Tootfinder

A graphical diagnostic of topological order using ZX calculus
Sergi Mas-Mendoza, Richard D. P. East, Michele Filippone, Adolfo G. Grushin
https://arxiv.org/abs/2509.12355 https:…

A graphical diagnostic of topological order using ZX calculus
Establishing a universal diagnostic of topological order remains an open theoretical challenge. In particular, diagnosing long-range entanglement through the entropic area law suffers from spurious contributions, failing to unambiguously identify topological order. Here we devise a protocol based on the ZX calculus, a graphical tensor network, to determine the topological order of a state circumventing entropy calculations. The protocol takes as input real-space bipartitions of a state and retu…

Anchored Planar Algebras and 3-Categorical Graphical Calculus
Brett Hungar
https://arxiv.org/abs/2509.00995 https://arxiv.org/pdf/2509.00995

Anchored Planar Algebras and 3-Categorical Graphical Calculus
Anchored planar algebras, a generalized notion of Vaughan Jones' planar algebras, have recently seen use in higher category theory, functional analysis, and TQFT applications. These algebras are equipped with a natural 3-dimensional graphical calculus. We compare this graphical calculus with the 3-dimensional graphical calculus associated to tricategories, and we show that anchored planar algebras can be thought of as living in a particular tricategory. This allows for more general techniques t…

Tilt Stability for Nonlinear Programs under Relaxed Constant Rank Constraint Qualification
Nguyen Huy Chieu, Nguyen Thi Quynh Trang, Nguyen Thi Hai Yen
https://arxiv.org/abs/2508.06927

Tilt Stability for Nonlinear Programs under Relaxed Constant Rank Constraint Qualification
This paper investigates the tilt stability of local minimizers for nonlinear programs under the relaxed constant rank constraint qualification in finite dimensions. By employing a neighborhood primal-dual approach and extending calculus rules for subgradient graphical derivative, we obtain some pointbased characterizations of tilt-stable local minimizers along with an explicit formula for calculating the exact bound of tilt stability. These results extend the corresponding ones of H. Gfrerer an…

String Diagrams for Defect-Based Surface Code Computing
Mateusz Kupper (Department of Informatics, University of Sussex), Dominic Horsman (Department of Computer Science, University of Oxford), Chris Heunen (School of Informatics, University of Edinburgh), Niel de Beaudrap (Department of Informatics, University of Sussex)
https://arxiv.org…

String Diagrams for Defect-Based Surface Code Computing
Surface codes are a popular choice for implementing fault-tolerant quantum computing. Two-qubit gates may be realised in these codes using only nearest-neighbour interactions, either by lattice surgery or by braiding defects around each other. The effect of lattice surgery operations may be simply described using the ZX-calculus: a graphical language that has proven effective for program design and optimisation. In this work, we formalise a similar description via the ZX-calculus of defect brai…

Crosslisted article(s) found for math.QA. https://arxiv.org/list/math.QA/new
[1/1]:
- Anchored Planar Algebras and 3-Categorical Graphical Calculus
Brett Hungar

$\sigma$-Maximal Ancestral Graphs
Binghua Yao, Joris M. Mooij
https://arxiv.org/abs/2507.00093 https://arxiv.org/pdf/2507.00093

$σ$-Maximal Ancestral Graphs
Maximal Ancestral Graphs (MAGs) provide an abstract representation of Directed Acyclic Graphs (DAGs) with latent (selection) variables. These graphical objects encode information about ancestral relations and d-separations of the DAGs they represent. This abstract representation has been used amongst others to prove the soundness and completeness of the FCI algorithm for causal discovery, and to derive a do-calculus for its output. One significant inherent limitation of MAGs is that they rule o…