• Kjaergaard, M. et al. Superconducting qubits: current state of play. Annu. Rev. Condens. Matter Phys. 11, 369–395 (2020).

    Article 
    ADS 

    Google Scholar
     

  • Bruzewicz, C. D., Chiaverini, J., McConnell, R. & Sage, J. M. Trapped-ion quantum computing: progress and challenges. Appl. Phys. Rev. 6, 021314 (2019).

    Article 
    ADS 

    Google Scholar
     

  • Henriet, L. et al. Quantum computing with neutral atoms. Quantum 4, 327 (2020).

    Article 

    Google Scholar
     

  • Google Quantum AI and Collaborators Quantum error correction below the surface code threshold. Nature 638, 920-926 (2024).

  • Bluvstein, D. et al. Logical quantum processor based on reconfigurable atom arrays. Nature 626, 58–65 (2024).

    Article 
    ADS 

    Google Scholar
     

  • Georgescu, I. M., Ashhab, S. & Nori, F. Quantum simulation. Rev. Mod. Phys. 86, 153–185 (2014).

    Article 
    ADS 

    Google Scholar
     

  • Daley, A. J. et al. Practical quantum advantage in quantum simulation. Nature 607, 667–676 (2022).

    Article 
    ADS 

    Google Scholar
     

  • Ludlow, A. D., Boyd, M. M., Ye, J., Peik, E. & Schmidt, P. O. Optical atomic clocks. Rev. Mod. Phys. 87, 637–701 (2015).

    Article 
    ADS 

    Google Scholar
     

  • Pezze, L., Smerzi, A., Oberthaler, M. K., Schmied, R. & Treutlein, P. Quantum metrology with nonclassical states of atomic ensembles. Rev. Mod. Phys. 90, 035005 (2018).

    Article 
    ADS 
    MathSciNet 

    Google Scholar
     

  • Bluvstein, D. et al. A quantum processor based on coherent transport of entangled atom arrays. Nature 604, 451–456 (2022).

    Article 
    ADS 

    Google Scholar
     

  • Lamata, L., Parra-Rodriguez, A., Sanz, M. & Solano, E. Digital-analog quantum simulations with superconducting circuits. Adv. Phys.: X 3, 1457981 (2018).


    Google Scholar
     

  • Andersen, T. I. et al. Thermalization and criticality on an analogue–digital quantum simulator. Nature 638, 79–85 (2025).

    Article 
    ADS 

    Google Scholar
     

  • Pedrozo-Peñafiel, E. et al. Entanglement on an optical atomic-clock transition. Nature 588, 414–418 (2020).

    Article 
    ADS 

    Google Scholar
     

  • Kaubruegger, R., Shankar, A., Vasilyev, D. V. & Zoller, P. Optimal and variational multiparameter quantum metrology and vector-field sensing. PRX Quantum 4, 020333 (2023).

    Article 
    ADS 

    Google Scholar
     

  • Marciniak, C. D. et al. Optimal metrology with programmable quantum sensors. Nature 603, 604–609 (2022).

    Article 
    ADS 

    Google Scholar
     

  • Zhou, S., Zhang, M., Preskill, J. & Jiang, L. Achieving the Heisenberg limit in quantum metrology using quantum error correction. Nat. Commun. 9, 78 (2018).

    Article 
    ADS 

    Google Scholar
     

  • Kielinski, T. & Schmidt, P. O. & Hammerer, K. GHZ protocols enhance frequency metrology despite spontaneous decay. Sci. Adv. 10, eadr1439 (2024).

    Article 

    Google Scholar
     

  • Evered, S. J. et al. Probing the Kitaev honeycomb model on a neutral-atom quantum computer. Nature 645, 341–347 (2025).

    Article 
    ADS 

    Google Scholar
     

  • Saffman, M. Quantum computing with atomic qubits and Rydberg interactions: progress and challenges. J. Phys. B 49, 202001 (2016).

    Article 
    ADS 

    Google Scholar
     

  • Reichardt, B. W., et al. Logical computation demonstrated with a neutral atom quantum processor. Preprint at https://arxiv.org/html/2411.11822v1 (2024).

