Recent advances in holography and quantum gravity have shown that conformal field theories (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 $\mathrm{complexity}=\text{volume}$ (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.

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• Gauge-gravity dualities
• Quantum gravity
• Computational complexity