• Krantz, P. et al. A quantum engineer’s guide to superconducting qubits. Appl. Phys. Rev. 6, 021318 (2019).

    Article 

    Google Scholar
     

  • Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Rev. Mod. Phys. 93, 025005 (2021).

    Article 
    MathSciNet 

    Google Scholar
     

  • Google Quantum AI and Collaborators et al. Quantum error correction below the surface code threshold. Nature 638, 920–926 (2025).

    Article 

    Google Scholar
     

  • Bravyi, S., Dial, O., Gambetta, J. M., Gil, D. & Nazario, Z. The future of quantum computing with superconducting qubits. J. Appl. Phys. 132, 160902 (2022).

    Article 

    Google Scholar
     

  • Kurpiers, P. et al. Deterministic quantum state transfer and remote entanglement using microwave photons. Nature 558, 264–267 (2018).

    Article 

    Google Scholar
     

  • Axline, C. J. et al. On-demand quantum state transfer and entanglement between remote microwave cavity memories. Nat. Phys. 14, 705–710 (2018).

    Article 

    Google Scholar
     

  • Campagne-Ibarcq, P. et al. Deterministic remote entanglement of superconducting circuits through microwave two-photon transitions. Phys. Rev. Lett. 120, 200501 (2018).

    Article 

    Google Scholar
     

  • Leung, N. et al. Deterministic bidirectional communication and remote entanglement generation between superconducting qubits. NPJ Quantum Inf. 5, 18 (2019).

    Article 

    Google Scholar
     

  • Magnard, P. et al. Microwave quantum link between superconducting circuits housed in spatially separated cryogenic systems. Phys. Rev. Lett. 125, 260502 (2020).

    Article 

    Google Scholar
     

  • Storz, S. et al. Loophole-free bell inequality violation with superconducting circuits. Nature 617, 265–270 (2023).

    Article 

    Google Scholar
     

  • Qiu, J. et al. Deterministic quantum state and gate teleportation between distant superconducting chips. Sci. Bull. 70, 351–358 (2025).

    Article 

    Google Scholar
     

  • Zhong, Y. et al. Deterministic multi-qubit entanglement in a quantum network. Nature 590, 571–575 (2021).

    Article 

    Google Scholar
     

  • Burkhart, L. D. et al. Error-detected state transfer and entanglement in a superconducting quantum network. PRX Quantum 2, 030321 (2021).

    Article 

    Google Scholar
     

  • Niu, J. et al. Low-loss interconnects for modular superconducting quantum processors. Nat. Electron. 6, 235–241 (2023).

    Article 

    Google Scholar
     

  • Kannan, B. et al. On-demand directional microwave photon emission using waveguide quantum electrodynamics. Nat. Phys. 19, 394–400 (2023).

    Article 

    Google Scholar
     

  • Mollenhauer, M., Irfan, A., Cao, X., Mandal, S. & Pfaff, W. A high-efficiency elementary network of interchangeable superconducting qubit devices. Nat. Electron. 8, 610–619 (2025).

    Article 

    Google Scholar
     

  • Song, J. et al. Realization of high-fidelity perfect entanglers between remote superconducting quantum processors. Phys. Rev. Lett. 135, 050603 (2025).

    Article 

    Google Scholar
     

  • Almanakly, A. et al. Deterministic remote entanglement using a chiral quantum interconnect. Nat. Phys. 21, 825–830 (2025).

    Article 

    Google Scholar
     

  • Deng, X. et al. Long-range zz interaction via resonator-induced phase in superconducting qubits. Phys. Rev. Lett. 134, 020801 (2025).

    Article 

    Google Scholar
     

  • Habraken, S. J. M., Stannigel, K., Lukin, M. D., Zoller, P. & Rabl, P. Continuous mode cooling and phonon routers for phononic quantum networks. New J. Phys. 14, 115004 (2012).

    Article 
    MathSciNet 

    Google Scholar
     

  • Xiang, Z.-L., Zhang, M., Jiang, L. & Rabl, P. Intracity quantum communication via thermal microwave networks. Phys. Rev. X 7, 11035 (2017).


    Google Scholar
     

  • Vermersch, B., Guimond, P.-O., Pichler, H. & Zoller, P. Quantum state transfer via noisy photonic and phononic waveguides. Phys. Rev. Lett. 118, 133601 (2017).

