Extending the Graph Formalism to Higher-Order Gates

• URL: http://arxiv.org/abs/2108.02686v1
• Date: Thu, 5 Aug 2021 15:39:31 GMT
• Title: Extending the Graph Formalism to Higher-Order Gates
• Authors: Andrey Boris Khesin and Kevin Ren
• Abstract summary: We show how a $mathcalC_3$ gate acting on a stabilizer state splits it into two stabilizer states. We discuss applications of our algorithm to circuit identities and finding low stabilizer rank representations of magic states.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present an algorithm for efficiently simulating a quantum circuit in the graph formalism. In the graph formalism, we represent states as a linear combination of graphs with Clifford operations on their vertices. We show how a $\mathcal{C}_3$ gate such as the Toffoli gate or $\frac\pi8$ gate acting on a stabilizer state splits it into two stabilizer states. We also describe conditions for merging two stabilizer states into one. We discuss applications of our algorithm to circuit identities and finding low stabilizer rank representations of magic states.

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