Unitary Entanglement Construction in Hierarchical Networks

TL;DR

This paper explores how hierarchical graph structures can optimize the creation of large-scale entangled states in modular quantum computer architectures, emphasizing efficiency and practical circuit placement.

Contribution

It introduces the hierarchical product framework for modular graph construction and demonstrates its advantages for quantum information processing.

Findings

Hierarchies have small diameter and edge weight, beneficial for quantum networks.

Large entangled states can be generated efficiently on hierarchy graphs.

A scheme for circuit placement on hierarchical quantum systems is proposed.

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.