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Multiplexed entanglement of multi-emitter quantum network nodes

Nature volume 639, pages 54–59 (2025)Cite this article

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Abstract

Quantum networks that distribute entanglement among remote nodes will unlock transformational technologies in quantum computing, communication and sensing1,2,3,4. However, state-of-the-art networks5,6,7,8,9,10,11,12,13,14 use only a single optically addressed qubit per node; this constrains both the quantum communication bandwidth and memory resources, greatly impeding scalability. Solid-state platforms15,16,17,18,19,20,21,22,23,24 provide a valuable resource for multiplexed quantum networking in which multiple spectrally distinguishable qubits can be hosted in nano-scale volumes. Here we harness this resource by implementing a two-node network consisting of several rare-earth ions coupled to nanophotonic cavities25,26,27,28,29,30,31. This is accomplished with a protocol that entangles distinguishable 171Yb ions through frequency-erasing photon detection combined with real-time quantum feedforward. This method is robust to slow optical frequency fluctuations occurring on timescales longer than a single entanglement attempt: a universal challenge amongst solid-state emitters. We demonstrate the enhanced functionality of these multi-emitter nodes in two ways. First, we mitigate the bottlenecks to the entanglement distribution rate through multiplexed entanglement of two remote ion pairs32,33. Second, we prepare multipartite W-states comprising three distinguishable ions as a resource for advanced quantum networking protocols34,35. These results lay the groundwork for scalable quantum networking based on rare-earth ions.

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Fig. 1: Schematic of a quantum network link based on multiple 171Yb qubits in nanophotonic cavities.
Fig. 2: Remote entanglement generation between two 171Yb qubits.
Fig. 3: Multiplexed entanglement rate enhancement using two pairs of 171Yb spin qubits.
Fig. 4: Tripartite W-state generation between three 171Yb spin qubits.

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Data availability

The data that support the findings of this study are available from the corresponding author upon request.

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Acknowledgements

This work was funded primarily by the Air Force Office of Scientific Research (grant no. FA9550-22-1-0178) and the Institute of Quantum Information and Matter, an NSF Physics Frontiers Center (PHY-1733907) with support from the Moore Foundation. We also acknowledge funding from NSF 2210570 and NSF 2137984. The device nanofabrication was performed at the Kavli Nanoscience Institute at the California Institute of Technology. A.R. acknowledges support from the Eddleman Graduate Fellowship. C.-J.W. acknowledges support from the J. Yang and Family Foundation and a Taiwanese government scholarship to study abroad. E.G. acknowledges support from the National Science Foundation Graduate Research Fellowship under grant no. 2139433 and the National Gem Consortium. S.L.N.H. acknowledges support from the AWS Quantum Postdoctoral Fellowship. J.C. acknowledges support from the Terman Faculty Fellowship at Stanford. We thank E. Paul for help with the experimental setup; J. Thompson and M. T. Uysal for discussion related to the entanglement protocol; J. Borregaard, D. Lukin, T. Xie, M. Lei, R. Fukumori, E. Liu and B. Grinkemeyer for useful discussions; and J. Rochman, T. Zheng, S. Gu and B. Baspinar for help with nanofabrication.

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Author notes

  1. A. Ruskuc

    Present address: Department of Physics, Harvard University, Cambridge, MA, USA

  2. These authors contributed equally: A. Ruskuc, C.-J. Wu

Authors and Affiliations

  1. Thomas J. Watson, Sr, Laboratory of Applied Physics, California Institute of Technology, Pasadena, CA, USA

    A. Ruskuc, C.-J. Wu, E. Green, S. L. N. Hermans, W. Pajak & A. Faraon

  2. Kavli Nanoscience Institute, California Institute of Technology, Pasadena, CA, USA

    A. Ruskuc, C.-J. Wu, E. Green, S. L. N. Hermans, W. Pajak & A. Faraon

  3. Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA

    A. Ruskuc, C.-J. Wu, E. Green, S. L. N. Hermans, W. Pajak & A. Faraon

  4. Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, CA, USA

    C.-J. Wu

  5. Department of Electrical Engineering, Stanford University, Stanford, CA, USA

    J. Choi

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Contributions

A.R. and A.F. conceived the experiments. A.R., C.-J.W. and E.G. fabricated the devices. A.R., C.-J.W. and W.P. performed the experiments and analysed the data. A.R., C.-J.W., S.L.N.H. and J.C. contributed to the interpretation of the data. A.R., C.-J.W. and A.F. wrote the paper with input from all authors. A.F. supervised the project.

