Adaptive Framework for Failure-Aware Protocols in Fusion-Based Graph-State Generation

TL;DR

This paper introduces an adaptive, graph-theoretic framework for optimizing the generation of photonic graph states in linear optics, significantly reducing fusion overhead by reusing leftover states and optimizing fusion sequences.

Contribution

It develops a novel adaptive protocol for fusion-based graph state generation that reuses leftover states and employs polynomial algorithms to optimize fusion orderings.

Findings

Reduces fusion overhead by several orders of magnitude.

Effective for fusion success probabilities between 50-75%.

Uses Markov process modeling to estimate hardware costs.

Abstract

We consider the generation of photonic graph states in a linear optics setting where sequential non-deterministic fusion measurements are used to build large graph states out of small linear clusters and develop a framework to optimize the building process using graph theoretic characterizations of fusion networks. We present graph state generation protocols for linear cluster resource states and Type-I/Type-II fusions which are adaptive to fusion failure, that is, they reuse leftover graph states in the remaining building process. To estimate hardware costs, we interpret our protocols as finite Markov processes. This viewpoint allows to cast the expected number of fusion measurements until success as a first passage problem. We then deploy a pipeline of polynomial algorithms to optimize arbitrary graph states, extract fusion networks and find beneficial orderings of fusions with the goal of lowering the corresponding mean first passage times. We evaluate our pipeline for different initial resource states and fusion mechanisms with varying success probabilities. Results show that our strategies can reduce the fusion overhead by several orders of magnitude when compared to simple repeat until success protocols, especially for realistic fusion success probabilities between 50-75 %.