Metropolitan-scale heralded entanglement of solid-state qubits

Abstract

A key challenge toward future quantum internet technology is connecting quantum processors at metropolitan scale. Here, we report on heralded entanglement between two independently operated quantum network nodes separated by 10 kilometers. The two nodes hosting diamond spin qubits are linked with a midpoint station via 25 kilometers of deployed optical fiber. We minimize the effects of fiber photon loss by quantum frequency conversion of the qubit-native photons to the telecom L-band and by embedding the link in an extensible phase-stabilized architecture enabling the use of the loss-resilient single-click entangling protocol. By capitalizing on the full heralding capabilities of the network link in combination with real-time feedback logic on the long-lived qubits, we demonstrate the delivery of a predefined entangled state on the nodes irrespective of the heralding detection pattern. Addressing key scaling challenges and being compatible with different qubit systems, our architecture establishes a generic platform for exploring metropolitan-scale quantum networks.

Fig. 1.. The metropolitan-scale quantum link.

Cartographic layout of the distant quantum link and the route of the deployed fiber bundle, with similar quantum processor nodes in Delft and The Hague. Fiber length between node Delft and midpoint is 15 km and between node The Hague and midpoint is 10 km, with losses on the quantum channels at 5.6 and 5.2 dB, respectively. Inset to the quantum processor are the used qubit energy levels where the qubit is encoded in the electronic ground state addressable with microwave (MW) pulses, and the spin-selective optical transition (λ = 637nm) is used for entanglement generation and state readout.

Fig. 2.. Quantum node components and metropolitan-scale stabilization performance.

(A) Detailed components of the quantum nodes and fiber link connections. A microcontroller (μc) orchestrates the experiment, which, together with an arbitrary waveform generator (AWG), shapes laser- and microwave pulses, all synchronized by a heartbeat (HB) generator. Solid-state qubit entangled photon emission and stabilization light from each node is converted to the telecom L-band by the NORA (ppLN)–based QFC in node Delft (node The Hague) and sent to a central midpoint. There, long distance qubit-qubit entanglement is heralded via single photon measurement [superconducting nanowire single photon detector (SNSPD), efficiency ≈ 60%, darkcount rate ≈ 5 s⁻¹] with detection outcomes fed back in real-time. The stabilization light is used for phase locking at the nodes (θ₁, θ₂), at the midpoint (θ₃, θ₄, θ₅), phase-lock desaturation to the QFC pump lasers at the nodes (ν), and polarization stabilization via an electronic polarization controller (EPC). The performance of stabilization over the deployed link over 24 hours is shown for (B) time of arrival, (C) phase and frequency, and (D) polarization. Hardware providing active feedback (header) keeps these parameter that are drifting over time (line histogram) stable (shaded histograms) by enabling continuous feedback faster than the experienced drifts (insets). Vertical lines show the modeled impact on fidelity and rate.

Fig. 3.. Postselected entanglement over the deployed link.

(A) Space-time diagram depicting the generation of entanglement in postselection. Horizontal gray lines indicate the periodic heartbeat of 100 kHz. Local qubit control used to generate entanglement and perform state readout (pop-out) all fit within one heartbeat period of 10 μs. A local phase (LP) pulse is followed by spin-photon entanglement (SPE) generation, an echo, and basis selection microwave pulse. Last, the state is readout (RO). (B) Outcome of correlation measurements, with different detector signature for the top and bottom panels. We show the qubit-qubit readout outcomes per correlators (left), as well as the resulting values per correlator (right). The calculated state fidelity is given inside each figure. The number in parentheses indicates the amount of events recorded for that correlator. Horizontal gray bars indicate the theoretical model. (C) Average state fidelity (left vertical axis) and entanglement generation rate (right vertical axis) for varying photon acceptance window length. Circling indicates the window used in (B), and the black solid line is a model (see the Supplementary Materials). Inset shows signal-to-noise ratio for the various window lengths. All measurement outcomes are corrected for tomography readout errors, and error bars are 1 SD.

Fig. 4.. Fully heralded entanglement over the deployed link.

(A) Space-time diagram of fully heralded entanglement generation. An attempt is successful upon registering a heralding signal at the polling time, after which a feed-forward is applied on the qubit, and readout is performed. The absence of a heralding signal communicates a failed attempt, where we retry for a maximum of 228 attempts or until success. Pop-out depicts the local qubit control, basis selection, and readout pulses. The time between spin-photon entanglement, heralding poll and basis selection is node dependent. (B) Hahn-echo experiment on the communication qubit, showing the revivals of the coherence (39). The solid vertical line indicates the heralding poll, and the dotted line indicates the time of the basis selection. All times are with respect to echo sequence start. (C) Correlation measurement for full heralding, showing both detector outcomes delivering the same Ψ⁻ state. Top (bottom) plot shows events per detector (combined). Bars indicate data, and the number in parentheses indicate the amount of events. Horizontal lines indicate the theoretical model. (D) Average state fidelity (left axis) and entanglement generation rate (right axis) for varying photon acceptance window length. Circling indicates the window used in (C), and the black line is a model (see the Supplementary Materials). Inset shows signal-to-noise ratio (SNR) for respective window lengths. Measurement outcomes are corrected for tomography readout errors, and error bars are 1 SD.