    Article 

    Google Scholar
     

  • Yam, W. K. et al. Cryogenic microwave link for quantum local area networks. NPJ Quantum Inf. 11, 87 (2025).

    Article 

    Google Scholar
     

  • Albanese, B. et al. Radiative cooling of a spin ensemble. Nat. Phys. 16, 751–755 (2020).

    Article 

    Google Scholar
     

  • Xu, M. et al. Radiative cooling of a superconducting resonator. Phys. Rev. Lett. 124, 33602 (2020).

    Article 

    Google Scholar
     

  • Wang, Z. et al. Quantum microwave radiometry with a superconducting qubit. Phys. Rev. Lett. 126, 180501 (2021).

    Article 

    Google Scholar
     

  • Xiang, Z.-L., Ashhab, S., You, J. Q. & Nori, F. Hybrid quantum circuits: superconducting circuits interacting with other quantum systems. Rev. Mod. Phys. 85, 623–653 (2013).

    Article 

    Google Scholar
     

  • Clerk, A. A., Lehnert, K. W., Bertet, P., Petta, J. R. & Nakamura, Y. Hybrid quantum systems with circuit quantum electrodynamics. Nat. Phys. 16, 257–267 (2020).

    Article 

    Google Scholar
     

  • Huang, G., Beccari, A., Engelsen, N. J. & Kippenberg, T. J. Room-temperature quantum optomechanics using an ultralow noise cavity. Nature 626, 512–516 (2024).

    Article 

    Google Scholar
     

  • Koch, J. et al. Charge-insensitive qubit design derived from the cooper pair box. Phys. Rev. A 76, 042319 (2007).

    Article 

    Google Scholar
     

  • Chen, Y. et al. Qubit architecture with high coherence and fast tunable coupling. Phys. Rev. Lett. 113, 220502 (2014).

    Article 

    Google Scholar
     

  • Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Phys. Rev. Lett. 112, 190504 (2014).

    Article 

    Google Scholar
     

  • Chang, H.-S. et al. A fast and large bandwidth superconducting variable coupler. Appl. Phys. Lett. 117, 244001 (2020).

    Article 

    Google Scholar
     

  • Jin, X. Y. et al. Thermal and residual excited-state population in a 3D transmon qubit. Phys. Rev. Lett. 114, 240501 (2015).

    Article 

    Google Scholar
     

  • Scigliuzzo, M. et al. Primary thermometry of propagating microwaves in the quantum regime. Phys. Rev. X 10, 41054 (2020).


    Google Scholar
     

  • Lvov, D. S., Lemziakov, S. A., Ankerhold, E., Peltonen, J. T. & Pekola, J. P. Thermometry based on a superconducting qubit. Phys. Rev. Appl. 23, 54079 (2025).

    Article 

    Google Scholar
     

  • Wootters, W. K. Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245–2248 (1998).

    Article 

    Google Scholar
     

  • Ramette, J., Sinclair, J., Breuckmann, N. P. & Vuletic, V. Fault-tolerant connection of error-corrected qubits with noisy links. NPJ Quantum Inf. 10, 58 (2024).

    Article 

    Google Scholar
     

  • Clauser, J. F., Horne, M. A., Shimony, A. & Holt, R. A. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880–884 (1969).

    Article 

    Google Scholar
     

  • Petit, L. et al. Universal quantum logic in hot silicon qubits. Nature 580, 355–359 (2020).

    Article 

    Google Scholar
     

  • Yang, C. H. et al. Operation of a silicon quantum processor unit cell above one kelvin. Nature 580, 350–354 (2020).

    Article 

    Google Scholar
     

  • Camenzind, L. C. et al. A hole spin qubit in a fin field-effect transistor above 4 kelvin. Nat. Electron. 5, 178–183 (2022).

    Article 

    Google Scholar
     

  • Huang, J. Y. et al. High-fidelity spin qubit operation and algorithmic initialization above 1 K. Nature 627, 772–777 (2024).

    Article 

    Google Scholar
     

  • Dijkema, J. et al. Cavity-mediated iSWAP oscillations between distant spins. Nat. Phys. 21, 168–174 (2025).

