Optimization complexity and resource minimization of emitter-based photonic graph state generation protocols

• URL: http://arxiv.org/abs/2407.15777v1
• Date: Mon, 22 Jul 2024 16:29:52 GMT
• Title: Optimization complexity and resource minimization of emitter-based photonic graph state generation protocols
• Authors: Evangelia Takou, Edwin Barnes, Sophia E. Economou,
• Abstract summary: Photonic graph states are important for measurement- and fusion-based quantum computing, quantum networks, and sensing. We develop locally minimize the number of entangling gates, reducing them by up to 75$%$ compared to naive schemes for moderately sized random graphs. We find the optimal emission orderings and circuits to prepare unencoded and encoded repeater graph states of any size.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Photonic graph states are important for measurement- and fusion-based quantum computing, quantum networks, and sensing. They can in principle be generated deterministically by using emitters to create the requisite entanglement. Finding ways to minimize the number of entangling gates between emitters and understanding the overall optimization complexity of such protocols is crucial for practical implementations. Here, we address these issues using graph theory concepts. We develop optimizers that minimize the number of entangling gates, reducing them by up to 75$\%$ compared to naive schemes for moderately sized random graphs. While the complexity of optimizing emitter-emitter CNOT counts is likely NP-hard, we are able to develop heuristics based on strong connections between graph transformations and the optimization of stabilizer circuits. These patterns allow us to process large graphs and still achieve a reduction of up to $66\%$ in emitter CNOTs, without relying on subtle metrics such as edge density. We find the optimal emission orderings and circuits to prepare unencoded and encoded repeater graph states of any size, achieving global minimization of emitter and CNOT resources despite the average NP-hardness of both optimization problems. We further study the locally equivalent orbit of graphs. Although enumerating orbits is $\#$P complete for arbitrary graphs, we analytically calculate the size of the orbit of repeater graphs and find a procedure to generate the orbit for any repeater size. Finally, we inspect the entangling gate cost of preparing any graph from a given orbit and show that we can achieve the same optimal CNOT count across the orbit.

