Generators and Relations for Un(Z[1/2,i])

@article{Bian2021GeneratorsAR,
  title={Generators and Relations for Un(Z[1/2,i])},
  author={Xiaoning Bian and Peter Selinger},
  journal={Electronic Proceedings in Theoretical Computer Science},
  year={2021}
}
Consider the universal gate set for quantum computing consisting of the gates X , CX , CCX , ω†H, and S. All of these gates have matrix entries in the ring Z[ 2 , i], the smallest subring of the complex numbers containing 1 2 and i. Amy, Glaudell, and Ross proved the converse, i.e., any unitary matrix with entries in Z[ 2 , i] can be realized by a quantum circuit over the above gate set using at most one ancilla. In this paper, we give a finite presentation by generators and relations of Un(Z… 

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