**12 pm, September 15, 2020**

**Invited Speaker: Andrew Glaudell, Booz Allen Hamilton & GMU Mathematical Sciences Department**

Topic: Optimal Two-Qubit Circuits for Universal Fault-Tolerant Quantum Computation

Location: Zoom

QSEC’s quantum computing subgroup will organize and host a seminar series throughout the upcoming semester. The series will be kicked off on Tuesday September 15 with Mathematics Adjunct faculty Dr. Andrew Glaudell giving a short presentation. These events are free and open to the public. For any questions, contact qsec@gmu.edu. Below is the abstract of Dr. Glaudell’s talk and meeting information:

**Abstract**

We study two-qubit circuits over the Clifford+CS gate set which consists of Clifford gates together with the controlled-phase gate CS=diag(1,1,1,i). The Clifford+CS gate set is universal for quantum computation and its elements can be implemented fault-tolerantly in most error-correcting schemes with magic state distillation. However, since non-Clifford gates are typically more expensive to perform in a fault-tolerant manner, it is desirable to construct circuits that use few CS gates. In the present paper, we introduce an algorithm to construct optimal circuits for two-qubit Clifford+CS operators. Our algorithm inputs a Clifford+CS operator U and efficiently produces a Clifford+CS circuit for U using the least possible number of CS gates. Because our algorithm is deterministic, the circuit it associates to a Clifford+CS operator can be viewed as a normal form for the operator. We give a formal description of these normal forms as walks over certain graphs and use this description to derive an asymptotic lower bound of 5log(1/epsilon)+O(1) on the number CS gates required to epsilon-approximate any 4×4 unitary matrix.

**Meeting Information**

Join Zoom Meeting ID: 913 3925 3115 Passcode: 570565

https://gmu.zoom.us/j/91339253115?pwd=RkNBMlY5Rnl1OFNYSGNMTVhBdzNKUT09

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