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Quantum repeaters based on concatenated bosonic and discrete-variable quantum codes
Abstract We propose an architecture of quantum-error-correction-based quantum repeaters that combines techniques used in discrete- and continuous-variable quantum information. Specifically, we propose to encode the transmitted qubits in a concatenated code consisting of two levels. On the first level we use a continuous-variable GKP code encoding the qubit in a single bosonic mode. On the second level we use a small discrete-variable code. Such an architecture has two important features. Firstly, errors on each of the two levels are corrected in repeaters of two different types. This enables for achieving performance needed in practical scenarios with a reduced cost with respect to an architecture for which all repeaters are the same. Secondly, the use of continuous-variable GKP code on the lower level generates additional analog information which enhances the error-correcting capabilities of the second-level code such that long-distance communication becomes possible with encodings consisting of only four or seven optical modes.
Error Mitigation Protocol for Multi-Photon Noise in Quantum Repeater Chains
Noise from multi-photon emissions can severely limit the use of probabilistic photon sources in quantum repeater chains. We present a Bell state measurement protocol that suppresses noise from multi-pair emissions in quantum repeaters.
Error Mitigation Protocol for Multi-Photon Noise in Quantum Repeater Chains
Noise from multi-photon emissions can severely limit the use of probabilistic photon sources in quantum repeater chains. We present a Bell state measurement protocol that suppresses noise from multi-pair emissions in quantum repeaters.
Field programmable spin arrays for scalable quantum repeaters
The large scale control over thousands of quantum emitters desired by quantum network technology is limited by the power consumption and cross-talk inherent in current microwave techniques. Here we propose a quantum repeater architecture based on densely-packed diamond color centers (CCs) in a programmable electrode array, with quantum gates driven by electric or strain fields. This ‘field programmable spin array’ (FPSA) enables high-speed spin control of individual CCs with low cross-talk and power dissipation. Integrated in a slow-light waveguide for efficient optical coupling, the FPSA serves as a quantum interface for optically-mediated entanglement. We evaluate the performance of the FPSA architecture in comparison to a routing-tree design and show an increased entanglement generation rate scaling into the thousand-qubit regime. Our results enable high fidelity control of dense quantum emitter arrays for scalable networking.
Practical quantum repeaters with linear optics and double-photon guns
We show how to create practical efficient quantum repeaters for optical quantum communication with double-photon guns. These latter devices create event-ready polarization-entangled photon pairs.
Realizing repeated quantum error correction in a distance-three surface code
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Quantum Network Repeater Simulation Package (QNPack) v1.0.0
Existing quantum network testbeds and prototypes are typically implemented in laboratory experiments with limited functionality and operate in a tightly coupled manner. These characteristics make it difficult to evaluate the behavior of emerging quantum platforms and protocols beyond local resource limitations. The QNPack software enables full-stack modeling of quantum repeater networks that allows researchers to simulate new approaches, and understand emergent behaviors, from local to national scales. Novel capabilities include: (1) performant and accurate quantum models that can be executed as independent simulations, which will allow users to characterize specific analog quantum processes, quantum devices, and protocols, (2) a modular and extensible approach to the simulation architecture to accommodate new quantum technologies, protocols, and topologies as they are developed across the quantum repeater generations under evaluation, and (3) a focus on managing the interactions between the simulation framework sub-components so that they may be re-used and composed in flexible ways.
Self-aligned heterogeneous quantum photonic integration
Integrated quantum photonics holds significant promise for scalable photonic quantum information processing, quantum repeaters, and quantum networks, but its development is hindered by the mismatch between materials hosting high-quality quantum emitters and those compatible with mature photonic technologies. Heterogeneous integration offers a potential solution to this challenge, yet practical implementations have been limited by inevitable insertion losses at material interfaces. Here, we present a self-aligned heterogeneous quantum photonic integration approach that enables near-unity coupling efficiency at the interface. To showcase our approach, we demonstrate Purcell enhancement of a silicon vacancy (SiV) center in diamond induced by a heterogeneous photonic crystal cavity defined by titanium dioxide (TiO 2 ), as well as optical spin control and readout via a TiO 2 photonic circuit. We further show that, when combined with inverse photonic design, our approach enables efficient and broadband collection of single photons from a color center into a heterogeneous waveguide. Our approach is not restricted to SiV centers or TiO 2 ; it has the potential to be broadly applied to integrate diverse solid-state quantum emitters with thin-film photonic devices where conformal deposition is possible. Together, these results establish a practical route to scalable quantum photonic integrated circuits that combine high-quality quantum emitters with technologically mature photonic platforms.