Corresponding author

Correspondence to A. Faraon.

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Extended data figures and tables

Extended Data Fig. 1 Hong-Ou-Mandel indistinguishability measurement on photons emitted by two remote 171Yb ions.

a, Experimental setup for Hong-Ou-Mandel (HOM) measurements. Orthogonally polarized photons emitted from the A transitions of two ions with frequency difference ω2 − ω1 = Δω12 ≈ 2π × 33 MHz (denoted \(| V,{\omega }_{1}\rangle \) and \(| H,{\omega }_{2}\rangle \)) are incident on a polarizing beamsplitter (PBS). Photon detections on two superconducting nanowire single photon detectors (SNSPD 1 and SNSPD 2 with detection times t1 and t2, respectively) are correlated. We maximize the HOM contrast by rotating the half waveplate (λ/2). The ions’ optical frequencies drift on week-long timescales, hence Δω12 is slightly different here compared to Fig. 2. b, After optical excitation of both ions with resonant π pulses, photon coincidences are histogrammed with respect to the detection time difference (Δt = t2 − t1) using a 160 ns bin size. We don’t see any signature of HOM interference due to the ≈ 2π × 33 MHz frequency difference, rendering the photons distinguishable. c, Frequency information is erased by reducing the bin size below 1/Δω12. We use a bin size of 4 ns and observe a quantum beat in coincidences, i.e. an oscillation between photon bunching and anti-bunching, at the optical frequency difference. Note that the number of coincidences has been re-normalized by the bin width to provide a direct comparison with b. d, We plot the number of coincidences using a 4 ns bin size but only at the trough of each oscillation (i.e. at the points of maximum anti-bunching), thereby recovering a conventional Hong-Ou-Mandel dip. Dip width is limited by optical Ramsey decoherence of the two ions between consecutive emission events. e, We extract a HOM visibility from the oscillation contrast, this is averaged over a two-sided window with width W i.e. −W/2 < Δt < W/2. For the smallest window size of 6 ns, a 96 ± 2% visibility is achieved. Solid lines are fits to a model detailed in Supplementary Information section III.

Extended Data Fig. 2 Measuring the optical spectral diffusion correlation timescale of a 171Yb ion.

a, Optical spectral diffusion on timescales longer than the optical lifetime is measured using a delayed echo pulse sequence. First, a superposition between the \(| 0\rangle \) and \(| e\rangle \) states, \(|\psi \rangle =1/\sqrt{2}(|0\rangle +|e\rangle )\), is used to probe the initial optical frequency, ω(0). A free evolution time, τ, yields the state \(|\psi \rangle \approx 1/\sqrt{2}(|0\rangle +|e\rangle {e}^{-i\omega (0)\tau })\). Next, the state is mapped to the qubit manifold, \(|\psi \rangle \approx 1/\sqrt{2}(|0\rangle +|1\rangle {e}^{-i\omega (0)\tau })\), and stored for a duration TW using an XY-8 pulse sequence with an odd number of pulses (2N + 1) that have a separation of 2τs = 5.8 μs. During this wait time the optical frequency undergoes spectral diffusion with correlation timescale τc (red line). Finally, the optical frequency is probed for a second time by mapping the qubit state back on to the optical transition. After a free evolution time, τ, the quantum state is \(|\psi \rangle \approx 1/\sqrt{2}(|0\rangle +|1\rangle {e}^{-i[\omega ({T}_{W})-\omega (0)]\tau })\). When the wait time is much less than the optical correlation timescale (TW ≪ τc), ω(TW) − ω(0) ≈ 0 and coherence is preserved. However, when TW ≫ τc, ω(TW) and ω(0) are uncorrelated, optical coherence isn’t rephased and the measurement contrast reduces. b, Experimental results plotting the final state coherence, C, against wait time, TW, with logarithmic y axis and fixed τ = 1.5 μs. We fit a decay profile with form \(\log (C)=a-b(1-{e}^{-{T}_{W}/{\tau }_{c}})-({T}_{W}/{T}_{2,s})\) (solid line) where a, b and τc are free parameters, and T2,s is the spin XY-8 coherence time, obtained from independent measurements. Note that the initial coherence contrast, a, is limited by optical decay during the two free evolution periods of duration τ. The red and green regions correspond to decays attributed to optical decorrelation and spin decoherence, respectively. We extract an optical frequency correlation timescale of τc = 1.42 ± 0.04 ms.

