How can we reliably test whether a quantum computer has achieved an advantage over existing classical computers?  A promising approach is to base these tests ("proofs of quantumness") on cryptographic hardness assumptions.  Such assumptions are the foundation for encryption and authentication protocols, and as such they are well-studied.  Brakerski et al. (arXiv:1804.00640) introduced an interactive proof quantumness based on a standard lattice-based assumption (learning with errors).  What would it take to make cryptographic proofs of quantumness realizable on near-term devices?  I will explore this question and exhibit some of the mathematics involved in this topic, with a focus on the paper "Depth-efficient proofs of quantumness" by Z. Liu and A. Gheorghiu (arXiv:2107.02163).

This is a Quantum Information Math RIT Seminar which is part of the larger MathQuantum RTG program at UMD.

https://mathquantum.umd.edu/rit/

(Please note that this talk starts at 4:05 pm).