Shaded tangles for the design and verification of quantum circuits

David Reutter, Jamie Vicary

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
125 Downloads (Pure)


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 are identical. We analyse 11 known quantum procedures in this way—including entanglement manipulation, error correction and teleportation—and in each case present a fully topological formal verification, yielding generalized procedures in some cases. We also use our methods to identify two new procedures, for topological state transfer and quantum error correction. Our formalism yields in some cases significant new insight into how the procedures work, including a description of quantum entanglement arising from topological entanglement of strands, and a description of quantum error correction where errors are ‘trapped by bubbles’ and removed from the shaded tangle.
Original languageEnglish
Article number20180338
Number of pages30
JournalProceedings of the Royal Society A
Issue number2224
Early online date3 Apr 2019
Publication statusPublished - Apr 2019


  • 2-category
  • 2Hilb
  • Graphical calculus
  • Knot theory
  • Quantum computing
  • Verification

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)


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