The point of building quantum computers is that we expect them to be capable of things that classical computers aren't. But how can we prove that this is the case? In this episode we talk to David Gosset, a professor at the University of Waterloo, about his research on quantum advantage for shallow circuits. Hosts: Vincent Russo (vprusso.github.io), William Slofstra (elliptic.space), Henry Yuen (henryyuen.net) Main papers discussed in this episode: 1) Sergey Bravyi, David Gosset, and Robert König. Quantum advantage with shallow circuits. Science Vol. 362, Issue 6412, pp. 308-311 (2018). https://doi.org/10.1126/science.aar3106 2) Sergey Bravyi, David Gosset, Robert König and Marco Tomamichel. Quantum advantage with noisy shallow circuits. Nat. Phys. 16, pp. 1040–1045 (2020). https://doi.org/10.1038/s41567-020-0948-z 3) Adam Bene Watts, Robin Kothari, Luke Schaeffer, and Avishay Tal. Exponential separation between shallow quantum circuits and unbounded fan-in shallow classical circuits. STOC 2019, pp. 515-526. https://doi.org/10.1145/3313276.3316404 4) Daniel Grier and Luke Schaeffer. Interactive shallow Clifford circuits: quantum advantage against NC1 and beyond. STOC 2020, pp. 875-888. https://doi.org/10.1145/3357713.3384332 5) David Gosset, Daniel Grier, Alex Kerzner, and Luke Schaeffer. Fast simulation of planar Clifford circuits. https://arxiv.org/abs/2009.03218 William got the citation to (1) slightly wrong in the episode: it appeared as an invited short talk at STOC, not in the proceedings. Theme music is WLIIAW by Vincent Russo.

Can you ever be sure that someone has deleted your data? Anne Broadbent (University of Ottawa) tells us about a protocol for "quantum certified deletion", where a recipient of your information can prove to you that they've deleted your information. We learn about her paper with Rabib Islam introducing quantum certified deletion and some of its possible applications to privacy. Hosts: Vincent Russo (vprusso.github.io), William Slofstra (elliptic.space), Henry Yuen (henryyuen.net) Broadbent, Islam. Quantum encryption with certified deletion (https://arxiv.org/abs/1910.03551). Rabib Islam's QCRYPT 2020 talk on their paper: https://www.youtube.com/watch?v=nT8MQC6d358 Theme music is WLIIAW by Vincent Russo.

Quantum channel capacities are known to exhibit counterintuitive properties (superadditivity and superactivation), which make them hard to calculate. In this episode we talk to Debbie Leung (Institute for Quantum Computing, University of Waterloo) about one of her favourite open problems, the capacity of the qubit depolarizing channel, as well as her 2017 paper with Felix Leditzky and Graeme Smith that makes some progress on this problem. Hosts: Vincent Russo (vprusso.github.io), William Slofstra (elliptic.space), Henry Yuen (henryyuen.net) Debbie's paper: https://doi.org/10.1103/PhysRevLett.120.160503 Beyond IID in Information Theory: https://sites.google.com/view/beyondiid8/ Link to Debbie's course on quantum channel capacities: https://www.math.uwaterloo.ca/~wcleung/co781-f2020.html Music by Vincent Russo. Theme is WLIIAW.

The Mermin-Peres magic square is a simple game which is at the heart of many results in quantum cryptography and quantum complexity theory. In this episode, we trace the origin of the Mermin-Peres square back to two short papers by N. David Mermin and Asher Peres. Mermin's paper: https://doi.org/10.1103/PhysRevLett.65.3373 Peres' paper: https://doi.org/10.1016/0375-9601(90)90172-K Hosts: Vincent Russo (vprusso.github.io), William Slofstra (elliptic.space), Henry Yuen (henryyuen.net) Theme music is WLIIAW by Vincent Russo