  • Chinnarasu, R. et al. Variational simulation of the Lipkin-Meshkov-Glick model on a neutral atom quantum computer. PRX Quantum 6, 020350 (2025).

    Article 
    ADS 

    Google Scholar
     

  • Browaeys, A. & Lahaye, T. Many-body physics with individually controlled Rydberg atoms. Nat. Phys. 16, 132–142 (2020).

    Article 

    Google Scholar
     

  • Semeghini, G. et al. Probing topological spin liquids on a programmable quantum simulator. Science 374, 1242–1247 (2021).

    Article 
    ADS 

    Google Scholar
     

  • Shaw, A. L. et al. Benchmarking highly entangled states on a 60-atom analogue quantum simulator. Nature 628, 71–77 (2024).

    Article 
    ADS 

    Google Scholar
     

  • Norcia, M. A. et al. Seconds-scale coherence on an optical clock transition in a tweezer array. Science 366, 93–97 (2019).

    Article 
    ADS 

    Google Scholar
     

  • Madjarov, I. S. et al. An atomic-array optical clock with single-atom readout. Phys. Rev. X 9, 041052 (2019).


    Google Scholar
     

  • Young, A. W. et al. Half-minute-scale atomic coherence and high relative stability in a tweezer clock. Nature 588, 408–413 (2020).

    Article 
    ADS 

    Google Scholar
     

  • Lis, J. W. et al. Midcircuit operations using the OMG architecture in neutral atom arrays. Phys. Rev. X 13, 041035 (2023).


    Google Scholar
     

  • Ma, S. et al. Universal gate operations on nuclear spin qubits in an optical tweezer array of 171Yb atoms. Phys. Rev. X 12, 021028 (2022).


    Google Scholar
     

  • Jenkins, A., Lis, J. W., Senoo, A., McGrew, W. F. & Kaufman, A. M. Ytterbium nuclear-spin qubits in an optical tweezer array. Phys. Rev. X 12, 021027 (2022).


    Google Scholar
     

  • Norcia, M. et al. Midcircuit qubit measurement and rearrangement in a 171Yb atomic array. Phys. Rev. X 13, 041034 (2023).


    Google Scholar
     

  • Madjarov, I. S. et al. High-fidelity entanglement and detection of alkaline-earth Rydberg atoms. Nat. Phys. 16, 857–861 (2020).

    Article 

    Google Scholar
     

  • Ma, S. et al. High-fidelity gates and mid-circuit erasure conversion in an atomic qubit. Nature 622, 279–284 (2023).

    Article 
    ADS 

    Google Scholar
     

  • Eckner, W. J. et al. Realizing spin squeezing with Rydberg interactions in a programmable optical clock. Nature 621, 734–739 (2023).

    Article 
    ADS 

    Google Scholar
     

  • Cao, A. et al. Multi-qubit gates and Schrödinger cat states in an optical clock. Nature 634, 315–320 (2024).

    Article 
    ADS 

    Google Scholar
     

  • Scholl, P. et al. Erasure conversion in a high-fidelity Rydberg quantum simulator. Nature 622, 273–278 (2023).

    Article 
    ADS 

    Google Scholar
     

  • Tsai, R. B.-S., Sun, X., Shaw, A. L., Finkelstein, R. & Endres, M. Benchmarking and fidelity response theory of high-fidelity Rydberg entangling gates. PRX Quantum 6, 010331 (2025).

    Article 
    ADS 

    Google Scholar
     

  • Peper, M. et al. Spectroscopy and modeling of 171Yb Rydberg states for high-fidelity two-qubit gates. Phys. Rev. X 15, 011009 (2025).


    Google Scholar
     

  • Zeng, Z. et al. Adiabatic echo protocols for robust quantum many-body state preparation. Phys. Rev. Lett. 136, 120404 (2026).

    Article 
    ADS 
    MathSciNet 

    Google Scholar
     

  • Glaser, S. J. et al. Training Schrödinger’s cat: quantum optimal control. Strategic report on current status, visions and goals for research in Europe. Eur. Phys. J. D 69, 279 (2015).

    Article 
    ADS 

    Google Scholar
     

  • Deist, E. et al. Mid-circuit cavity measurement in a neutral atom array. Phys. Rev. Lett. 129, 203602 (2022).

