Unitary Entanglement Construction in Hierarchical Networks

Abstract

The construction of large-scale quantum computers will require modular architectures that allow physical resources to be localized in easy-to-manage packages. In this work, we examine the impact of different graph structures on the preparation of entangled states. We begin by explaining a formal framework, the hierarchical product, in which modular graphs can be easily constructed. This framework naturally leads us to suggest a class of graphs, which we dub hierarchies. We argue that such graphs have favorable properties for quantum information processing, such as a small diameter and small total edge weight, and use the concept of Pareto efficiency to identify promising quantum graph architectures. We present numerical and analytical results on the speed at which large entangled states can be created on nearest-neighbor grids and hierarchy graphs. We also present a scheme for performing circuit placement--the translation from circuit diagrams to machine qubits--on quantum systems whose connectivity is described by hierarchies.

arXiv comment22 pages, 14 figures

References in corpus (23)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• Hyperbolic Geometry of Complex Networks
• Large Scale Modular Quantum Computer Architecture with Atomic Memory and Photonic Interconnects
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Experimental Comparison of Two Quantum Computing Architectures
• Sustaining the Internet with Hyperbolic Mapping
• ProjectQ: An Open Source Software Framework for Quantum Computing
• Deterministic Quantum State Transfer and Generation of Remote Entanglement using Microwave Photons
• Entanglement Percolation in Quantum Networks
• Fast Quantum Modular Exponentiation
• Optimal and Secure Measurement Protocols for Quantum Sensor Networks
• Quantum complex networks
• Percolation, renormalization, and quantum computing with non-deterministic gates
• Quantum Circuit Placement
• Entanglement percolation in quantum complex networks
• Quantum Circuits with Unbounded Fan-out
• Distribution of entanglement in large-scale quantum networks
• Fast State Transfer and Entanglement Renormalization Using Long-Range Interactions
• Arithmetic on a Distributed-Memory Quantum Multicomputer
• Limited path entanglement percolation in quantum complex networks
• Growth of graph states in quantum networks
• Optimal path for a quantum teleportation protocol in entangled networks

Cited by in corpus (6)

• A quantum network stack and protocols for reliable entanglement-based networks
• Time-Sliced Quantum Circuit Partitioning for Modular Architectures
• Circuit Transformations for Quantum Architectures
• Modeling Short-Range Microwave Networks to Scale Superconducting Quantum Computation
• Entanglement bounds on the performance of quantum computing architectures
• Implementing a Fast Unbounded Quantum Fanout Gate Using Power-Law Interactions