Name
Abstract | ||
|---|---|---|
We give a finite presentation by generators and relations for the group $\mathrm{O}_n(\mathbb{Z}[1/2])$ of $n$-dimensional orthogonal matrices with entries in $\mathbb{Z}[1/2]$. 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. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.4204/EPTCS.343.11 | International Workshop on Quantum Physics and Logic (QPL) |
DocType | Citations | PageRank |
Conference | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sarah Meng Li | 1 | 0 | 0.34 |
| Neil J. Ross | 2 | 0 | 1.35 |
| Peter Selinger | 3 | 434 | 36.65 |