Extended Data Fig. 3 Experimental setup for remote entanglement generation.

a, Nanophotonic cavities (Devices 1 and 2) are cooled by a 3He cryostat to 0.5 K. Optical control of ions’ A and F transitions is achieved using lasers L1, L3 and L4 which are modulated by a series of acousto-optic modulator (AOM) setups for pulse generation and frequency tuning (AOM 3–8). All lasers are frequency-locked to a reference cavity. Photons exiting the devices are combined on a polarizing beamsplitter (PBS 1), AOM 9 routes photons towards the Detection setup (depicted in b). Heterodyne phase measurement of the optical path difference between Devices 1 and 2 is achieved using light pulses from laser L2 which are routed by AOM 9 to an avalanche photodiode (APD) for measurement. b, There are three possible detection setups used for entanglement heralding and readout. Setup 1 consists of a single superconducting nanowire single photon detector (SNSPD) and heralds entanglement of two ions within the same device. Setup 2 uses a single SNSPD combined with a time-delayed interferometer to entangle two ions with different optical frequencies located in separate devices. Setup 3 uses two SNSPDs for entanglement experiments involving more than two ions. c, Setups AOM 5 and 6 each consist of a single AOM in double pass configuration and enable simultaneous, phase-stable driving of ions in the same device. d, Setups AOM 7 and 8 consist of three acousto-optic modulators, each in double pass configuration, enabling pulse generation with a 2π × 600 MHz optical frequency tuning range. e, Microwave setup for driving the ground and excited state spin transitions at ≈ 2π × 675 MHz and ≈ 2π × 3.37 GHz, respectively. The ground state (qubit) pulses are generated by heterodyne modulation combined with filters for image rejection before being amplified, combined with the excited state pulses on a diplexer and sent to the device.

Extended Data Fig. 4 Pulse sequence for remote entanglement generation between two 171Yb spin qubits.

a, Energy levels of 171Yb ions at B = 0 with optical and spin transitions indicated. A and E optical transitions have polarization aligned with the cavity and are Purcell enhanced. The \(| {\rm{e}}\rangle \) state referred to in the main text was labelled \(| {0}_{e}\rangle \) in previous work. b, Flow chart showing steps for remote entanglement generation between Ions 1 and 2. c, \(| {\rm{aux}}\rangle \) initialization involves 400 pulses, each 2.5 μs long, applied alternately to the F1 and F2 transitions of the two ions, emptying \(| {\rm{aux}}\rangle \) into the qubit manifold via decay on E. d, Initialization into \(| 0\rangle \) is achieved with pairs of consecutively applied π pulses on A and fe followed by decay on E. The optical path phase difference, ΔΦ, is measured and compensated by a Z rotation, Θ, on Ion 1’s A transition (defined in Methods). A weak superposition is prepared on each qubit, the ions are optically excited and entanglement is heralded via detection of a single photon at stochastic time t0 in a window of duration τh. e, After several periods of dynamical decoupling (inter-pulse separation 2τs = 5.8 μs) the spin coherence is rephased for a duration of τh − t0. Optical coherence is rephased for a duration t0 between two A transition π pulses. A Z rotation is applied to Ion 2’s qubit by angle \(\Delta {\widetilde{\omega }}_{12}{t}_{0}\) where \(\Delta {\widetilde{\omega }}_{12}\) is the A transition driving frequency difference between the two ions. f, Each Ion’s state is read out via repeated excitation on the A transition followed by photodetection. We use four readout periods: the first two determine whether the ions are in \(| 1\rangle \). A qubit π pulse is applied and the final two periods measure \(| 0\rangle \). States are ascribed according to conditions in the table, all other photodetection outcomes are discarded.

Extended Data Fig. 5 Stabilizing the relative path length between two remote quantum network nodes.

