Unitary entanglement construction in hierarchical networks

Area of Science:

• Quantum Computing
• Graph Theory
• Quantum Information Science

Background:

• Modular architectures are essential for building large-scale quantum computers.
• Efficiently managing localized physical resources is a key challenge.
• Graph structures significantly influence quantum information processing capabilities.

Purpose of the Study:

• To investigate the impact of different graph structures on the preparation of entangled states.
• To introduce a formal framework (hierarchical product) for constructing modular graphs.
• To identify promising quantum graph architectures using Pareto efficiency.

Main Methods:

• Formalizing modular graph construction using the hierarchical product.
• Defining and analyzing a class of graphs termed 'hierarchies'.
• Comparing entanglement preparation speeds on nearest-neighbor grids and hierarchy graphs using numerical and analytical methods.
• Developing a circuit placement scheme for hierarchy-based quantum systems.

Main Results:

• Hierarchy graphs exhibit favorable properties for quantum information processing, including small diameter and total edge weight.
• Hierarchy graphs demonstrate efficient speed for creating large entangled states compared to nearest-neighbor grids.
• A practical scheme for circuit placement on hierarchy-connected quantum systems was presented.

Conclusions:

• Hierarchy graphs represent a promising architecture for scalable quantum computing.
• The proposed framework and identified graph structures facilitate efficient quantum state preparation and circuit mapping.
• This work provides a foundation for designing optimized modular quantum computer architectures.