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Proceedings - International Symposium on Computer Architecture/Proceedings

Reinforcement Learning-Guided Graph State Generation in Photonic Quantum Computers

Yingheng Li, Yue Dai, Aditya Pawar, Rongchao Dong, Jun Yang, Youtao Zhang, Xulong Tang

Published Jun 20, 2025• 2 citations
Publisher

Abstract

The photonic quantum computer (PQC) is an emerging and promising quantum computing paradigm that has gained momentum in recent years.In PQC, computations are executed by performing measurements on photons in graph states (i.e., a collection of entangled photons).The graph state generation process is fulfilled by applying a sequence of quantum gates to quantum emitters, referred to as the "generation sequence".In a generation sequence, i) the time required to complete the generation sequence, ii) the number of quantum emitters used, and iii) the number of CZ gates performed between emitters greatly affect the fidelity of the generated graph state.In this paper, we propose RLGS (Reinforcement Learningguided Graph State generation), a novel compilation framework to identify optimal generation sequences that optimize the three fidelity metrics.Experimental results show that RLGS achieves an average reduction in generation time of 31.1%,49.6%, and 57.5% for small, medium, and large graph states compared to the baseline.Additionally, the reductions in the number of quantum emitters are 13.9%, 16.7%, and 17.5%, whereas the reductions in the number of CZ gates are 37.7%, 53.4%, and 57.8%, respectively.

