Math and Stats - ATCAT seminar - "Generators and Relations for the Group On(Z[1/2])" (Joint work with Neil Julien Ross and Peter Selinger)

Speaker : Sarah Meng Li, Dalhousie University

Abstract: We give a finite presentation by generators and relations for the group On(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 (1/\sqrt{2})^k M, 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 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.


Lectures, Seminars


Location Meeting ID: 818 7275 6284 Passcode: ATCAT2020


Ellen Lynch