Sarah Meng Li (Dalhousie University) |
Neil J. Ross (Dalhousie University) |
Peter Selinger (Dalhousie University) |

We give a finite presentation by generators and relations for the group O_n(Z[1/2]) of n-dimensional orthogonal matrices with entries in Z[1/2]. We then obtain a similar presentation for the group of n-dimensional orthogonal matrices of the form M/sqrt(2)^k, where k is a nonnegative integer and M is an integer matrix. Both groups arise in the study of quantum circuits. In particular, when the dimension is a power of 2, the elements of the latter group are precisely the unitary matrices that can be represented by a quantum circuit over the universal gate set consisting of the Toffoli gate, the Hadamard gate, and the computational ancilla. |

Published: 18th September 2021.

ArXived at: http://dx.doi.org/10.4204/EPTCS.343.11 | bibtex | |

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