Scott Aaronson on Computational Complexity Theory and Quantum Computers

TL;DR

Scott Aaronson explains that quantum computers do not solve problems by trying all solutions at once; they use interference of amplitudes to amplify correct answers and cancel wrong ones. He describes a near‑term application (provably random bits using 50–70 qubit quantum computers), shadow tomography (gentle measurement of quantum states with connections to differential privacy), the Busy Beaver

Key insights

• Quantum computers gain speed not from “trying all solutions at once” but from choreographing interference where wrong‑answer amplitudes cancel and right‑answer amplitudes reinforce.
• Quantum error correction and fault tolerance changed the feasibility of scalable quantum computing from a physical impossibility to a “staggeringly hard engineering problem.”
• A 50–70 qubit quantum computer can produce cryptographically secure public random bits by sampling hard‑to‑simulate random circuits; classical verification of the samples under a cryptographic hardnes