Isolation of individual Er quantum emitters in anatase TiO 2 on Si photonics
Defects and dopant atoms in solid state materials are a promising platform for realizing single photon sources and quantum memories, which are the basic building blocks of quantum repeaters needed for long distance quantum networks. In particular, trivalent erbium (Er 3+ ) is of interest because it couples C-band telecom optical transitions with a spin-based memory platform. In order to produce quantum repeaters at the scale required for quantum networks it is imperative to integrate these necessary building blocks with mature and scalable semiconductor processes. Here, in this work, we demonstrate the optical isolation of single Er 3+ ions in CMOS-compatible titanium dioxide (TiO 2 ) thin films monolithically integrated on a silicon-on-insulator photonics platform. Our results demonstrate an initial step toward the realization of a monolithically integrated and scalable quantum photonics package based on Er 3+ doped thin films.
Coexistent Quantum Channel Characterization Using Spectrally Resolved Bayesian Quantum Process Tomography
The coexistence of quantum and classical signals over the same optical fiber with minimal degradation of the transmitted quantum information is critical for operating large-scale quantum networks over the existing communications infrastructure. In this work, we systematically characterize the quantum channel that results from simultaneously distributing approximate single-photon polarization-encoded qubits and classical light of varying intensities through fiber-optic channels of up to 15 km. Using spectrally resolved quantum process tomography with a Bayesian reconstruction method that we develop, we estimate the full quantum channel from experimental photon counting data, both with and without classical background. Furthermore, although we find the exact channel description to be a weak function of the pump polarization, we nevertheless show that the coexistent fiber-based quantum channel has high process fidelity with an ideal depolarizing channel when the noise is dominated by Raman scattering. These results provide a basis for the future development of quantum repeater designs and quantum error-correcting codes for real-world channels and inform models used in the analysis and simulation of quantum networks.
Coexistent quantum channel characterization using quantum process tomography with spectrally resolved detection
The coexistence of classical and quantum signals over the same optical fiber is critical for quantum networks operating within the existing communications infrastructure. Here, we characterize the quantum channel that results from distributing approximate single-photon polarization-encoded qubits simultaneously with classical light of varying intensities through a 25 km fiber-optic channel. We use spectrally resolved quantum process tomography with a newly developed Bayesian reconstruction method to estimate the quantum channel from experimental data, both with and without classical noise. Furthermore, we show that the coexistent fiber-based quantum channel has high process fidelity with an ideal depolarizing channel if the noise is dominated by Raman scattering. These results aid future development of quantum repeater designs and quantum error-correcting codes which benefit from realistic channel error models.
Zero-added-loss entanglement multiplexing using time-bin spectral shearing
High-quality quantum communications that enable important capabilities, such as distributed quantum computing and sensing, will require quantum repeaters for providing high-quality entanglement. To realize high-rate heralded entanglement for quantum repeaters, Chen et al . [Phys. Rev. Appl. 19 , 054029 (2023)] proposed a scheme for heralded-multiplexed generation of quasideterministic entangled photon pairs, called zero-added-loss multiplexing (ZALM). Here, we propose a design of the ZALM source using time-bin entanglement and spectral shearing. Additionally, we provide an analysis of experimentally relevant spectral-shearing parameters to optimize the spectral multiplexing. Moreover, we experimentally verify the compatibility of time-bin pulses and spectral shearing, as supported by observation of no appreciable phase shift when the same shearing is applied to both time bins. These results expand the benefits of applying a ZALM source to time-bin entanglement use cases. Moreover, more fully demonstrating time-bin and spectral shearing compatibility clears a path toward a broader use of spectral shearing that provides a deterministic frequency shift of high utility.
