Computing by collapsing
Date:
Alt Title: Measurement-Based Quantum Computing & the stunning efficiency of graphical calculi
Introductory talk organized by the Stellenbosch University Cosmic Conversations (CC) society for an undergraduate audience.
Overview
This talk closely follows a paper by Kissinger and van de Wetering (2019), but expands a little on the presentation from a pedagogical point of view. In a nutshell, the paper (and hence my talk) introduces the concepts of measurement-based quantum computing (MBQC) and the ZX-calculus, applying the latter to prove the completeness of the former.
Sales pitch
The talk marries two distinct remarkably powerful and counter-intuitive ideas:
- The idea of MBQC: that mere (non-deterministic) quantum measurements suffice to perform any quantum computation (even deterministic ones).
- The idea of graphical calculi: that one can perform calculations and proofs by simply drawing and manipulating pictures.
Note that the graphical calculus approach generalizes to computations in all kinds of (suitable) monoidal categories. Such graphical calculi therefore encompass an incredibly versatile collection of related methods, with applications across a surprisingly wide range of fields!
In fact, I discuss a similar graphical calculus in the 3rd talk in my seminar series on quantum groups, though the subject matter there requires a slightly higher level of mathematical maturity.