### 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.

Original language | English (US) |
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Article number | 10391 |

Pages (from-to) | 150-156 |

Number of pages | 7 |

Journal | Theoretical Computer Science |

Volume | 598 |

DOIs | |

State | Published - Sep 20 2015 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Morton, J., & Turner, J. (2015). Computing the Tutte polynomial of lattice path matroids using determinantal circuits.

*Theoretical Computer Science*,*598*, 150-156. [10391]. https://doi.org/10.1016/j.tcs.2015.07.042