75 citations · 544 across the 41 of their papers we have counts for
43 papers
Algebraic Priors for Approximately Equivariant Networks
Riccardo Ali, Pietro Liò, Jamie Vicary
Equivariant neural networks incorporate symmetries through group actions, embedding them as an inductive bias to improve performance. Existing methods learn an equivariant action o…
Posetal Diagrams for Logically-Structured Semistrict Higher Categories
Chiara Sarti, Jamie Vicary
We now have a wide range of proof assistants available for compositional reasoning in monoidal or higher categories which are free on some generating signature. However, none of th…
A layout algorithm for higher-dimensional string diagrams
Calin Tataru, Jamie Vicary
The algebraic zigzag construction has recently been introduced as a combinatorial foundation for a higher dimensional notion of string diagram. For use in a proof assistant, a layo…
From dual-unitary to biunitary: a 2-categorical model for exactly-solvable many-body quantum dynamics
Pieter W. Claeys, Austen Lamacraft, Jamie Vicary
Dual-unitary brickwork circuits are an exactly-solvable model for many-body chaotic quantum systems, based on 2-site gates which are unitary in both the time and space directions.…
A Syntax for Strictly Associative and Unital -Categories
Eric Finster, Alex Rice, Jamie Vicary
We present the first definition of strictly associative and unital -category. Our proposal takes the form of a type theory whose terms describe the operations of such struc…
Exact dynamics in dual-unitary quantum circuits with projective measurements
Pieter W. Claeys, Marius Henry, Jamie Vicary +1
Dual-unitary circuits have emerged as a minimal model for chaotic quantum many-body dynamics in which the dynamics of correlations and entanglement remains tractable. Simultaneousl…
Zigzag normalisation for associative -categories
Lukas Heidemann, David Reutter, Jamie Vicary
The theory of associative -categories has recently been proposed as a strictly associative and unital approach to higher category theory. As a foundation for a proof assistant,…
Traced Monoidal Categories as Algebraic Structures in Prof
Nick Hu, Jamie Vicary
We define a traced pseudomonoid as a pseudomonoid in a monoidal bicategory equipped with extra structure, giving a new characterisation of Cauchy complete traced monoidal categorie…
A Type Theory for Strictly Associative Infinity Categories
Eric Finster, Alex Rice, Jamie Vicary
Many definitions of weak and strict -categories have been proposed. In this paper we present a definition for -categories with strict associators, but which is othe…
Traced monoidal categories as algebraic structures in
Nick Hu, Jamie Vicary
We define a traced pseudomonoid as a pseudomonoid in a monoidal bicategory equipped with extra structure, giving a new characterisation of Cauchy complete traced monoidal categorie…
The Word Problem for Braided Monoidal Categories is Unknot-Hard
Antonin Delpeuch, Jamie Vicary
We show that the word problem for braided monoidal categories is at least as hard as the unknotting problem. As a corollary, so is the word problem for Gray categories. We conjectu…
Proceedings of the 3rd Annual International Applied Category Theory Conference 2020
David I. Spivak, Jamie Vicary
The third annual International Applied Category Theory Conference (ACT2020) was planned to take place at MIT in Cambridge, Massachusetts USA. However, the global COVID-19 pandemic…
A Type Theory for Strictly Unital -Categories
Eric Finster, David Reutter, Alex Rice +1
We use type-theoretic techniques to present an algebraic theory of -categories with strict units. Starting with a known type-theoretic presentation of fully weak -c…
High-level methods for homotopy construction in associative -categories
David Reutter, Jamie Vicary
A combinatorial theory of associative -categories has recently been proposed, with strictly associative and unital composition in all dimensions, and the weak structure arising…
Shaded tangles for the design and verification of quantum circuits
David J. Reutter, Jamie Vicary
We give a scheme for interpreting shaded tangles as quantum circuits, with the property that if two shaded tangles are ambient isotopic, their corresponding computational effects a…
Normalization for planar string diagrams and a quadratic equivalence algorithm
Antonin Delpeuch, Jamie Vicary
In the graphical calculus of planar string diagrams, equality is generated by exchange moves, which swap the heights of adjacent vertices. We show that left- and right-handed excha…
Orthogonality for Quantum Latin Isometry Squares
Benjamin Musto, Jamie Vicary
Goyeneche et al recently proposed a notion of orthogonality for quantum Latin squares, and showed that orthogonal quantum Latin squares yield quantum codes. We give a simplified ch…
Quantum teleportation with infinite reference frame uncertainty and without prior alignment
Dominic Verdon, Jamie Vicary
We present two new schemes for quantum teleportation between parties whose local reference frames are misaligned by the action of a compact Lie group G. These schemes require no pr…
Perfect tight quantum teleportation without a shared reference frame
Dominic Verdon, Jamie Vicary
We present a new scheme for teleporting a quantum state between two parties whose local reference frames are misaligned by the action of a finite symmetry group. Unlike other propo…
A classical groupoid model for quantum networks
David J. Reutter, Jamie Vicary
We give a mathematical analysis of a new type of classical computer network architecture, intended as a model of a new technology that has recently been proposed in industry. Our a…
Surface Proofs for Nonsymmetric Linear Logic (Extended Abstract)
Lawrence Dunn, Jamie Vicary
We show that a proof in multiplicative linear logic can be represented as a decorated surface, such that two proofs are logically equivalent just when their surfaces are geometrica…
Shaded Tangles for the Design and Verification of Quantum Programs (Extended Abstract)
David Reutter, Jamie Vicary
We give a scheme for interpreting shaded tangles as quantum programs, with the property that isotopic tangles yield equivalent programs. We analyze many known quantum programs in t…
Globular: an online proof assistant for higher-dimensional rewriting
Krzysztof Bar, Aleks Kissinger, Jamie Vicary
This article introduces Globular, an online proof assistant for the formalization and verification of proofs in higher-dimensional category theory. The tool produces graphical visu…
Data structures for quasistrict higher categories
Krzysztof Bar, Jamie Vicary
We present new data structures for quasistrict higher categories, in which associativity and unit laws hold strictly. Our approach has low axiomatic complexity compared to traditio…