Photonic cluster states are fundamental resource for measurement-based quantum computing (MBQC), which is a promising approach for scalable quantum computing. These highly entangled states enable computation with applying local measurements rather than gate operations, which makes them essential for fault-tolerant quantum computing. Generation of the photonic cluster states requires high-quality entanglement and stability, which can be done by making use of cavity quantum electrodynamics (cavity QED), which is embedding quantum dots (QDs) into photonic microcavities. This method enables controlled single-photon emission and the entanglement of them, helping with key challenges in generating photonic cluster states. Enhancing the generation of the photonic cluster state requires improvement in the quality factor (Q-factor) and therefore, cooperativity of cavity and QD systems. A high Q-factor helps with reduction in photon loss and decoherence, ensuring more stable and high-fidelity quantum states. It also enables better light-matter interactions, improving cluster state quality. Cooperativity, which is a measure for the light-matter coupling strength relative to dissipation, directly impacts photon emission efficiency. Optimization of these parameters improves entanglement generation, which is essential for producing high-quality photonic cluster states. Therefore, optimized cavities are essential for improving the generation of the photonic cluster states. Scalability is also an important parameter for the generation of the large-scale cluster states used in quantum computing. In this paper, after reviewing MBQC, cluster states, and the generation of the photonic cluster states, we investigate the deterministic generation of the photonic cluster state resource for the purpose of MBQC, and highlights the importance of the inverse design techniques for this goal.
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8 pages, 8 figures. Qualifying exam paper, originally presented March 2025
Photonic cluster states are fundamental resource for measurement-based quantum computing (MBQC), which is a promising approach for scalable quantum computing. These highly entangled states enable computation with applying local measurements rather than gate operations, which makes them essential for fault-tolerant quantum computing. Generation of the photonic cluster states requires high-quality entanglement and stability, which can be done by making use of cavity quantum electrodynamics (cavity QED), which is embedding quantum dots (QDs) into photonic microcavities. This method enables controlled single-photon emission and the entanglement of them, helping with key challenges in generating photonic cluster states. Enhancing the generation of the photonic cluster state requires improvement in the quality factor (Q-factor) and therefore, cooperativity of cavity and QD systems. A high Q-factor helps with reduction in photon loss and decoherence, ensuring more stable and high-fidelity quantum states. It also enables better light-matter interactions, improving cluster state quality. Cooperativity, which is a measure for the light-matter coupling strength relative to dissipation, directly impacts photon emission efficiency. Optimization of these parameters improves entanglement generation, which is essential for producing high-quality photonic cluster states. Therefore, optimized cavities are essential for improving the generation of the photonic cluster states. Scalability is also an important parameter for the generation of the large-scale cluster states used in quantum computing. In this paper, after reviewing MBQC, cluster states, and the generation of the photonic cluster states, we investigate the deterministic generation of the photonic cluster state resource for the purpose of MBQC, and highlights the importance of the inverse design techniques for this goal.
Abstract The central technological appeal of quantum science resides in exploiting quantum effects, such as entanglement, for a variety of applications, including computing, communication and sensing 1 . The overarching challenge in these fields is to address, control and protect systems of many qubits against decoherence 2 . Against this backdrop, optical photons, naturally robust and easy to manipulate, represent ideal qubit carriers. However, the most successful technique so far for creating photonic entanglement 3 is inherently probabilistic and, therefore, subject to severe scalability limitations. Here we report the implementation of a deterministic protocol 4–6 for the creation of photonic entanglement with a single memory atom in a cavity 7 . We interleave controlled single-photon emissions with tailored atomic qubit rotations to efficiently grow Greenberger–Horne–Zeilinger (GHZ) states 8 of up to 14 photons and linear cluster states 9 of up to 12 photons with a fidelity lower bounded by 76(6)% and 56(4)%, respectively. Thanks to a source-to-detection efficiency of 43.18(7)% per photon, we measure these large states about once every minute, which is orders of magnitude faster than in any previous experiment 3,10–13 . In the future, this rate could be increased even further, the scheme could be extended to two atoms in a cavity 14,15 or several sources could be quantum mechanically coupled 16 , to generate higher-dimensional cluster states 17 . Overcoming the limitations encountered by probabilistic schemes for photonic entanglement generation, our results may offer a way towards scalable measurement-based quantum computation 18,19 and communication 20,21 .
