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Fusion-based quantum computation is a promising quantum computing model where small-sized photonic resource states are simultaneously entangled and measured by fusion gates. Such operations can be readily implemented with scalable photonic hardware: resource states can be deterministically generated by quantum emitters and fusions require only shallow linear-optical circuits. Here, we propose fusion-based architectures tailored to the capabilities and noise models in quantum emitters. We show that high tolerance to dominant physical error mechanisms can be achieved, with fault-tolerance thresholds of 8% for photon loss, 4% for photon distinguishability between emitters, and spin noise thresholds well below coherence times for typical spin-photon interfaces. Our construction and analysis provide guidelines for the development of photonic quantum hardware targeting fault-tolerant applications with quantum emitters.

Entanglement, the non-local correlations present in multipartite quantum systems, is a curious feature of quantum mechanics and the fuel of quantum technology. It is therefore a major priority to develop energy-conserving and simple methods for generating high-fidelity entangled states. In the case of light, entanglement can be realized by interactions with matter, although the required nonlinear interaction is typically weak, thereby limiting its applicability. Here, we show how a single two-level emitter deterministically coupled to light in a nanophotonic waveguide is used to realize genuine photonic quantum entanglement for excitation at the single photon level. By virtue of the efficient optical coupling, two-photon interactions are strongly mediated by the emitter realizing a giant nonlinearity that leads to entanglement. We experimentally generate and verify energy-time entanglement by violating a Bell inequality (Clauder-Horne-Shimony-Holt Bell parameter of $S=2.67(16)>2$) in an interferometric measurement of the two-photon scattering response. As an attractive feature of this approach, the two-level emitter acts as a passive scatterer initially prepared in the ground state, i.e., no advanced spin control is required. This experiment is a fundamental advancement that may pave a new route for ultra-low energy-consuming synthesis of photonic entangled states for quantum simulators or metrology., Comment: the manuscript of 6 pages with 3 figures and a Supplementary Material file of 12 pages with 7 figures

One-way quantum repeaters where loss and operational errors are counteracted by quantum error correcting codes can ensure fast and reliable qubit transmission in quantum networks. It is crucial that the resource requirements of such repeaters, for example, the number of qubits per repeater node and the complexity of the quantum error correcting operations are kept to a minimum to allow for near-future implementations. To this end, we propose a one-way quantum repeater that targets both the loss and operational error rates in a communication channel in a resource-efficient manner using code concatenation. Specifically, we consider a tree-cluster code as an inner loss-tolerant code concatenated with an outer 5-qubit code for protection against Pauli errors. Adopting flag-based stabilizer measurements, we show that intercontinental distances of up to 10,000 km can be bridged with a minimal resource overhead by interspersing repeater nodes that each specializes in suppressing either loss or operational errors. Our work demonstrates how tailored error-correcting codes can significantly lower the experimental requirements for long-distance quantum communication., Comment: 25 pages, 16 figures, 4 tables

Photon emission is the hallmark of light-matter interaction and the foundation of photonic quantum science, enabling advanced sources for quantum communication and computing. Although single-emitter radiation can be tailored by the photonic environment, the introduction of multiple emitters extends this picture. A fundamental challenge, however, is that the radiative dipole-dipole coupling rapidly decays with spatial separation, typically within a fraction of the optical wavelength. We realize distant dipole-dipole radiative coupling with pairs of solid-state optical quantum emitters embedded in a nanophotonic waveguide. We dynamically probe the collective response and identify both super- and subradiant emission as well as means to control the dynamics by proper excitation techniques. Our work constitutes a foundational step toward multiemitter applications for scalable quantum-information processing., Comment: 6 pages 3 figures, Supplementary materials 18 pages 18 figures

