The research team proposes the use of ZX-calculus as a language for this intermediate stage of compilation. ZX-calculus is a 2D diagrammatic language developed in the late 2000s expressly to allow an intuitive representation of qubit processes. More importantly, it comes with a complete set of manipulation rules.
In their paper, the researchers harness ZX-calculus by discovering the translation relations between ZX-calculus and the components of the braided circuit. The researchers have shown that these two representations of logical gate circuits can be mapped to one another by identifying a new interpretation that had been hidden within ZX-calculus all along.
The ZX-calculus language can apply a set of transformation rules to alter the structure of the circuit without altering its underlying mathematical meaning and therefore ensuring its correctness. By altering that conceptual structure carefully, the volume of the circuit can be minimized, achieving considerable compression rates once this new structure is mapped to the actual braided quantum circuit. Applying this technique, the researchers report compression reductions of up to 77 percent, equivalent to a 40 percent reduction compared to the best previous efforts.