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arXiv:2607.09373

Deterministic Generation of Linear Photonic Cluster States with Semiconductor Quantum Dots: A Detailed Comparison of Different Schemes

Nikolas Köcher, Stefan Schumacher

quant-phSubmitted Jul 10, 2026• Announced Jul 13, 2026• 0 citations
arXivHTMLPDF

Abstract

Photonic graph states are key resource states for measurement based quantum information processing. As semiconductor quantum dots are excellent deterministic photon emitters, several protocols using them for the generation of linear cluster states have been proposed, either based on constant precession of a hole or electron spin in a weak magnetic field, or based on optical spin control, in a stronger magnetic field. We theoretically compare four such schemes, using polarization or time-bin encoding, respectively, for a range of cavity environments and spin coherence times. In particular we study how different error mechanisms affect the different schemes, using a microscopic model of the spin control, the excitation and emission dynamics, and of the phonon bath. We find the spin-precession based schemes to scale well with strong cavity enhancement and to be naturally robust against phonon-induced decoherence, while the schemes using optical spin control can perform well for lower spin coherence times and are strongly dependent on the cooperativity of the cavity induced cycling transition. Our results provide a regime map for choosing between magnetic-field-driven and optically controlled protocols depending on spin coherence time, Purcell enhancement, and suppression of unwanted decay channels.

