Transpiling Quantum Circuits using the Pentagon Equation

Understand

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.