Simple magic state calculations using `Improved Simulation of Stabilizer Circuits'

TL;DR

This paper applies analytical techniques to simplify the calculation of magic states in quantum circuits involving T gates, focusing on their use in gate teleportation and surface code injection.

Contribution

It introduces a simplified analytical approach for calculating magic states in stabilizer circuits with T gates, enhancing understanding of their role in quantum error correction.

Findings

Analytical methods for T gate magic state calculations

Application to gate teleportation protocols

Insights into magic state injection in surface codes

Abstract

We employed the techniques from [Phys. Rev. A \textbf{70}, 052328 (2004)/arXiv:0406196] to analytically study two set of quantum circuits containing one $T$ gate/magic $|T\rangle = \frac{|0\rangle+\sqrt{i}|1\rangle}{\sqrt{2}}$ state. These include the $T$ state via gate teleportation and magic state injection on the rotated surface code.