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Quantum Algorithms
Biunitary constructions in quantum information
arXiv
Authors: David J. Reutter, Jamie Vicary
Year
2016
Paper ID
43365
Status
Preprint
Abstract Read
~2 min
Abstract Words
82
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Abstract
We present an infinite number of construction schemes involving unitary error bases, Hadamard matrices, quantum Latin squares and controlled families, many of which have not previously been described. Our results rely on biunitary connections, algebraic objects which play a central role in the theory of planar algebras. They have an attractive graphical calculus which allows simple correctness proofs for the constructions we present. We apply these techniques to construct a unitary error basis that cannot be built using any previously known method.
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- It adds a 2016 reference point for readers tracking recent quantum research.
- We present an infinite number of construction schemes involving unitary error bases, Hadamard matrices, quantum Latin squares and controlled families, many of which have not...
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