Three Lectures on Complexity and Black Holes

TL;DR

This paper presents three lectures exploring quantum complexity, its relation to black hole interiors, and the thermodynamics of complexity, highlighting its significance in understanding spacetime and computational resources.

Contribution

It offers a comprehensive overview of quantum complexity concepts, their connection to black hole physics, and introduces the idea of uncomplexity as a computational resource.

Findings

Complexity relates to black hole interiors.

Non-increasing complexity periods linked to firewalls.

Uncomplexity as a resource for computation and spacetime understanding.

Abstract

Given at PiTP 2018 summer program entitled "From Qubits to Spacetime." The first lecture describes the meaning of quantum complexity, the analogy between entropy and complexity, and the second law of complexity. Lecture two reviews the connection between the second law of complexity and the interior of black holes. I discuss how firewalls are related to periods of non-increasing complexity which typically only occur after an exponentially long time. The final lecture is about the thermodynamics of complexity, and "uncomplexity" as a resource for doing computational work. I explain the remarkable power of "one clean qubit," in both computational terms and in space-time terms. The lectures can also be found online at \url{https://static.ias.edu/pitp/2018/node/1796.html} .