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Shaded tangles for the design and verification of quantum circuits.

ABSTRACT: 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.

SUBMITTER: Reutter DJ

PROVIDER: S-EPMC6501654 | biostudies-literature | 2019 Apr

REPOSITORIES: biostudies-literature

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Shaded tangles for the design and verification of quantum circuits.

Reutter David J DJ Vicary Jamie J

Proceedings. Mathematical, physical, and engineering sciences 20190403 2224

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 topologica ...[more]

PMID: 31105445

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