The realization of on-chip quantum gates between photons and solid-state spins is a key building block for quantum-information processors, enabling, e.g., distributed quantum computing, where remote quantum registers are interconnected by flying photons. Self-assembled quantum dots integrated in nanostructures are one of the most promising systems for such an endeavor thanks to their near-unity photon-emitter coupling and fast spontaneous emission rate. Here we demonstrate an on-chip entangling gate between an incoming photon and a stationary quantum-dot spin qubit. The gate is based on sequential scattering of a time-bin encoded photon with a waveguide-embedded quantum dot and operates on sub-microsecond timescale; two orders of magnitude faster than other platforms. Heralding on detection of a reflected photon renders the gate fidelity fully immune to spectral wandering of the emitter. These results represent a major step in realizing a quantum node capable of both photonic entanglement generation and on-chip quantum logic, as demanded in quantum networks and quantum repeaters., Comment: Published version. Popular summary: https://physicscommunity.nature.com/posts/creating-light-matter-entanglement-on-a-chip

Deterministic sources of multi-photon entanglement are highly attractive for quantum information processing but are challenging to realize experimentally. In this paper, we demonstrate a route towards a scaleable source of time-bin encoded Greenberger-Horne-Zeilinger and linear cluster states from a solid-state quantum dot embedded in a nanophotonic crystal waveguide. By utilizing a self-stabilizing double-pass interferometer, we measure a spin-photon Bell state with $(67.8\pm0.4)\%$ fidelity and devise steps for significant further improvements. By employing strict resonant excitation, we demonstrate a photon indistinguishability of $(95.7\pm0.8)\%$, which is conducive to fusion of multiple cluster states for scaling up the technology and producing more general graph states., Comment: Manuscript: 7 pages, 3 figures. Supplementary information: 23 pages, 12 figures

We study the emergence of two types of two-photon bounds states in waveguides of any chirality. Specifically, we present a systematic way of analytically determining the eigenstates of a system consisting of a waveguide coupled to a partially chiral, infinite array of equidistant two-level emitters. Using an effective Hamiltonian approach, we determine the properties of the two-photon bound states by determining their dispersion relation and internal structure. The bound states come in two varieties, depending on the two-photon momentum and emitter spacing. One of these states is a long-lived true bound state, whereas the other, a scattering resonance, decays in time via coupling to free two-photon states, leading to resonances and corresponding phase shifts in the photon-photon scattering., Comment: 6+1 pages, 4 figures

We consider a nonlinearly coupled electromechanical system, and develop a quantitative theory for two-phonon cooling. In the presence of two-phonon cooling, the mechanical Hilbert space is effectively reduced to its ground and first excited states, allowing for quantum operations at the level of individual phonons and preparing nonclassical mechanical states with negative Wigner functions. We propose a scheme for performing arbitrary Bloch sphere rotations, and derive the fidelity in the specific case of a $\pi$-pulse. We characterise detrimental processes that reduce the coherence in the system, and demonstrate that our scheme can be implemented in state-of-the-art electromechanical devices., Comment: 13 pages main text + 9 pages appendix, 5 figures

We devise a mathematical framework for assessing the fidelity of multi-photon entangled states generated by a single solid-state quantum emitter, such as a quantum dot or a nitrogen-vacancy center. Within this formalism, we theoretically study the role of imperfections present in real systems on the generation of time-bin encoded Greenberger-Horne-Zeilinger and one-dimensional cluster states. We consider both fundamental limitations, such as the effect of phonon-induced dephasing, interaction with the nuclear spin bath, and second-order emissions, as well as technological imperfections, such as branching effects, non-perfect filtering, and photon losses. In a companion paper, we consider a particular physical implementation based on a quantum dot emitter embedded in a photonic crystal waveguide and apply our theoretical formalism to assess the fidelities achievable with current technologies.

We propose a complete architecture for deterministic generation of entangled multiphoton states. Our approach utilizes periodic driving of a quantum-dot emitter and an efficient light-matter interface enabled by a photonic crystal waveguide. We assess the quality of the photonic states produced from a real system by including all intrinsic experimental imperfections. Importantly, the protocol is robust against the nuclear spin bath dynamics due to a naturally built-in refocussing method reminiscent to spin echo. We demonstrate the feasibility of producing Greenberger-Horne-Zeilinger and one-dimensional cluster states with fidelities and generation rates exceeding those achieved with conventional 'fusion' methods in current state-of-the-art experiments. The proposed hardware constitutes a scalable and resource-efficient approach towards implementation of measurement-based quantum communication and computing.

