Computing the Tutte Polynomial of Lattice Path Matroids Using Determinantal Circuits

Abstract

We give a quantum-inspired $O(n^4)$ algorithm computing the Tutte polynomial of a lattice path matroid, where $n$ is the size of the ground set of the matroid. Furthermore, this can be improved to $O(n^2)$ arithmetic operations if we evaluate the Tutte polynomial on a given input, fixing the values of the variables. The best existing algorithm, found in 2004, was $O(n^5)$, and the problem has only been known to be polynomial time since 2003. Conceptually, our algorithm embeds the computation in a determinant using a recently demonstrated equivalence of categories useful for counting problems such as those that appear in simulating quantum systems.

References in corpus (4)

• Novel schemes for measurement-based quantum computation
• Matchgates and classical simulation of quantum circuits
• Trading inverses for an irrep in the Solovay-Kitaev theorem
• Pfaffian Circuits

Cited by in corpus (4)

• Delta-matroids as subsystems of sequences of Higgs lifts
• Facial structures of lattice path matroid polytopes
• The Young matroid: A multiset extension of the Catalan matroid to arbitrary Young diagrams
• On lattice path matroid polytopes: integer points and Ehrhart polynomial