Transpiling Quantum Circuits using the Pentagon Equation

TL;DR

This paper explores how the pentagon equation can be used to optimize quantum circuits by transpiling complex interactions into simpler, depth-reduced Heisenberg-type circuits, with specific solutions identified for certain non-local gates.

Contribution

It demonstrates that solutions to the pentagon equation enable circuit transpilation and depth reduction, introducing a novel approach for quantum circuit optimization.

Findings

Solutions to the pentagon equation can be found for certain non-local gates.

Transpiling reduces circuit depth while converting to Heisenberg interactions.

The approach applies to specific parameter regimes of the A gate.

Abstract

We consider the application of the pentagon equation in the context of quantum circuit compression. We show that if solutions to the pentagon equation are found, one can transpile a circuit involving non-Heisenberg-type interactions to a circuit involving only Heisenberg-type interactions while, in parallel, reducing the depth of a circuit. In this context, we consider a model of non-local two-qubit operations of Zhang \emph{et. al.} (the $A$ gate), and show that for certain parameters it is a solution of the pentagon equation.