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arXiv:2405.13263 · npj Quantum Information

Heralded photonic graph states with inefficient quantum emitters

Maxwell Gold, Jianlong Lin, Eric Chitambar, Elizabeth A. Goldschmidt

Published Jan 15, 2026• 1 citation
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Abstract

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.

DOI
10.1038/s41534-026-01181-7

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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.
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.
Since linear-optical two-photon gates are inherently probabilistic, measurement-based implementations are particularly well suited for photonic platforms: a large highly-entangled photonic resource state, called a graph state, is consumed through measurements to perform a computation. The challenge is thus to produce these graph states. Several generation procedures, which use either interacting quantum emitters or efficient spin-photon interface, have been proposed to create these photonic graph states deterministically. Yet, these solutions are still out of reach experimentally since the state-of-the-art is the generation of a linear graph state. Here, we introduce near-deterministic solutions for the generation of graph states using the current quantum emitter capabilities. We propose hybridizing quantum-emitter-based graph state generation with all-photonic fusion gates to produce graph states of complex topology near-deterministically. Our results should pave the way towards the practical implementation of resource-efficient quantum information processing, including measurement-based quantum communication and quantum computing.
Graph states constitute the main building block for quantum computing with photons. Quantum emitters with a hosted spin can deterministically generate photonic graph states, strongly lowering the overhead of multiplexing highly probabilistic linear-optics graph state generation. However, they generally suffer from various noise sources, resulting in reduced fidelities of the produced states. To mitigate this issue, we develop purification schemes for entangled photonic states. We first develop purification schemes to purify arbitrary photonic GHZ and other CSS states, which we generalize to all photonic graph states and stabilizer states. The proposed purification schemes have a high success probability of up to 1/21/21/2 and require only linear optics and photon detectors. We optimize cascaded purification schemes for various graph states, taking into account phenomenological Pauli errors or physical noise in time-bin-encoded graph state generation with quantum emitters.
Photonic graph states constitute important resources in quantum information processing. They are used in measurement-based and fusion-based quantum computing and in all-photonic repeaters for quantum networks. However, generating such highly entangled states is challenging due to the fact that photons do not interact with each other. We propose a protocol for generating arbitrary graph states using matter qubits as quantum emitters. Our approach guarantees the minimal number of emitters and provides in polynomial time the quantum circuit for the graph state generation (which includes the non-unitary process of photon emission). We find that the quantum circuit depth for general graphs also scale polynomially with system size.
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We propose and analyze deterministic protocols to generate qudit photonic graph states from quantum emitters. We show that our approach can be applied to generate any qudit graph state and we exemplify it by constructing protocols to generate one- and two-dimensional qudit cluster states, absolutely maximally entangled states, and logical states of quantum error-correcting codes. Some of these protocols make use of time-delayed feedback, while others do not. The only additional resource requirement compared to the qubit case is the ability to control multilevel emitters. These results significantly broaden the range of multiphoton entangled states that can be produced deterministically from quantum emitters. Published by the American Physical Society 2024