26 citations · 54 across the 5 of their papers we have counts for
7 papers
A Complete and Natural Rule Set for Multi-Qudit Clifford Circuits in All Odd Prime Dimensions
Xiaoning Bian, Sarah Meng Li, Neil J. Ross +2
We present a complete set of rewrite rules for multi-qudit Clifford circuits in all odd prime dimensions. Completeness means that any two Clifford circuits representing the sa…
Generators and Relations for 3-Qubit Clifford+CS Operators
Xiaoning Bian, Peter Selinger
We give a presentation by generators and relations of the group of 3-qubit Clifford+CS operators. The proof roughly consists of two parts: (1) applying the Reidemeister-Schreier th…
Generators and Relations for 2-Qubit Clifford+T Operators
Xiaoning Bian, Peter Selinger
We give a presentation by generators and relations of the group of Clifford+T operators on two qubits. The proof relies on an application of the Reidemeister-Schreier theorem to an…
Generators and Relations for Un(Z[1/2,i])
Xiaoning Bian, Peter Selinger
Consider the universal gate set for quantum computing consisting of the gates X, CX, CCX, omega^dagger H, and S. All of these gates have matrix entries in the ring Z[1/2,i], the sm…
Fast and effective techniques for T-count reduction via spider nest identities
Niel de Beaudrap, Xiaoning Bian, Quanlong Wang
In fault-tolerant quantum computing systems, realising (approximately) universal quantum computation is usually described in terms of realising Clifford+T operations, which is to s…
Techniques to Reduce -Parity-Phase Circuits, Motivated by the ZX Calculus
Niel de Beaudrap, Xiaoning Bian, Quanlong Wang
To approximate arbitrary unitary transformations on one or more qubits, one must perform transformations which are outside of the Clifford group. The gate most commonly considered…
Qutrit Dichromatic Calculus and Its Universality
Quanlong Wang, Xiaoning Bian
We introduce a dichromatic calculus (RG) for qutrit systems. We show that the decomposition of the qutrit Hadamard gate is non-unique and not derivable from the dichromatic calculu…