    Article 
    ADS 

    Google Scholar
     

  • Radnaev, A. et al. Universal neutral-atom quantum computer with individual optical addressing and nondestructive readout. PRX Quantum 6, 030334 (2025).

    Article 
    ADS 

    Google Scholar
     

  • Huie, W. et al. Repetitive readout and real-time control of nuclear spin qubits in 171Yb atoms. PRX Quantum 4, 030337 (2023).

    Article 
    ADS 

    Google Scholar
     

  • Hu, B. et al. Site-selective cavity readout and classical error correction of a 5-bit atomic register. Phys. Rev. Lett. 134, 120801 (2025).

    Article 
    ADS 

    Google Scholar
     

  • Muniz, J. et al. High-fidelity universal gates in the 171Yb ground-state nuclear-spin qubit. PRX Quantum 6, 020334 (2025).

    Article 
    ADS 

    Google Scholar
     

  • Mølmer, K., Castin, Y. & Dalibard, J. Monte Carlo wave-function method in quantum optics. J. Opt. Soc. Am. B 10, 524–538 (1993).

    Article 
    ADS 

    Google Scholar
     

  • Jandura, S. & Pupillo, G. Time-optimal two- and three-qubit gates for Rydberg atoms. Quantum 6, 712 (2022).

    Article 

    Google Scholar
     

  • Evered, S. J. et al. High-fidelity parallel entangling gates on a neutral-atom quantum computer. Nature 622, 268–272 (2023).

    Article 
    ADS 

    Google Scholar
     

  • Wu, Y., Kolkowitz, S., Puri, S. & Thompson, J. D. Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays. Nat. Commun. 13, 4657 (2022).

    Article 
    ADS 

    Google Scholar
     

  • Baranes, G. et al. Leveraging qubit loss detection in fault-tolerant quantum algorithms. Phys. Rev. X 16, 011002 (2026).


    Google Scholar
     

  • Omran, A. et al. Generation and manipulation of Schrödinger cat states in Rydberg atom arrays. Science 365, 570–574 (2019).

    Article 
    ADS 
    MathSciNet 

    Google Scholar
     

  • Saffman, M., Walker, T. G. & Mølmer, K. Quantum information with Rydberg atoms. Rev. Mod. Phys. 82, 2313–2363 (2010).

    Article 
    ADS 

    Google Scholar
     

  • Wu, H., Richaud, R., Raimond, J.-M., Brune, M. & Gleyzes, S. Millisecond-lived circular Rydberg atoms in a room-temperature experiment. Phys. Rev. Lett. 130, 023202 (2023).

    Article 
    ADS 

    Google Scholar
     

  • Finkelstein, R. et al. Universal quantum operations and ancilla-based read-out for tweezer clocks. Nature 634, 321–327 (2024).

    Article 
    ADS 

    Google Scholar
     

  • Kaubruegger, R., Vasilyev, D. V., Schulte, M., Hammerer, K. & Zoller, P. Quantum variational optimization of Ramsey interferometry and atomic clocks. Phys. Rev. X 11, 041045 (2021).


    Google Scholar
     

  • Pichler, H., Zhu, G., Seif, A., Zoller, P. & Hafezi, M. Measurement protocol for the entanglement spectrum of cold atoms. Phys. Rev. X 6, 041033 (2016).


    Google Scholar
     

  • Ott, R. et al. Probing topological entanglement on large scales. Phys. Rev. Lett. 135, 090401 (2025).

    Article 
    ADS 
    MathSciNet 

    Google Scholar
     

  • Martin, A., Lamata, L., Solano, E. & Sanz, M. Digital-analog quantum algorithm for the quantum Fourier transform. Phys. Rev. Res. 2, 013012 (2020).

    Article 

    Google Scholar
     

  • Bauer, B., Bravyi, S., Motta, M. & Chan, G. K.-L. Quantum algorithms for quantum chemistry and quantum materials science. Chem. Rev. 120, 12685–12717 (2020).

    Article 

    Google Scholar
     

  • Bornet, G. et al. Scalable spin squeezing in a dipolar Rydberg atom array. Nature 621, 728–733 (2023).