DOI
10.1145/3695053.3731085

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The photonic quantum computer (PQC) is an emerging and promising quantum computing paradigm that has gained momentum in recent years.In PQC, computations are executed by performing measurements on photons in graph states (i.e., a collection of entangled photons).The graph state generation process is fulfilled by applying a sequence of quantum gates to quantum emitters, referred to as the "generation sequence".In a generation sequence, i) the time required to complete the generation sequence, ii) the number of quantum emitters used, and iii) the number of CZ gates performed between emitters greatly affect the fidelity of the generated graph state.In this paper, we propose RLGS (Reinforcement Learningguided Graph State generation), a novel compilation framework to identify optimal generation sequences that optimize the three fidelity metrics.Experimental results show that RLGS achieves an average reduction in generation time of 31.1%,49.6%, and 57.5% for small, medium, and large graph states compared to the baseline.Additionally, the reductions in the number of quantum emitters are 13.9%, 16.7%, and 17.5%, whereas the reductions in the number of CZ gates are 37.7%, 53.4%, and 57.8%, respectively.
Photonic quantum computer (PQC) is an emerging and promising quantum computing paradigm that has gained momentum in recent years. In PQC, which leverages the measurement-based quantum computing (MBQC) model, computations are executed by performing measurements on photons in graph states (i.e., sets of entangled photons) that are generated before measurements. The graph state in PQC is generated deterministically by quantum emitters. The generation process is achieved by applying a sequence of quantum gates to quantum emitters. In this process, i) the time required to complete the process, ii) the number of quantum emitters used, and iii) the number of CZ gates performed between emitters greatly affect the fidelity of the generated graph state. However, prior work for determining the generation sequence only focuses on optimizing the number of quantum emitters. Moreover, identifying the optimal generation sequence has vast search space. To this end, we propose RLGS, a novel compilation framework to identify optimal generation sequences that optimize the three metrics. Experimental results show that RLGS achieves an average reduction in generation time of 31.1%, 49.6%, and 57.5% for small, medium, and large graph states compared to the baseline.
Graph states are a fundamental resource for measurement and fusion-based quantum computing, quantum networks, and sensing. Preparing them in a photonic system deterministically is, in principle, possible, but finding efficient schemes to prepare them was a long-standing problem addressed recently. Additionally, heuristic optimization schemes for reducing the required number of two-qubit gates were developed. However, the problem of reducing the number of emitters by optimizing the emission ordering was not addressed, due to its computational complexity, as it is connected to a well-known NP-hard problem from graph theory, the linear rank width computation. In this work, we focus on developing heuristic polynomial algorithms to reduce the number of emitters required. In total, we propose four distinct algorithms, which demonstrate up to 30%30\%30% emitter reduction on random graphs. Furthermore, we provide numerical and statistical evidence that the combination of our optimization schemes with the preexisting algorithms for optimizing the two-qubit gates of the preparation protocol can further reduce them by around 20%20\%20%. Finally, we examine the developed algorithms for various useful graph state families, such as graphs useful for measurement-based quantum algorithms, and cluster states and graph codes used for quantum error correction, to determine the performance of each algorithm.
Photonic graph states are essential resources for quantum computation and communication. Deterministic emitter-based generation of graph states overcomes the scalability issues of probabilistic approaches; nonetheless, their experimental realization is constrained by technological demands, often expressed by the number of two-qubit gates and the depth and/or width of the quantum circuits used to model the generation process. Here, we introduce a cost-aware framework for the generation of photonic graph states of arbitrary size and shape, built on a complete set of necessary and sufficient conditions and a universal set of elementary graph operations that govern the evolution of the state toward the target. Within this framework, we develop Graph Builder, a deterministic generation algorithm that achieves substantial reductions (up to an order of magnitude) in two-qubit gate usage for both random and structured graphs, compared with alternative approaches. Furthermore, we show that this framework enables the identification of elementary building blocks in specific cases, such as encoded 6-ring states. The algorithm uses the minimum number of emitters possible for a fixed emission sequence, while also supporting the use of extra emitters for controlled trade-offs between emitter count and other cost metrics. Moreover, by systematically identifying the degrees of freedom at each stage of the generation process, this framework fully characterizes the optimization landscape, enabling analytic, heuristic, or exhaustive strategies for further cost reductions. Our approach provides a general and versatile tool for designing and optimizing emitter-based photonic graph state generation protocols, essential for scalable and resource-efficient photonic quantum information processing.
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.
Quantum graph states are critical resources for various quantum algorithms, and also determine essential interconnections in distributed quantum computing. There are two schemes for generating graph states - probabilistic scheme and deterministic scheme. While the all-photonic probabilistic scheme has garnered significant attention, the emitter-photonic deterministic scheme has been proved to be more scalable and feasible across several hardware platforms. This paper studies the GraphState-to-Circuit compilation problem in the context of the deterministic scheme. Previous research has primarily focused on optimizing individual circuit parameters, often neglecting the characteristics of quantum hardware, which results in impractical implementations. Additionally, existing algorithms lack scalability for larger graph sizes. To bridge these gaps, 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. Furthermore, we incorporate local complementation to transform graph states and minimize entanglement overhead. Evaluation of our framework on various graph types demonstrates significant reductions in CNOT gates and circuit duration, up to 52% and 56%. Moreover, it enhances the suppression of photon loss, achieving improvements of up to ×1.9\times 1.9×1.9.
Abstract Quantum emitter-based schemes for the generation of photonic graph states offer a promising, resource-efficient methodology for realizing distributed quantum computation and communication protocols on near-term hardware. We present a heralded scheme for making photonic graph states that is compatible with the typically poor photon collection from state-of-the-art coherent quantum emitters. We demonstrate that the construction time for large graph states can be polynomial in the photon collection efficiency, as compared to the exponential scaling of current emitter-based schemes, which assume deterministic photon collection. The additional overhead here consists of an extra spin qubit plus one additional spin-spin entangling gate per photon added to the graph. While the proposed scheme requires both non-demolition measurement and efficient storage of photons in order to generate graph states for arbitrary applications, we show that many useful tasks, including measurement-based quantum computation, can be implemented without these requirements. As a use case of our scheme, we construct a protocol for secure two-party computation that can be implemented efficiently on current hardware. Estimates of the fidelity to produce graph states used in the computation are given assuming current and near-term fidelities for highly coherent quantum emitters.