Classical Verification of Quantum Computations

Explore a comprehensive lecture on the classical verification of quantum computations delivered by Urmila Mahadev from UC Berkeley. Delve into the challenges of quantum computation, comparing classical and quantum computers, and examine verification methods through interactive proofs. Learn about relaxations and verification using post-quantum cryptography, focusing on core primitives and superposition creation. Understand the verification outline, including Hadamard and standard basis measurements, and the measurement protocol definition and soundness. Investigate the quantum analogue of NP and verification with a quantum verifier. Study the measurement protocol construction, testing, and delegation of Hadamard and standard basis measurements. Gain insights into soundness intuition, hardcore bit properties, and the process of proving soundness in the measurement protocol.

Intro
Classical versus Quantum Computers
Verification through Interactive Proofs
Relaxations
Verification with Post Quantum Cryptography
Core Primitive
How to Create a Superposition Over a Claw
Verification Outline
Hadamard and Standard Basis Measurements
Measurement Protocol Definition
Measurement Protocol Soundness
Using the Measurement Protocol for Verification
Quantum Analogue of NP
Verification with a Quantum Verifier
Measurement Protocol Construction
Measurement Protocol Testing
Delegating Hadamard Basis Measurements
Measurement Protocol So Far
Delegating Standard Basis Measurements
Soundness Intuition: Example of Cheating Prover
Hardcore Bit Properties
How to Prove Soundness: Measurement Protocol
Conclusion