Measurement-based quantum computation relies on single qubit measurements of large multipartite entangled states, so-called lattice-graph or cluster states. Graph states are also an important resource for quantum communication, where tree cluster states are a key resource for one-way quantum repeaters. A photonic realization of this kind of state would inherit many of the benefits of photonic platforms, such as very little dephasing due to weak environmental interactions and the well-developed infrastructure to route and measure photonic qubits. In this work, a linear cluster state and GHZ state generation scheme is developed for group-IV color centers. In particular, this article focuses on an in-depth investigation of the required control operations, including the coherent spin and excitation gates. We choose an off-resonant Raman scheme for the spin gates, which can be much faster than microwave control. We do not rely on a reduced level scheme and use efficient approximations to design high-fidelity Raman gates. We benchmark the spin-control and excitation scheme using the tin vacancy color center coupled to a cavity, assuming a realistic experimental setting. Additionally, the article investigates the fidelities of the Raman and excitation gates in the presence of radiative and non-radiative decay mechanisms. Finally, a quality measure is devised, which emphasizes the importance of fast and high-fidelity spin gates in the creation of large entangled photonic states.
Entanglement between particles is a basic concept of quantum sciences. The ability to produce entangled particles in a controllable manner is essential for any quantum technology. Entanglement between light particles (photons) is particularly crucial for quantum communication due to light's non-interactive nature and long-lasting coherence. Resources producing entangled multiphoton cluster states will enable communication between remote quantum nodes, as the inbuilt redundancy of cluster photons allows for repeated local measurements-compensating for losses and probabilistic Bell measurements. For feasible applications, the cluster generation should be fast, deterministic and, most importantly, its photons indistinguishable, which will allow measurements and fusion of clusters by interfering photons. Here, using periodic excitation of a semiconductor quantum-dot-confined spin, we demonstrate a multi-indistinguishable photon cluster, featuring a continuously generated string of photons at deterministic gigahertz generation rates, and an optimized entanglement length of about ten photons. The indistinguishability of the photons opens up new possibilities for scaling up the cluster's dimensionality by fusion, thus building graph states suited for measurement-based photonic quantum computers and all-photonic quantum repeaters.
Quantum computation using photons offers one possible route towards the long-standing goal of scalable, fault-tolerant quantum computing. Within this realm, measurement-based quantum computing offers a promising approach exploiting many of the advantages of photons. Implementing photonic measurement-based architectures relies upon the deterministic generation of graph states composed of many entangled photons. Semiconductor quantum dots (QDs) are sources of indistinguishable single photons and hosts of solid-state spins, marking them desirable platforms for controlled entanglement generation. Such a platform consisting of a single charged QD coupled to a photonic cavity has been proven for the generation of multipartite spin-photon graph states. This dissertation will present advancements in the versatility and coherence of such entanglement generation. First, background on quantum dots, single photon generation, spin control, and entanglement will be introduced. Then, sources of error and decoherence will be addressed using control of the hole g-factor and dynamical decoupling techniques. The aim of versatility is advanced through results on the generation of four-partite graph states with on-demand reconfigurability of the type of state produced. Finally, a different paradigm using quantum dot molecules will be introduced, and novel estimation of important physical parameters in this system is developed.
Entanglement in multiphoton graph states is an important resource with various applications, such as measurement-based quantum computing and memory-less quantum repeaters. While some primitive instances have been successfully prepared, scalable generation of large-scale graph states with programmable connections remains an outstanding challenge. Fusion provides a promising "divide-and-conquer" approach by linking smaller resource states into larger, more complex graphs. However, its practical scalability has been limited by the probabilistic nature of conventional fusion protocols, which necessitates extensive hardware overhead and feed-forward resources to achieve deterministic outcomes. Here, we introduce and experimentally demonstrate a deterministic fusion operation with built-in error mitigation, capable of connecting small time-bin-encoded cluster states--originally generated on-demand from a quantum emitter--into larger, reconfigurable photonic graph states of increased sizes. The fusion operation is realized by nondestructively projecting pairs of flying microwave photonic qubits into Bell states using superconducting circuits with in-situ programmability. Crucially, the protocol features active reset and reuse of matter qubits during graph state generation, thereby circumventing the coherence constraints of the quantum emitter and enabling the generation of genuine multipartite entanglement across 13 photonic qubits. Our results establish a scalable framework for photonic graph-state synthesis, paving the way for fault-tolerant measurement-based quantum computation and distributed quantum networks.
Semiconductor quantum dots (QDs) have emerged as a premier solid-state platform for the deterministic generation of nonclassical light, offering a compelling pathway toward scalable quantum photonic systems. While single-photon emission from QDs has reached a high level of maturity, the realization of high-fidelity entangled photon-pair sources remains an active and rapidly evolving frontier. In this review, we survey the recent progress in QD-based entangled photon sources, highlighting the conceptual evolution from the established biexciton-exciton cascade to the emerging paradigm of spontaneous two-photon emission. We further examine how advances in nanophotonic architectures and coherent control strategies are redefining fundamental performance limits, enabling concurrent improvements in source brightness, coherence, and entanglement fidelity. Finally, we discuss the key physical and technological challenges that must be addressed to bridge the gap between laboratory demonstrations and large-scale deployment. We conclude by outlining the future opportunities for integrating QD-based entangled photon sources into practical quantum communication, computation, and sensing platforms.