- Type Theory married Homotopy Theory.
- Classical programming languages are cartesian closed categories.
- Quantum computers need a totally different type of programming language.
I go over all of this with theoretical physicist Urs Schreiber. He is Senior Research Scientist at the Mathematics Division of Science of New York University in Abu Dhabi. He applies tools from algebraic topology, homotopy theory and topos theory to understand quantum phenomena. His current research includes quantum computing programming languages and questions left unanswered by quantum field theory.
In this episode we go over:
- Why toposes are not scary. They are actually simple. Just unfamiliar
- How to extract information from (probe) a topos
- The history of toposes in physics
- The questions left unanswered by quantum field theory
- What toposes have to say about the collapse of the wave function
- Using toposes to find possible quantum computing materials
- The different type of logic needed for quantum computers
- The different type of programming language needed for quantum computers
- The influence of Hegel on his work
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