    Article 
    ADS 

    Google Scholar
     

  • Zhang, Y., Carrasquilla, J. & Kim, Y. B. Observation of a non-Hermitian supersonic mode on a trapped-ion quantum computer. Nat. Commun. 16, 3286 (2025).

    Article 
    ADS 

    Google Scholar
     

  • Halati, C.-M., Sheikhan, A., Morigi, G., Kollath, C. & Jäger, S. B. From light-cone to supersonic propagation of correlations by competing short- and long-range couplings. Phys. Rev. Lett. 135, 190402 (2025).

    Article 
    ADS 
    MathSciNet 

    Google Scholar
     

  • Zhang, B. et al. Leveraging erasure errors in logical qubits with metastable 171Yb atoms. Preprint at https://arxiv.org/abs/2506.13724 (2025).

  • Brown, M. O., Thiele, T., Kiehl, C., Hsu, T.-W. & Regal, C. A. Gray-molasses optical-tweezer loading: controlling collisions for scaling atom-array assembly. Phys. Rev. X 9, 011057 (2019).


    Google Scholar
     

  • Tian, W. et al. Parallel assembly of arbitrary defect-free atom arrays with a multitweezer algorithm. Phys. Rev. Appl. 19, 034048 (2023).

    Article 
    ADS 

    Google Scholar
     

  • Höhn, T. O., Staub, E., Brochier, G., Darkwah Oppong, N. & Aidelsburger, M. State-dependent potentials for the 1S0 and 3P0 clock states of neutral ytterbium atoms. Phys. Rev. A 108, 053325 (2023).

    Article 
    ADS 

    Google Scholar
     

  • Su, L. et al. Fast single atom imaging for optical lattice arrays. Nat. Commun. 16, 1017 (2025).

    Article 
    ADS 

    Google Scholar
     

  • Bergschneider, A. et al. Spin-resolved single-atom imaging of 6Li in free space. Phys. Rev. A 97, 063613 (2018).

    Article 
    ADS 

    Google Scholar
     

  • Miranda, M., Inoue, R., Okuyama, Y., Nakamoto, A. & Kozuma, M. Site-resolved imaging of ytterbium atoms in a two-dimensional optical lattice. Phys. Rev. A 91, 063414 (2015).

    Article 
    ADS 

    Google Scholar
     

  • Schine, N., Young, A. W., Eckner, W. J., Martin, M. J. & Kaufman, A. M. Long-lived Bell states in an array of optical clock qubits. Nat. Phys. 18, 1067–1073 (2022).

    Article 

    Google Scholar
     

  • Wilson, A. C. et al. A 750-mW, continuous-wave, solid-state laser source at 313 nm for cooling and manipulating trapped 9Be+ ions. Appl. Phys. B 105, 741–748 (2011).

    Article 
    ADS 

    Google Scholar
     

  • Levine, H. et al. High-fidelity control and entanglement of Rydberg-atom qubits. Phys. Rev. Lett. 121, 123603 (2018).

    Article 
    ADS 

    Google Scholar
     

  • Lorenz, N. A Rydberg Tweezer Platform with Potassium Atoms. PhD thesis, Ludwig-Maximilians-Univ. München (2021).

  • Marciniak, C. D. Design and Operation of a Penning Ion Trap for Quantum Simulation. PhD thesis, Univ. of Sydney (2019).

  • Burgers, A. P. et al. Controlling Rydberg excitations using ion-core transitions in alkaline-earth atom-tweezer arrays. PRX Quantum 3, 020326 (2022).

    Article 
    ADS 

    Google Scholar
     

  • Shaw, A. L. Learning, Verifying, and Erasing Errors on a Chaotic and Highly Entangled Programmable Quantum Simulator. PhD thesis, California Institute of Technology (2024).

  • Wilk, T. et al. Entanglement of two individual neutral atoms using Rydberg blockade. Phys. Rev. Lett. 104, 010502 (2010).

    Article 
    ADS 

    Google Scholar
     

  • Khaneja, N., Reiss, T., Kehlet, C., Schulte-Herbrüggen, T. & Glaser, S. J. Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms. J. Magn. Reson. 172, 296–305 (2005).

    Article 
    ADS 

    Google Scholar