Comments
15 pages, 9 figures

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Photonic graph states are key resource states for measurement based quantum information processing. As semiconductor quantum dots are excellent deterministic photon emitters, several protocols using them for the generation of linear cluster states have been proposed, either based on constant precession of a hole or electron spin in a weak magnetic field, or based on optical spin control, in a stronger magnetic field. We theoretically compare four such schemes, using polarization or time-bin encoding, respectively, for a range of cavity environments and spin coherence times. In particular we study how different error mechanisms affect the different schemes, using a microscopic model of the spin control, the excitation and emission dynamics, and of the phonon bath. We find the spin-precession based schemes to scale well with strong cavity enhancement and to be naturally robust against phonon-induced decoherence, while the schemes using optical spin control can perform well for lower spin coherence times and are strongly dependent on the cooperativity of the cavity induced cycling transition. Our results provide a regime map for choosing between magnetic-field-driven and optically controlled protocols depending on spin coherence time, Purcell enhancement, and suppression of unwanted decay channels.
Abstract By precisely timed optical excitation of their spin, optical emitters such as semiconductor quantum dots or atoms can be harnessed as sources of linear photonic cluster states. This significantly reduces the required resource overhead to reach fault-tolerant optical quantum computing. Here, we develop an algorithm that analytically tracks the global density matrix through the process of the protocol for generating linear-cluster states by Lindner and Rudolph. From this we derive a model to calculate the entangling gate fidelity and the state fidelity of the generated linear optical cluster states. Our model factors in various sources of error, such as spin decoherence and the finite excited state lifetime. Additionally, we highlight the presence of partial reinitialization of spin coherence with each photon emission, eliminating the hard limitation of coherence time. Our framework provides valuable insight into the cost-to-improvement trade-offs for device design parameters as well as the identification of optimal working points. For a combined state-of-the-art quantum dot with a spin coherence time of T2∗=535{T}_{2}^{*}=535T2∗​=535 T 2 ∗ = 535 ns and an excited state lifetime of τ=23\tau =23τ=23 τ = 23 ps, we show that a near-unity entangling gate fidelity as well as near-unity state fidelity for 3-photon and 7-photon linear cluster states can be reached. Graphical Abstract
In the framework of optical quantum computing and communications, a major objective consists in building receiving nodes that implement conditional operations on incoming photons, using the interaction with a single stationary qubit. In particular, the quest for scalable nodes motivated the development of cavity-enhanced spin-photon interfaces with solid-state emitters. An important challenge remains, however, to produce a stable, controllable, spin-dependant photon state, in a deterministic way. Here we use a pillar-based high-Q cavity, embedding a singly-charged semiconductor quantum dot, to demonstrate the control of giant polarisation rotations induced by a single electron spin. A complete tomography approach is used to deduce the output polarisation Stokes vector, conditioned by a single spin state. We experimentally demonstrate rotation amplitudes such as ±π2\pm \fracπ{2}±2π​ and πππ in the Poincaré sphere, as required for applications based on spin-polarisation mapping and spin-mediated photon-photon gates. In agreement with our modeling, we observe that the environmental noise does not limit the amplitude of the spin-induced rotation, yet slightly degrades the polarisation purity of the output states. We find that the polarisation state of the reflected photons can be manipulated in most of the Poincaré sphere, through controlled spin-induced rotations, thanks to moderate cavity birefringence and limited noise. This control allows the operation of spin-photon interfaces in various configurations, including at zero or low magnetic fields, which ensures compatibility with key protocols for photonic cluster state generation.
We theoretically investigate strategies for the deterministic creation of trains of time-bin entangled photons using an individual quantum emitter described by a Λ-type electronic system. We explicitly demonstrate the theoretical generation of linear cluster states with substantial numbers of entangled photonic qubits in full microscopic numerical simulations. The underlying scheme is based on the manipulation of ground state coherences through precise optical driving. One important finding is that the most easily accessible quality metrics, the achievable rotation fidelities, fall short in assessing the actual quantum correlations of the emitted photons in the face of losses. To address this, we explicitly calculate stabilizer generator expectation values as a superior gauge for the quantum properties of the generated many-photon state. With widespread applicability in other emitter and excitation–emission schemes also, our work lays the conceptual foundations for an in-depth practical analysis of time-bin entanglement based on full numerical simulations with predictive capabilities for realistic systems and setups, including losses and imperfections. The specific results shown in the present work illustrate that with controlled minimization of losses and realistic system parameters for quantum-dot type systems, useful linear cluster states of significant lengths can be generated in the calculations, discussing the possibility of scalability for quantum information processing endeavors.
Photonic cluster states are a key resource for photonic quantum information processing. So far, deterministic generation of these states has been limited to the near-infrared wavelength range. To achieve quantum advantage in communication while maintaining compatibility with silicon photonics, operation in the telecom wavelength range is required. In this work, we demonstrate deterministic cluster state generation directly in the telecom C-band. This is achieved through repetitive excitation of a hole spin confined in an indium-arsenide quantum dot subjected to an external magnetic field. We characterize the quantum process that generates the cluster state by measuring its process map, obtaining a fidelity of F=0.71±0.01\mathrm{F} = 0.71 \pm 0.01F=0.71±0.01 to the ideal case. As part of this characterization, we observe spin--photon polarization entanglement with a negativity of N=0.27±0.02\mathrm{N} = 0.27 \pm 0.02N=0.27±0.02. The emitted photons exhibit indistinguishability of at least 83%, demonstrating the potential for future fusion gates necessary for photonic cluster state generation beyond linear connectivity.
Cluster states are key resources for measurement-based quantum information processing. Photonic cluster and graph states, in particular, play indispensable roles in quantum network and quantum metrology. We demonstrate a semiconductor quantum dot based device in which the confined hole spin acts as a needle in a quantum knitting machine producing continuously and deterministically at sub-Gigahertz repetition rate single indistinguishable photons which are all polarization entangled to each other and to the spin in a one dimensional cluster state. By projecting two nonadjacent photons onto circular polarization bases we disentangle the spin from the photons emitted in between. This way we demonstrate a novel way for producing deterministic and continuous all-photonic cluster states. We use polarization tomography on four sequentially detected photons to demonstrate and to directly quantify the robustness of the cluster's entanglement and the determinism in its photon generation.
Measurement-based quantum communication relies on the availability of highly entangled multi-photon cluster states. The inbuilt redundancy in the cluster allows communication between remote nodes using repeated local measurements, compensating for photon losses and probabilistic Bell-measurements. For feasible applications, the cluster generation should be fast, deterministic, and its photons - indistinguishable. We present a novel source based on a semiconductor quantum-dot device. The dot confines a heavy-hole, precessing in a finely tuned external weak magnetic field while periodically excited by a sequence of optical pulses. Consequently, the dot emits indistinguishable polarization-entangled photons, where the field strength optimizes the entanglement. We demonstrate Gigahertz rate deterministic generation of >90% indistinguishable photons in a cluster state with more than 10 photons characteristic entanglement-length.