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# Deterministic quantum state transfer and remote entanglement using microwave photons

## Abstract

Sharing information coherently between nodes of a quantum network is fundamental to distributed quantum information processing. In this scheme, the computation is divided into subroutines and performed on several smaller quantum registers that are connected by classical and quantum channels1. A direct quantum channel, which connects nodes deterministically rather than probabilistically, achieves larger entanglement rates between nodes and is advantageous for distributed fault-tolerant quantum computation2. Here we implement deterministic state-transfer and entanglement protocols between two superconducting qubits fabricated on separate chips. Superconducting circuits3 constitute a universal quantum node4 that is capable of sending, receiving, storing and processing quantum information5,6,7,8. Our implementation is based on an all-microwave cavity-assisted Raman process9, which entangles or transfers the qubit state of a transmon-type artificial atom10 with a time-symmetric itinerant single photon. We transfer qubit states by absorbing these itinerant photons at the receiving node, with a probability of 98.1 ± 0.1 per cent, achieving a transfer-process fidelity of 80.02 ± 0.07 per cent for a protocol duration of only 180 nanoseconds. We also prepare remote entanglement on demand with a fidelity as high as 78.9 ± 0.1 per cent at a rate of 50 kilohertz. Our results are in excellent agreement with numerical simulations based on a master-equation description of the system. This deterministic protocol has the potential to be used for quantum computing distributed across different nodes of a cryogenic network.

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## Acknowledgements

This work was supported by the European Research Council (ERC) through the ‘Superconducting Quantum Networks’ (SuperQuNet) project, by the National Centre of Competence in Research ‘Quantum Science and Technology’ (NCCR QSIT), a research instrument of the Swiss National Science Foundation (SNSF), by ETH Zurich and NSERC, the Canada First Research Excellence Fund and the Vanier Canada Graduate Scholarships.

## Author information

Authors

### Contributions

The experiment was designed and developed by P.K., T.W., P.M. and M.P. The samples were fabricated by J.-C.B., T.W. and S.G. The experiments were performed by P.K., P.M. and T.W. The data were analysed and interpreted by P.K., P.M., B.R., A.B. and A.W. The FPGA firmware and experiment automation was implemented by J.H., Y.S., A.A., S.S., P.M. and P.K. The master-equation simulations were performed by B.R., M.P., P.M. and P.K. The manuscript was written by P.K., P.M., T.W., B.R. and A.W. All authors commented on the manuscript. The project was led by A.W.

### Corresponding authors

Correspondence to P. Kurpiers or A. Wallraff.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data figures and tables

### Extended Data Fig. 1 Overview of remote-entanglement experiments.

a, Entanglement generation rate Γent. b, CHSH–Bell inequality49,50 correlation S. c, Concurrence $${\mathscr{C}}$$. d, Entangled state fidelity $${{\mathscr{F}}}^{{\rm{s}}}$$. The experiments are grouped by physical system: atomic ensembles (‘ae’)12,21,51,52,53, trapped ions (‘ion’)15,17,54,55,56, single-atom Bose–Einstein condensate (‘sab’)57, vibrational state of diamonds (‘vs’)18, rare-Earth-doped crystals (‘rec’)58, single atoms (‘sa’)19,22, nitrogen–vacancy centres (‘nv’)20,36,59,60, superconducting circuits (‘sc’)14,23,24,35,61 or quantum dots (‘qd’)16,62. The colours indicate different implementations: probabilistic unheralded (red), probabilistic heralded (blue), guaranteeing a deterministic delivery of an entangled state at a pre-specified time (yellow) or fully deterministic (green). The plot markers indicate different schemes for realizing the remote interaction: measurement-induced (triangles), single-photon (crosses) or two-photon (squares) interference and detection, direct transfer (diamond) or direct transfer with shaped photons (circles). The lines in c are bounds34 on the concurrence $${\mathscr{C}}$$ calculated from measured CHSH–Bell correlations S. The shaded column highlights this study.

### Extended Data Fig. 2 Micrograph of sample and energy-level diagram.

a, False-colour micrograph of a sample of the same design co-fabricated with the one used for node A. The circuit elements are colour coded as in Fig. 1: transfer circuit (yellow), readout circuit (grey), transmon (orange) and input lines of the transmon and readout circuit (blue). The input to the transfer circuit is used as an auxiliary port to perform resonator spectroscopy in transmission. The inset shows a scanning electron microscopy (SEM) micrograph of the asymmetric SQUID with a ratio of 5:1 between the areas of the Josephson junctions used in the transmon. b, Schematic of the energy-level diagram of the coupled transmon-transfer resonator system. The numerical values of all parameters are listed in Extended Data Table 1.

### Extended Data Fig. 3 a.c. Stark shift and Rabi rate of the $$\left|f,0\right\rangle \leftrightarrow \left|g,1\right\rangle$$ transition.

a, b, Measurement (filled circles) of the a.c. Stark shift Δf0g1/(2π) (a) and the effective coupling $$\widetilde{g}/\left(2{\rm{\pi }}\right)$$ of the $$\left|f,0\right\rangle \leftrightarrow \left|g,1\right\rangle$$ transition (b) versus drive amplitude εf0g1 for sample A (blue) and B (red). The solid lines in a (b) are quadratic (linear) fits to the data30.

### Extended Data Fig. 4 Qutrit single-shot readout characterization.

af, Scatter plot of the measured integrated quadrature values u and v for qutrit A (ac) and B (df) when prepared in state $$\left|g\right\rangle$$ (blue; a, d), $$\left|e\right\rangle$$ (red; b, e) and $$\left|f\right\rangle$$ (green; c, f). We plot only the first 1,000 of the 25,000 repetitions for each state-preparation experiment. The dashed lines are the qutrit-state discrimination thresholds used to obtain the assignment probabilities (numbers, which are also listed in Extended Data Table 2).

### Extended Data Fig. 5 Characterization of entangled states in a two-qutrit basis.

ac, Two-qutrit state tomography: real (a) and imaginary (b) part of the density matrix and expectation values of the Gell–Mann operators λ k (c). The ideal Bell state $$\left|{\psi }^{+}\right\rangle$$ and numerical master-equation simulation are depicted as grey and red outlines, respectively. λ0 denotes the identity operation, λ1,2,3 denote the Pauli matrices $${\sigma }_{x,y,z}^{{\rm{ge}}}$$ in the qubit subspace, λ4,5 correspond to $${\sigma }_{x,y}^{{\rm{gf}}}$$, λ6,7 correspond to $${\sigma }_{x,y}^{{\rm{ef}}}$$ and λ8 is the diagonal matrix $$\left({\sigma }_{z}^{{\rm{ge}}}+2{\sigma }_{z}^{{\rm{ef}}}\right){\rm{/}}\sqrt{3}$$. The trace distance between the measurement and the simulation is 0.107.

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Kurpiers, P., Magnard, P., Walter, T. et al. Deterministic quantum state transfer and remote entanglement using microwave photons. Nature 558, 264–267 (2018). https://doi.org/10.1038/s41586-018-0195-y

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• DOI: https://doi.org/10.1038/s41586-018-0195-y

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