Braiding operators are universal quantum gates
By Louis H. Kauffman, Samuel J. Lomonaco Jr.. 2004
286 citations recorded by the source corpus.
This paper explores the role of unitary braiding operators in quantum computing. We show that a single specific solution R (the Bell basis change matrix) of the Yang–Baxter equation is a universal gate for quantum computing, in the presence of local unitary transformations. We show that this same R generates a new non-trivial invariant of braids, knots and links. Other solutions of the Yang–Baxter equation are also shown to be universal for quantum computation. The paper discusses these results in the context of comparing quantum and topological points of view. In particular, we discuss quantum computation of link invariants, the relationship between quantum entanglement and topological entanglement, and the structure of braiding in a topological quantum field theory.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/736fcaa61b50be1f8e8835d7482489f23d1e28f8
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In Artificial Intelligence
In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Extraspecial 2-groups and images of braid group representations (2005, methodology): “The importance of this particular braid operator R was pointed out in the work of Kauffman and Lomonaco [KL], and the connection of R with quantum computing was explored there which is another reason for our interest.”
- Geometric (2019, background): “Crucially, stimuli sharing the same MIC orientation (e.g., right-titled, red) were interspersed among those with the opposing orientation (i.e., left-tilted, blue), indicating that the classification of MIC orientations presents a linearly inseparable problem within this stimulus space.”