EQB: Synthesizing Permutative Quantum Gates and Circuits Using Rotation-Based Group Decomposition

TL;DR

This paper introduces a method for synthesizing permutative quantum gates and circuits using rotation-based group decomposition, optimizing for quantum layout constraints and circuit simplicity.

Contribution

It extends group theory-based decomposition methods to design binary quantum cascades with local transformations, improving circuit structure for quantum hardware.

Findings

Effective synthesis of quantum gates using rotation-based group decomposition

Circuit designs avoid complex connectivity, suitable for quantum hardware

Simplification of quantum cascades through local transformations

Abstract

The decomposition from the group theory-based methods of Sasao and Saraivanov is extended to design binary quantum cascades, using the quantum rotational gates by the X-axis (CNOT and RX), Y-axis (RY), and Z-axis (controlled-Z) of the Bloch sphere. A class of local transformations is also presented to simplify the final canonical cascade circuits. Our proposed methodology is well suited for quantum layouts, as each single-qubit gate has one target qubit and each double-qubit gate has one control qubit and one target qubit, thereby never creating a graph of triangular connectivity.