a, Simplified optical setup and pulse sequence. The stabilization laser, L2, at 987.9 nm measures the relative optical path phase. This is achieved using AOM 2, 3 and 4 to generate 10 μs long pulses with a 2π × 5 MHz frequency difference that travel along the two separate device paths with distances L1 and L2. AOM 9 routes the pulses to an avalanche photodetector (APD) which detects the resulting beat-note phase, thereby measuring the optical path phase difference, ΔΦ. After a delay of 30 μs, the optical phase is probed using L1 at 984.5 nm using pulses generated by AOM 1, 3 and 4 with a 2π × 26 MHz frequency difference. However, this time, the driving phase of AOM 3 is adjusted to correct the optical phase difference by an angle Θ (defined in Methods), thereby counteracting phase drift and rendering the optical phase constant between consecutive probe periods. The optical phase during each probe period is measured using the APD. b, With the phase correction turned off (Θ = 0), we measure the optical phase stability by plotting the RMS difference between values of ΔΦ in probe periods of varying separation, yielding a 1/e phase correlation timescale of ≈ 282 μs. c, The resulting Fourier transform of the optical phase noise with the correction, Θ, turned off and on are shown in the top and bottom panels, respectively. d, With the phase stabilization turned on, a normalized histogram of the optical phases during the probe periods yields a Gaussian distribution with standard deviation 0.037 × 2π rad, corresponding to an entangled state fidelity limitation of \({\mathcal{F}} < 0.987\). e, The probe pulses are attenuated to the single-photon level and detected using a superconducting nanowire single photon detector (SNSPD), the resulting contrast of 0.944 verifies that SNSPD timing jitter does not contribute significantly to these measurements.

Extended Data Fig. 6 Lifetime-limited entanglement using the dynamic rephasing protocol.

After heralding an entangled state between Ions 1 and 2 and applying the dynamic rephasing protocol described in the main text, the entangled state coherence is probed via a measurement of the X-basis parity expectation value, \(\langle \widehat{X}\widehat{X}\rangle \), correlated with the photon emission time, t0. The coherence oscillates at the relative difference in driving laser frequencies, \(\Delta {\widetilde{\omega }}_{12}\), and undergoes an exponential decay with a 1/e timescale of 970 ± 30 ns, limited by the Purcell-enhanced optical lifetimes of the two ions. Markers and solid lines correspond to experimental data and simulations, respectively, as detailed in Supplementary Information section VII.

Extended Data Fig. 7 Analysis of fidelities and rates when entangling two remote 171Yb spin qubits.

a, Entanglement fidelity analysis. We characterize the entanglement fidelity by performing simulations based on independently measured experimental parameters. This leads to a simulated fidelity of \({\mathcal{F}}=0.729\,\pm \,0.004\) (dashed vertical line with grey region for error bar), consistent with experimental results. We characterize the individual fidelity contributions in two ways: first by simulating the fidelity when a given error source is removed (blue bars), and secondly, by simulating the fidelity when the error source is exclusively present (orange bars). We find three dominant sources of error: undetected spontaneous emission during the dynamic rephasing protocol; noise counts i.e. photons that don’t originate from our two 171Yb ions; and errors in the optical gates applied to the ions. Error bars are obtained by performing 50 simulation repetitions, each with input parameters sampled from Gaussian distributions with mean and standard deviation given by the experimentally determined values and errors presented in Supplementary Information section V. More detail on the fidelity estimation can be found in Supplementary Information sections VII and VIII. b, Entanglement rate analysis. The predicted entanglement rate of \({\mathcal{R}}=3.48\,\pm \,0.03\) Hz is obtained from the experiment repetition rate, 12.3 kHz, multiplied by the entanglement success probability, (2.83 ± 0.02) × 10−4. A slight deviation from the measured result is due to slow drift of experimental parameters on the timescale of several days between measurement and calibration. The dominant limitation to the experiment repetition rate arises from the qubit initialization time, requiring 33 μs per attempt. We also list contributions to the success rate consisting of: the photon detection efficiency, the fraction of photons within the 500 ns acceptance window, and the weak superposition states used in the single photon heralding protocol. More detail on this estimation can be found in Supplementary Information section IX.

Extended Data Fig. 8 Entanglement heralding between two remote 171Yb ions using a two photon protocol.

a, Pulse sequence for remote entanglement generation. Each qubit is prepared in a superposition state, \(1/\sqrt{2}(| 0\rangle +| 1\rangle )\), and optically excited in two rounds, separated by a qubit π pulse. Photon detections in both rounds at stochastic times t0 and t1 (measured relative to the start of their respective heralding windows) carve out \(| 00\rangle \) and \(| 11\rangle \), respectively, thereby heralding entanglement. Subsequently, a dynamical decoupling sequence is applied with inter-pulse spacing 2τs = 5.8 μs. In cases where t1 < t0 optical and spin coherences are rephased for durations τh − t0 + t1 and t0 − t1, respectively, after an even number of dynamical decoupling periods. In cases where t1 > t0 optical and spin coherences are rephased for durations τh − t1 + t0 and t1 − t0, respectively, after an odd number of dynamical decoupling periods. Note that we also apply a Z rotation to Ion 2’s qubit by an angle \(\Delta {\widetilde{\omega }}_{12}({t}_{0}-{t}_{1})\) (not labelled). b, Entanglement rate and fidelity plotted against window size, W, where heralding events are accepted under the condition ∣t1 − t0∣ < W/2. The smallest window size, W = 200 ns, leads to a fidelity and rate of \({\mathcal{F}}=0.84\,\pm \,0.03\) and \({\mathcal{R}}=17\) mHz, respectively. The largest window size of W = 1.6 μs corresponds to a fidelity and rate of \({\mathcal{F}}=0.75\,\pm \,0.02\) and \({\mathcal{R}}=91\) mHz, respectively. c, Density matrix obtained via maximum likelihood tomography with a window size W = 600 ns (vertical dashed line in b) leading to a fidelity and rate of \({\mathcal{F}}=0.81\,\pm \,0.02\) and \({\mathcal{R}}=49\) mHz, respectively.