Related papers

• A Scalable and Robust Compilation Framework for Emitter-Photonic Graph State [1.3624495460189865]
  We study the GraphState-to-Circuit compilation problem in the context of the deterministic scheme. We propose a novel compilation framework that partitions the target graph state into subgraphs, compiles them individually, and subsequently combines and schedules the circuits to maximize emitter resource utilization.
  arXiv  Detail & Related papers  (2025-03-20T17:01:33Z)
• OMEGA: A Low-Latency GNN Serving System for Large Graphs [8.51634655687174]
  Graph Neural Networks (GNNs) have been widely adopted for their ability to compute expressive node representations in graph datasets. Existing approximation techniques in training can mitigate the overheads but, in serving, still lead to high latency and/or accuracy loss. We propose OMEGA, a system that enables low-latency GNN serving for large graphs with minimal accuracy loss.
  arXiv  Detail & Related papers  (2025-01-15T03:14:18Z)
• Scalable Graph Compressed Convolutions [68.85227170390864]
  We propose a differentiable method that applies permutations to calibrate input graphs for Euclidean convolution. Based on the graph calibration, we propose the Compressed Convolution Network (CoCN) for hierarchical graph representation learning.
  arXiv  Detail & Related papers  (2024-07-26T03:14:13Z)
• CoRe-GD: A Hierarchical Framework for Scalable Graph Visualization with GNNs [20.706469085872516]
  We introduce a scalable Graph Neural Network (GNN) based Graph Drawing framework with sub-quadratic that can learn to optimize stress. Inspired by classical stress optimization techniques and force-directed layout algorithms, we create a coarsening hierarchy for the input graph. To enhance information propagation within the network, we propose a novel positional rewiring technique.
  arXiv  Detail & Related papers  (2024-02-09T10:50:45Z)
• Resource-efficient and loss-aware photonic graph state preparation using an array of quantum emitters, and application to all-photonic quantum repeaters [0.8409980020848168]
  We propose an algorithm that can trade the number of emitters with the graph-state depth, while minimizing the number of emitter CNOTs. We find that our scheme achieves a far superior rate-vs.-distance performance than using the least number of emitters needed to generate the repeater graph state.
  arXiv  Detail & Related papers  (2024-02-01T16:29:07Z)
• Optimization of deterministic photonic graph state generation via local operations [3.2106353278518105]
  We introduce an optimization method for such protocols based on the local Clifford equivalency of states and the graph theoretical correlations of the generation cost parameters. We achieve a 50% reduction in use of the 2-qubit gates for generation of the arbitrary large repeater graph states and similar significant reductions in the total gate count for generation of random dense graphs.
  arXiv  Detail & Related papers  (2024-01-01T02:11:49Z)
• Graph Transformers for Large Graphs [57.19338459218758]
  This work advances representation learning on single large-scale graphs with a focus on identifying model characteristics and critical design constraints. A key innovation of this work lies in the creation of a fast neighborhood sampling technique coupled with a local attention mechanism. We report a 3x speedup and 16.8% performance gain on ogbn-products and snap-patents, while we also scale LargeGT on ogbn-100M with a 5.9% performance improvement.
  arXiv  Detail & Related papers  (2023-12-18T11:19:23Z)
• T-GAE: Transferable Graph Autoencoder for Network Alignment [79.89704126746204]
  T-GAE is a graph autoencoder framework that leverages transferability and stability of GNNs to achieve efficient network alignment without retraining. Our experiments demonstrate that T-GAE outperforms the state-of-the-art optimization method and the best GNN approach by up to 38.7% and 50.8%, respectively.
  arXiv  Detail & Related papers  (2023-10-05T02:58:29Z)
• NodeFormer: A Scalable Graph Structure Learning Transformer for Node Classification [70.51126383984555]
  We introduce a novel all-pair message passing scheme for efficiently propagating node signals between arbitrary nodes. The efficient computation is enabled by a kernerlized Gumbel-Softmax operator. Experiments demonstrate the promising efficacy of the method in various tasks including node classification on graphs.
  arXiv  Detail & Related papers  (2023-06-14T09:21:15Z)
• $\rm A^2Q$: Aggregation-Aware Quantization for Graph Neural Networks [18.772128348519566]
  We propose the Aggregation-Aware mixed-precision Quantization ($rm A2Q$) for Graph Neural Networks (GNNs) Our method can achieve up to 11.4% and 9.5% accuracy improvements on the node-level and graph-level tasks, respectively, and up to 2x speedup on a dedicated hardware accelerator.
  arXiv  Detail & Related papers  (2023-02-01T02:54:35Z)
• Optimal Propagation for Graph Neural Networks [51.08426265813481]
  We propose a bi-level optimization approach for learning the optimal graph structure. We also explore a low-rank approximation model for further reducing the time complexity.
  arXiv  Detail & Related papers  (2022-05-06T03:37:00Z)
• Generating Target Graph Couplings for QAOA from Native Quantum Hardware Couplings [3.2622301272834524]
  We present methods for constructing any target coupling graph using limited global controls in an Ising-like quantum spin system. Our approach is motivated by implementing the quantum approximate optimization algorithm (QAOA) on trapped ion quantum hardware. Noisy simulations of Max-Cut QAOA show that our implementation is less susceptible to noise than the standard gate-based compilation.
  arXiv  Detail & Related papers  (2020-11-16T18:43:09Z)
• Graph Ordering: Towards the Optimal by Learning [69.72656588714155]
  Graph representation learning has achieved a remarkable success in many graph-based applications, such as node classification, prediction, and community detection. However, for some kind of graph applications, such as graph compression and edge partition, it is very hard to reduce them to some graph representation learning tasks. In this paper, we propose to attack the graph ordering problem behind such applications by a novel learning approach.
  arXiv  Detail & Related papers  (2020-01-18T09:14:16Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.