The Parity Flow Formalism: Tracking Quantum Information Throughout Computation

Understand

We propose the Parity Flow formalism, a method for tracking the information flow in quantum circuits.

• This method adds labels to quantum circuit diagrams such that the action of Clifford gates can be understood as a recoding of quantum information.
• The action of non-Clifford gates in the encoded space can be directly deduced from those labels without backtracking.
• An application of flow tracking is to design resource-efficient quantum circuits by changing any present encoding via a simple set of rules.