Extended Data Fig. 9 Multiplexed entanglement: sequence detail and parity measurements.

a, After parallelized initialization of all four ions, two consecutive entanglement attempts are performed, first on Pair 2 (consisting of Ions 3 and 4), then on Pair 1 (consisting of Ions 1 and 2), as depicted in the pulse sequences. We note that all four ions have frequency-resolved optical transitions enabling independent optical control. However, due to the narrow distribution of qubit transition frequencies, all microwave control pulses are globally applied to ions in the same device. If either entanglement attempt is successful, the sequence proceeds to apply dynamic rephasing and phase compensation protocols exclusively to the corresponding ion pair. Details of these pulse sequences can be found in Extended Data Fig. 4. Finally, we measure two-qubit populations of the entangled pair in the XX, YY or ZZ bases. b, We segregate our multiplexed experimental results into two separate data sets corresponding to successful heralding attempts for Pair 1 and Pair 2. For each data set we plot population histograms in the XX, YY and ZZ bases for a photon acceptance window size of 500 ns with corresponding fidelities of \({{\mathcal{F}}}_{{\rm{m}}{\rm{u}}{\rm{l}}{\rm{t}}}^{(1)}=0.700\,\pm \,0.005\) and \({{\mathcal{F}}}_{{\rm{m}}{\rm{u}}{\rm{l}}{\rm{t}}}^{(2)}=0.668\,\pm \,0.006\) for Pair 1 and Pair 2, respectively.

Extended Data Fig. 10 Heralded entanglement between two 171Yb ions in the same nanophotonic cavity.

a, The entanglement protocol requires single-qubit Z rotations which cannot be achieved using global microwave driving. Instead, we utilize a differential a.c. Stark shift of the qubits generated by an optical pulse with Rabi frequency Ω, oppositely detuned from the ions’ optical transition frequencies. We embed these pulses in alternate periods of an XY-8 dynamical decoupling sequence, preserving qubit coherence whilst simultaneously accumulating a differential phase39. The sequence consists of 32 π pulses separated by 2τs = 5.8 μs; we vary the differential phase by adjusting the a.c. Stark intensity which scales with Ω2. b, We verify the a.c. Stark control in two ways. First, we independently initialize Ions 1 and 3 in superposition states, apply the a.c. Stark sequence, and measure the spin populations \(\langle \widehat{X}\rangle \) and \(\langle \widehat{Y}\rangle \). We calculate the difference between the qubits’ phase rotations, Φa.c., and plot this for different a.c. Stark intensities, Ω2 (solid line). We also probe the differential phase using heralded Bell states, detailed in c (markers), these independently derived measurements exhibit close correspondence. c, After heralding an entangled state on Ions 1 and 3, we apply an a.c. Stark sequence prior to measurement. This adds a Bell state phase and corresponding shift to the parity oscillation of coherence with photon emission time, t0. We measure this shift for different a.c. Stark intensity values, Ω2; the four parity oscillations correspond to the labelled markers in b. d, We dynamically adjust the a.c. Stark intensity in each experiment to counteract the stochastic heralding phase \(\Delta {\widetilde{\omega }}_{13}{t}_{0}\), rendering the entangled state coherence independent of t0. We accept photons in a 500 ns window and perform maximum likelihood tomography on the quantum state. We plot the resulting density matrix which has a fidelity of \({\mathcal{F}}=0.763\,\pm \,0.005\), the heralding rate is \({\mathcal{R}}=4.5\) Hz.

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Ruskuc, A., Wu, CJ., Green, E. et al. Multiplexed entanglement of multi-emitter quantum network nodes. Nature 639, 54–59 (2025). https://doi.org/10.1038/s41586-024-08537-z

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