A perspective on the pathway to a scalable quantum internet using rare-earth ions
The ultimate realization of a global quantum internet will require advances in scalable technologies capable of generating, storing, and manipulating quantum information. The essential devices that will perform these tasks in a quantum network are quantum repeaters, which will enable the long-range distribution of entanglement between distant network nodes. Here, in this review, we provide an overview of the primary functions of a quantum repeater and discuss progress that has been made toward the development of repeaters with rare-earth ion doped materials while noting challenges that are being faced as the technologies mature. We give particular attention to erbium, which is well suited for networking applications. Finally, we provide a discussion of near-term benchmarks that can further guide rare-earth ion platforms for impact in near-term quantum networks.
Indistinguishable telecom band photons from a single Er ion in the solid state
Atomic defects in the solid state are a key component of quantum repeater networks for long-distance quantum communication1. Recently, there has been significant interest in rare earth ions, in particular Er 3+ for its telecom band optical transition that allows long-distance transmission in optical fibres. However, the development of repeater nodes based on rare earth ions has been hampered by optical spectral diffusion, precluding indistinguishable single-photon generation. Here, we implant Er 3+ into CaWO 4 , a material that combines a non-polar site symmetry, low decoherence from nuclear spins and is free of background rare earth ions, to realize significantly reduced optical spectral diffusion. For shallow implanted ions coupled to nanophotonic cavities with large Purcell factor, we observe single-scan optical linewidths of 150 kHz and long-term spectral diffusion of 63 kHz, both close to the Purcell-enhanced radiative linewidth of 21 kHz. This enables the observation of Hong–Ou–Mandel interference between successively emitted photons with a visibility of V = 80(4)%, measured after a 36 km delay line. We also observe spin relaxation times T 1,s = 3.7 s and T 2,s > 200 μs, with the latter limited by paramagnetic impurities in the crystal instead of nuclear spins. Furthermore, this represents a notable step towards the construction of telecom band quantum repeater networks with single Er 3+ ions.
A parametrically programmable delay line for microwave photons
Delay lines that store quantum information are crucial for advancing quantum repeaters and hardware efficient quantum computers. Traditionally, they are realized as extended systems that support wave propagation but provide limited control over the propagating fields. Here, we introduce a parametrically addressed delay line for microwave photons that provides a high level of control over the stored pulses. By parametrically driving a three-wave mixing circuit element that is weakly hybridized with an ensemble of resonators, we engineer a spectral response that simulates that of a physical delay line, while providing fast control over the delay line’s properties. We demonstrate this novel degree of control by choosing which photon echo to emit, translating pulses in time, and even swapping two pulses, all with pulse energies on the order of a single photon. We also measure the noise added from our parametric interactions and find it is much less than one photon.
Hyperentangled Time-Bin and Polarization Quantum Key Distribution
Fiber-based quantum communication networks are currently limited without quantum repeaters. Satellite-based quantum links have been proposed to extend the network domain. Here, we develop a quantum communication system, suitable for realistic satellite-to-ground communication. With this system, we execute an entanglement-based quantum key distribution (QKD) protocol developed by Bennett, Brassard, and Mermin (BBM92), achieving quantum bit-error rates (QBERs) below 2% in all bases. More importantly, we demonstrate low-QBER execution of a higher-dimensional hyperentanglement-based QKD protocol, using photons simultaneously entangled in polarization and time bin, leading to significantly higher secure key rates, at the cost of increased technical complexity and system size. We show that our protocol is suitable for a space-to-ground link, after incorporating Doppler-shift compensation, and verify its security using a rigorous finite-key analysis. Additionally, we discuss system-engineering considerations relevant to those and other quantum communication protocols and their dependence on what photonic degrees of freedom are utilized.