    Article 

    Google Scholar
     

  • Aspelmeyer, M., Kippenberg, T. J. & Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391–1452 (2014).

    Article 

    Google Scholar
     

  • Mirhosseini, M., Sipahigil, A., Kalaee, M. & Painter, O. Superconducting qubit to optical photon transduction. Nature 588, 599–603 (2020).

    Article 

    Google Scholar
     

  • Tu, H. T. et al. High efficiency coherent microwave-to-optics conversion via off-resonant scattering. Nat. Photon. 16, 291–296 (2022).

    Article 

    Google Scholar
     

  • Kumar, A. et al. Quantum-enabled millimetre wave to optical transduction using neutral atoms. Nature 615, 614–619 (2023).

    Article 

    Google Scholar
     

  • Sahu, R. et al. Entangling microwaves with light. Science 380, 718–721 (2023).

    Article 
    MathSciNet 

    Google Scholar
     

  • Jiang, W. et al. Optically heralded microwave photon addition. Nat. Phys. 19, 1423–1428 (2023).

    Article 

    Google Scholar
     

  • Meesala, S. et al. Quantum entanglement between optical and microwave photonic qubits. Phys. Rev. X 14, 031055 (2024).


    Google Scholar
     

  • Anferov, A., Harvey, S. P., Wan, F., Simon, J. & Schuster, D. I. Superconducting qubits above 20 GHz operating over 200 mK. PRX Quantum 5, 30347 (2024).

    Article 

    Google Scholar
     

  • Anferov, A., Wan, F., Harvey, S. P., Simon, J. & Schuster, D. I. Millimeter-wave superconducting qubit. PRX Quantum 6, 020336 (2025).

    Article 

    Google Scholar
     

  • Sun, L. et al. Measurements of quasiparticle tunneling dynamics in a band-gap-engineered transmon qubit. Phys. Rev. Lett. 108, 230509 (2012).

    Article 

    Google Scholar
     

  • Wang, C. et al. Measurement and control of quasiparticle dynamics in a superconducting qubit. Nat. Commun. 5, 5836 (2014).

    Article 

    Google Scholar
     

  • Stas, P.-J. et al. Robust multi-qubit quantum network node with integrated error detection. Science 378, 557–560 (2022).

    Article 

    Google Scholar
     

  • Grebel, J. et al. Bidirectional multiphoton communication between remote superconducting nodes. Phys. Rev. Lett. 132, 47001 (2024).

    Article 

    Google Scholar
     

  • Valenzuela, S. O. et al. Microwave-induced cooling of a superconducting qubit. Science 314, 1589–1592 (2006).

    Article 

    Google Scholar
     

  • Gely, M. F. et al. Observation and stabilization of photonic fock states in a hot radio-frequency resonator. Science 363, 1072–1075 (2019).

    Article 

    Google Scholar
     

  • Aamir, M. A. et al. Thermally driven quantum refrigerator autonomously resets a superconducting qubit. Nat. Phys. 21, 318–323 (2025).

    Article 

    Google Scholar
     

  • Steffen, M. et al. Measurement of the entanglement of two superconducting qubits via state tomography. Science 313, 1423–1425 (2006).

    Article 
    MathSciNet 

    Google Scholar
     

  • Diamond, S. & Boyd, S. CVXPY: a Python-embedded modeling language for convex optimization. J. Mach. Learn. Res. 17, 2909–2913 (2016).

    MathSciNet 

    Google Scholar
     

  • Neeley, M. et al. Process tomography of quantum memory in a Josephson-phase qubit coupled to a two-level state. Nat. Phys. 4, 523–526 (2008).

    Article 

    Google Scholar
     

  • Massar, S. & Popescu, S. Optimal extraction of information from finite quantum ensembles. Phys. Rev. Lett. 74, 1259–1263 (1995).

    Article 
    MathSciNet 

    Google Scholar
     

  • Horodecki, M., Horodecki, P. & Horodecki, R. General teleportation channel, singlet fraction, and quasidistillation. Phys. Rev. A 60, 1888–1898 (1999).

    Article 
    MathSciNet 

    Google Scholar
     

  • Steffen, L. et al. Deterministic quantum teleportation with feed-forward in a solid state system. Nature 500, 319–322 (2013).

    Article 

    Google Scholar