quantum computation in the dual CFT, revealing the need for multiple thread types to account for nonlocality.

Contribution

It introduces a modified Lorentzian threads framework with multiple flavors, enabling the modeling of nonlocal computations in holography, and proposes a tentative interpretation involving Lorentzian hyperthreads.

Findings

Standard Lorentzian threads cannot account for mutual complexity negativity.

Multiple thread flavors are necessary for nonlocal computation modeling.

The new framework suggests additional types of gates in the dual CFT.

Abstract

Recent advances in holography and quantum gravity have shown that CFTs with classical gravity duals can implement nonlocal quantum computation protocols that appear local from the bulk perspective. We examine the extent to which current prescriptions for holographic complexity support this claim, focusing on the Complexity=Volume (CV) proposal. The reformulation of CV in terms of Lorentzian threads suggests that bulk computations are performed with local gates. However, we find that the original formalism is insufficient when it comes to analyzing the complexity of subsystems and their inequalities. Specifically, standard Lorentzian threads cannot account for the negativity of `mutual complexity' and its higher-partite generalizations. To address this deficiency, we modify the Lorentzian threads program by introducing multiple flavors of threads. Our analysis reveals that an optimal solution for this new program implies the existence of additional types of gates that enable nonlocal computations in the dual CFT. We give a tentative interpretation of the multiflavor program in terms of Lorentzian `hyperthreads,' in analogy with the Riemannian case.