Homotopy Type Theory and Computing — Classical and Quantum

Homotopy Type Theory and Computing – Classical and Quantum ... The aim of this conference is to discuss Homotopy Type Theory Theory (HoTT) as a ...

(PDF) Integrating Homotopy Type Theory with Quantum Computing

The integration of Homotopy Type Theory (HoTT) with quantum computing marks a significant milestone in the evolution of computational ...

Schreiber Topological Quantum Gates in Homotopy Type Theory

Abstract. Despite the plausible necessity of topological protection for realizing scalable quantum computers, the conceptual underpinnings ...

Quantum Homotopy Computer | Bartosz Milewski's Programming Cafe

Their choice for the foundation of mathematics was the theory of homotopy. Homotopy is about paths — continuous maps from real numbers between 0 ...

Towards Quantum Programming via Linear Homotopy Types in ...

Towards Quantum Programming via Linear Homotopy Types. talk at. Homotopy Type Theory and Computing – Classical and Quantum,. CQTS @ New York ...

Topological Quantum Gates in Homotopy Type Theory - YouTube

Talk at Applied Category Theory 2023 In this talk, we will propose a remarkably simple formalization of topological quantum gates in ...

Center for Quantum and Topological Systems - NYU Abu Dhabi

It is these topological stabilization mechanisms that make a practically useful Quantum Computer a realistic possibility. ... M-theory and Mathematics: Classical ...

[1904.04371] A HoTT Quantum Equational Theory (Extended Version)

The embedding takes advantage of features of homotopy type theory to encode unitary transformations as higher inductive paths, simplifying the ...

Anders Mörtberg - Talks

Talks. Computational Proofs in Synthetic Homotopy Theory - invited talk at Homotopy Type Theory and Computing - Classical and Quantum 2024.

Homotopy Type Theory in Quantum Mechanics: A New Framework ...

The integration of Homotopy Type Theory (HoTT) with quantum mechanics proposes a revolutionary approach to understanding and interpreting ...

[2303.02382] Topological Quantum Gates in Homotopy Type Theory

Abstract:Despite the evident necessity of topological protection for realizing scalable quantum computers, the conceptual underpinnings of ...

Homotopy Type Theory - a summary of what I've learned : r/math

This is all that Homotopy Type Theory is about: it makes types behave less like just collections of things and more like structures determined ...

Examples of the benefits of Homotopy Type Theory for computer ...

A place where the HoTT approach really helps computer formalization, is with higher types. The Blakers–Massey theorem in homotopy theory is ...

Posters - QUACC (2023)

To solve this problem we present Linear Homotopy Type Theory (LHoTT) as a programming and certification language for quantum computers with classical control ...

Seminar - Homotopy Type Theory at CMU - Department of Philosophy

Gödel as in _Gödel, Escher, Bach_) share the same topological structure as the quantum paradoxes, by reformatting the topological model of contextuality into a ...

What is Homotopy Type Theory Good For? | The n-Category Café

The same symbolic logical expressions are interpreted by homotopy type theory in a way that makes them correct for higher gauge theory.

Effective Quantum Certification via Linear Homotopy Types - YouTube

... quantum enhancement LHoTT of classical HoTT, now with semantics in parameterized stable homotopy theory. This linear homotopy type theory ...

Homotopy Type Theory Electronic Seminar Talks

In this expository talk we will outline the relationship between HoTT and classical homotopy theory by first using the simplicial set semantics and then ...

3 Homotopy Type Theory: A Synthetic Approach to Higher Equalities

Homotopy type theory and univalent foundations (HoTT/UF) is a new foundation of mathematics, based not on set theory but on “infinity-groupoids”, ...

What is Homotopy Type Theory, and what implications does it hold?

Homotopy theory is an advanced branch of topology which studies a weak notion of equivalence between spaces called homotopy equivalence.