The Parity Flow Formalism: Tracking Quantum Information Throughout Computation

TL;DR

The paper introduces the Parity Flow formalism, a novel method for tracking quantum information flow in circuits, enabling efficient circuit design and optimization through label-based analysis of Clifford and non-Clifford gates.

Contribution

It presents a new formalism that allows direct deduction of gate actions in encoded space and improves quantum circuit design using label-based flow tracking.

Findings

Enables understanding of Clifford gate actions as recoding of quantum information.

Allows deduction of non-Clifford gate effects without backtracking.

Facilitates resource-efficient circuit design and depth reduction.

Abstract

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. Finally, the Parity Flow formalism can be used in combination with stabilizer codes to further reduce quantum circuit depth and to reveal additional operations that can be implemented in parallel.