Simulating quantum computations with Tutte polynomials

Ryan L. Mann*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

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We establish a classical heuristic algorithm for exactly computing quantum probability amplitudes. Our algorithm is based on mapping output probability amplitudes of quantum circuits to evaluations of the Tutte polynomial of graphic matroids. The algorithm evaluates the Tutte polynomial recursively using the deletion–contraction property while attempting to exploit structural properties of the matroid. We consider several variations of our algorithm and present experimental results comparing their performance on two classes of random quantum circuits. Further, we obtain an explicit form for Clifford circuit amplitudes in terms of matroid invariants and an alternative efficient classical algorithm for computing the output probability amplitudes of Clifford circuits.
Original languageEnglish
Article number141 (2021)
Number of pages5
Journalnpj Quantum Information
Publication statusPublished - 24 Sep 2021

Bibliographical note

13 pages, 0 figures, published version


  • quant-ph
  • cs.CC
  • cs.DS
  • math.CO


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