Cluster states are useful in many quantum information processing applications. In particular, universal measurement-based quantum computation (MBQC) utilizes two-dimensional cluster states [R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188 (2001)] and topologically fault-tolerant MBQC requires cluster states of dimension 3 or higher [R. Raussendorf et al., New J. Phys. 9, 199 (2007)]. This work proposes a protocol to deterministically generate multidimensional photonic cluster states using a single atom-cavity system and time-delay feedback. The dimensionality of the cluster state increases linearly with the number of time-delay feedbacks. We first give a diagrammatic derivation of the tensor network states, which is valuable in simulating matrix product states and projected entangled pair states generated from sequential photons. Our method also provides a simple way to bridge and analyze the experimental imperfections and the logical errors of the generated states. In this method, we analyze the generated cluster states under realistic experimental conditions and address both one-qubit and two-qubit errors. Through numerical simulation, we observe an optimal atom-cavity cooperativity for the fidelity of the generated states, which is surprising given the prevailing assumption that higher-cooperativity systems are inherently better for photonic applications.
Cluster states are useful in many quantum information processing applications. In particular, universal measurement-based quantum computation (MBQC) utilizes two-dimensional cluster states [R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188 (2001)] and topologically fault-tolerant MBQC requires cluster states of dimension 3 or higher [R. Raussendorf et al., New J. Phys. 9, 199 (2007)]. This work proposes a protocol to deterministically generate multidimensional photonic cluster states using a single atom-cavity system and time-delay feedback. The dimensionality of the cluster state increases linearly with the number of time-delay feedbacks. We first give a diagrammatic derivation of the tensor network states, which is valuable in simulating matrix product states and projected entangled pair states generated from sequential photons. Our method also provides a simple way to bridge and analyze the experimental imperfections and the logical errors of the generated states. In this method, we analyze the generated cluster states under realistic experimental conditions and address both one-qubit and two-qubit errors. Through numerical simulation, we observe an optimal atom-cavity cooperativity for the fidelity of the generated states, which is surprising given the prevailing assumption that higher-cooperativity systems are inherently better for photonic applications.
Measurement-based quantum computation offers exponential computational speed-up through simple measurements on a large entangled cluster state. We propose and demonstrate a scalable scheme for the generation of photonic cluster states suitable for universal measurement-based quantum computation. We exploit temporal multiplexing of squeezed light modes, delay loops, and beam-splitter transformations to deterministically generate a cylindrical cluster state with a two-dimensional (2D) topological structure as required for universal quantum information processing. The generated state consists of more than 30,000 entangled modes arranged in a cylindrical lattice with 24 modes on the circumference, defining the input register, and a length of 1250 modes, defining the computation depth. Our demonstrated source of two-dimensional cluster states can be combined with quantum error correction to enable fault-tolerant quantum computation.
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.
Cluster states, as highly entangled multi-qubit states, are widely used as essential resources for quantum communication and quantum computing. However, due to the diverse requirements of applications for cluster states with specific entanglement structures, a universal generation protocol is still lacking. Here we develop a matrix representation according to the characteristics of time-delayed feedback (TDF) and propose a protocol for generating arbitrary cluster states with multiple TDFs. The matrix representation also allows us to optimize the generation process to reduce TDF usage, thus improving efficiency. In particular, we demonstrate a tree-cluster-state generation process that requires only one TDF. Moreover, accounting for the critical loss mechanisms and imperfections in our protocol, we discuss the additional losses caused by multiple TDFs and evaluate the fidelity of the resulting cluster states.
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 .
Multidimensional cluster states are a key resource for robust quantum communication, measurement-based quantum computing and quantum metrology. Here, we present a device capable of emitting large-scale entangled microwave photonic states in a two dimensional ladder structure. The device consists of a pair of coupled superconducting transmon qubits which are each tuneably coupled to a common output waveguide. This architecture permits entanglement between each transmon and a deterministically emitted photonic qubit. By interleaving two-qubit gates with controlled photon emission, we generate 2 × n grids of time- and frequency-multiplexed cluster states of itinerant microwave photons. We generate states with fidelities above 0.50 for up to eight qubits and, in addition, observe nonzero localizable entanglement for states of up to 16 qubits. We expect the device architecture to be capable of generating a wide range of other tensor network states such as tree graph states, repeater states or the ground state of the toric code, and to be readily scalable to generate larger and higher dimensional states. Cluster states are a key resource in quantum technologies, but generation of large-scale 2D cluster states faces several difficulties. Here, the authors show how to generate a 2 × n ladder-like cluster state via sequential emission of time- and frequency multiplexed photonic qubits from a transmon-based device.
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