Generation of Graph State

Introduction

Building large-scale quantum computers, essential to demonstrating quantum advantage, is a key challenge. Quantum Networks (QNs) can help address this challenge by enabling the construction of large, robust, and more capable quantum computing platforms by connecting smaller quantum computers. Moreover, unlike classical systems, QNs can enable fully secured long-distance communication. Thus, quantum networks lie at the heart of the success of future quantum information technologies. In quantum networks, multipartite entangled states distributed over the network help implement and support many quantum network applications for communications, sensing, and computing. Our work focuses on developing optimal techniques to generate and distribute multipartite entanglement states efficiently.

Prior works on generating general multipartite entanglement states have focused on the objective of minimizing the number of maximally entangled pairs (EPs) while ignoring the heterogeneity of the network nodes and links as well as the stochastic nature of underlying processes. In this work, we develop a hyper-graph-based linear programming framework that delivers optimal (under certain assumptions) generation schemes for general multipartite entanglement represented by graph states, under the network resources, decoherence, and fidelity constraints, while considering the stochasticity of the underlying processes.

Below is an example of Level-based fusion structure found by our algorithms, which is the "aggregation" of two fusion trees. The leaf node is a's generation rate of 36 units is "split" into 9 and 27 for the two different (red and blue) fusion operations. The root node represents the final/target graph state formed in two different ways for a total generation rate of 6 (3 from each fusion operation). We assume that a parent's generation rate is 1/3 of the rate of its children/operands (which are equal).

Papers

1. Fan Xiaojie, Caitao Zhan, Himanshu Gupta, and C. R. Ramakrishnan. "Optimized Distribution of Entanglement Graph States in Quantum Networks." arXiv preprint arXiv:2405.00222 (2024).