We show that spin squeezing criteria commonly used for entanglement detection can be erroneous, if the probe is not symmetric. We then derive a lower bound on squeezing for separable states in spin systems probed asymmetrically. Using this we further develop a procedure that allows us to verify the degree of entanglement of a quantum state in the spin system. Finally, we apply our method for entanglement verification to existing experimental data, and use it to prove the existence of tri-partite entanglement in a spin squeezed atomic ensemble., Comment: 7 pages, 2 figures (Include Supplemental material)

We provide a microscopic theory for semiconductor quantum dots that explains the pronounced deviations from the prevalent point-dipole description that were recently observed in spectroscopic experiments on quantum dots in photonic nanostructures. At the microscopic level the deviations originate from structural inhomogeneities generating a large circular quantum current density that flows inside the quantum dot over mesoscopic length scales. The model is supported by the experimental data, where a strong variation of the multipolar moments across the emission spectrum of quantum dots is observed. Our work enriches the physical understanding of quantum dots and is of significance for the fields of nanophotonics, quantum photonics, and quantum-information science, where quantum dots are actively employed., Comment: 6 pages, 5 figures

The electromagnetic-vacuum-field fluctuations are intimately linked to the process of spontaneous emission of light. Atomic emitters cannot probe electric- and magnetic-field fluctuations simultaneously because electric and magnetic transitions correspond to different selection rules. In this paper we show that semiconductor quantum dots are fundamentally different and are capable of mediating electric-dipole, magnetic-dipole, and electric-quadrupole transitions on a single electronic resonance. As a consequence, quantum dots can probe electric and magnetic fields simultaneously and can thus be applied for sensing the electromagnetic environment of complex photonic nanostructures. Our study opens the prospect of interfacing quantum dots with optical metamaterials for tailoring the electric and magnetic light-matter interaction at the single-emitter level., Comment: 6 pages, 4 figures

Semiconductor quantum dots (QDs) provide an essential link between light and matter in emerging fields such as light-harvesting, all-solid-state quantum communication, and quantum computing. QDs are excellent single-photon sources and can store quantum bits for extended periods making them promising interconnects between light and matter in integrated quantum information networks. To this end the light-matter interaction strength must be strongly enhanced using nanophotonic structures such as photonic crystal cavities and waveguides or plasmonic nanowires. So far it has been assumed that QDs can be treated just like atomic photon emitters where the spatial properties of the wavefunction can be safely ignored. Here we demonstrate that the point-emitter description for QDs near plasmonic nanostructures breaks down. We observe that the QDs can excite plasmons eight times more efficiently depending on their orientation due to their mesoscopic character. Either enhancement or suppresion of the rate of plasmon excitation is observed depending on the geometry of the plasmonic nanostructure in full agreement with a new theory. This discovery has no equivalence in atomic systems and paves the way for novel nanophotonic devices that exploit the extended size of QDs as a resource for increasing the light-matter interaction strength., Comment: 9 pages, 4 figures

Quantum repeaters promise to deliver long-distance entanglement overcoming noise and loss in realistic quantum channels. A promising class of repeaters, based on atomic ensemble quantum memories and linear optics, follow the proposal by Duan et al [Nature 414, 413, 2001]. Here we analyse this protocol in terms of a very general model for the quantum memories employed. We derive analytical expressions for scaling of entanglement with memory imperfections, dark counts, loss and distance, and apply our results to two specific quantum memory protocols. Our methods apply to any quantum memory with an interaction Hamiltonian at most quadratic in the mode operators and are in principle extendible to more recent modifications of the original DLCZ proposal., Comment: 15 pages, 12 figures