Classical Commitment to Quantum States

Explore a comprehensive lecture on quantum computing verification and cryptography delivered by Urmila Mahadev from Microsoft Research at the Quantum Wave in Computing Boot Camp. Delve into the concept of classical commitment to quantum states and its implications for verifying quantum computations. Learn about testing quantum computers, interactive proofs, and post-quantum cryptography. Examine the role of trapdoor claw-free functions in quantum computing and verification, including their construction from Learning With Errors (LWE). Discover how to create superpositions, test for quantumness, and implement classical commitment protocols for quantum states. Investigate the process of delegating Hadamard basis measurements and enforcing structure with cryptography. Gain insights into the Pauli twirl in interactive proofs and its computational counterpart. This 56-minute talk provides a deep dive into cutting-edge research at the intersection of quantum computing and cryptography.

Intro
Testing Quantum Computers
Verification through Interactive Proofs
Verification with Post Quantum Cryptography
Talk Outline
Standard Basis Measurements
How to create a superposition over a claw
Test for Quantumness
Trapdoor Claw-free Functions in Quantum Computing
Trapdoor Claw-free Functions in Verification
TCF Construction from LWE
Classical Commitment to a Quantum State
Linking the Commitment Protocol to Verifiability
Verifying Quantum Computations
How to Commit using a TCF
Classical Commitment to Quantum States
Delegating Hadamard Basis Measurements
Commitment Protocol So Far
Enforcing Structure with Cryptography
The Pauli Twirl in Interactive Proofs
The Computational Pauli Twirl
Conclusion