Call me a qunatum pragmatist

I use algebra and diagrams to design efficient and reliable quantum circuits, with a focus on qudit quantum computing and fault-tolerant compilation.

2021: Generators and Relations for the Group of orthogonal dyadic operators

Joint work with Neil J. Ross and Peter Selinger.

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.

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