- Open Access
Multiqubit parity gates for Rydberg atoms in various configurations
Phys. Rev. Research 7, 033269 – Published 22 September, 2025
DOI: https://doi.org/10.1103/56qk-rmsz
Abstract
We present a native approach for realizing multiqubit parity phase gates in neutral-atom systems through global phase modulation of a Rydberg excitation laser. By shaping the temporal profile of the laser’s phase, we enable high-fidelity, time efficient entangling operations between multiple qubits without requiring individual qubit addressing. To mitigate intrinsic noise sources including spontaneous decay and motional effects, we develop a noise-aware optimal control framework that reduces gate errors under the presence of noise while maintaining smooth pulse profiles suitable for experimental implementation. In addition to equidistant qubit arrangements, we explore the impact of nonequidistant atomic configurations, where interaction inhomogeneity becomes significant. In these cases, the flexibility of our control approach helps to compensate for such variations, supporting reliable gate performance across different spatial layouts. These results facilitate the practical implementation of complex, multiqubit quantum operations in near-term neutral-atom quantum processors.
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References (81)
- D. Basilewitsch, C. Dlaska, and W. Lechner, Comparing planar quantum computing platforms at the quantum speed limit, Phys. Rev. Res. 6, 023026 (2024).
- S. Jandura, V. Srivastava, L. Pecorari, G. K. Brennen, and G. Pupillo, Nonlocal multiqubit quantum gates via a driven cavity, Phys. Rev. A 110, 062610 (2024).
- H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuletić, H. Pichler et al., Parallel implementation of high-fidelity multiqubit gates with neutral atoms, Phys. Rev. Lett. 123, 170503 (2019).
- S. J. Evered, D. Bluvstein, M. Kalinowski, S. Ebadi, T. Manovitz, H. Zhou, S. H. Li, A. A. Geim, T. T. Wang, N. Maskara et al., High-fidelity parallel entangling gates on a neutral-atom quantum computer, Nature (London) 622, 268 (2023).
- A. Cao, W. J. Eckner, T. Lukin Yelin, A. W. Young, S. Jandura, L. Yan, K. Kim, G. Pupillo, J. Ye, N. Darkwah Oppong et al., Multi-qubit gates and Schrödinger cat states in an optical clock, Nature (London) 634, 315 (2024).
- P. K. Barkoutsos, J. F. Gonthier, I. Sokolov, N. Moll, G. Salis, A. Fuhrer, M. Ganzhorn, D. J. Egger, M. Troyer, A. Mezzacapo et al., Quantum algorithms for electronic structure calculations: Particle-hole Hamiltonian and optimized wave-function expansions, Phys. Rev. A 98, 022322 (2018).
- N. Maskara, S. Ostermann, J. Shee, M. Kalinowski, A. McClain Gomez, R. Araiza Bravo, D. S. Wang, A. I. Krylov, N. Y. Yao, M. Head-Gordon et al., Programmable simulations of molecules and materials with reconfigurable quantum processors, Nat. Phys. 21, 289 (2025).
- R. Irmejs, M.-C. Bañuls, and J. I. Cirac, Quantum simulation of lattice gauge theory with minimal resources, Phys. Rev. D 108, 074503 (2023).
- M. Kalinowski, N. Maskara, and M. D. Lukin, Non-Abelian Floquet spin liquids in a digital Rydberg simulator, Phys. Rev. X 13, 031008 (2023).
- J. Mildenberger, W. Mruczkiewicz, J. C. Halimeh, Z. Jiang, and P. Hauke, Confinement in a lattice gauge theory on a quantum computer, Nat. Phys. 21, 312 (2025).
- W. Lechner, P. Hauke, and P. Zoller, A quantum annealing architecture with all-to-all connectivity from local interactions, Sci. Adv. 1, e1500838 (2015).
- M. Fellner, A. Messinger, K. Ender, and W. Lechner, Universal parity quantum computing, Phys. Rev. Lett. 129, 180503 (2022).
- M. Fellner, A. Messinger, K. Ender, and W. Lechner, Applications of universal parity quantum computation, Phys. Rev. A 106, 042442 (2022).
- C. Dlaska, K. Ender, G. B. Mbeng, A. Kruckenhauser, W. Lechner, and R. van Bijnen, Quantum optimization via four-body Rydberg gates, Phys. Rev. Lett. 128, 120503 (2022).
- M. Lanthaler, B. E. Niehoff, and W. Lechner, Scalable set of reversible parity gates for integer factorization, Commun. Phys. 6, 73 (2023).
- A. Weidinger, G. B. Mbeng, M. Fellner, D. Khachatryan, and W. Lechner, Performance of parity QAOA for the signed max-cut problem, arXiv:2409.14786.
- A. Messinger, V. Torggler, B. Klaver, M. Fellner, and W. Lechner, Fault-tolerant quantum computing with the parity code and biased-noise qubits, Phys. Rev. Appl. 23, 044032 (2025).
- A. Radnaev, W. Chung, D. Cole, D. Mason, T. Ballance, M. Bedalov, D. Belknap, M. Berman, M. Blakely, I. Bloomfield et al., A universal neutral-atom quantum computer with individual optical addressing and non-destructive readout, arXiv:2408.08288.
- R. B.-S. Tsai, X. Sun, A. L. Shaw, R. Finkelstein, and M. Endres, Benchmarking and fidelity response theory of high-fidelity Rydberg entangling gates, PRX Quantum 6, 010331 (2025).
- M. Peper, Y. Li, D. Y. Knapp, M. Bileska, S. Ma, G. Liu, P. Peng, B. Zhang, S. P. Horvath, A. P. Burgers et al., Spectroscopy and modeling of Rydberg states for high-fidelity two-qubit gates, Phys. Rev. X 15, 011009 (2025).
- D. Bluvstein, H. Levine, G. Semeghini, T. T. Wang, S. Ebadi, M. Kalinowski, A. Keesling, N. Maskara, H. Pichler, M. Greiner et al., A quantum processor based on coherent transport of entangled atom arrays, Nature (London) 604, 451 (2022).
- H. J. Manetsch, G. Nomura, E. Bataille, K. H. Leung, X. Lv, and M. Endres, A tweezer array with 6100 highly coherent atomic qubits, arXiv:2403.12021.
- M. Norcia, H. Kim, W. Cairncross, M. Stone, A. Ryou, M. Jaffe, M. Brown, K. Barnes, P. Battaglino, T. Bohdanowicz et al., Iterative assembly of atom arrays with cavity-enhanced optical lattices, PRX Quantum 5, 030316 (2024).
- R. Tao, M. Ammenwerth, F. Gyger, I. Bloch, and J. Zeiher, High-fidelity detection of large-scale atom arrays in an optical lattice, Phys. Rev. Lett. 133, 013401 (2024).
- D. Bluvstein, S. J. Evered, A. A. Geim, S. H. Li, H. Zhou, T. Manovitz, S. Ebadi, M. Cain, M. Kalinowski, D. Hangleiter et al., Logical quantum processor based on reconfigurable atom arrays, Nature (London) 626, 58 (2024).
- P. Sales Rodriguez, J. M. Robinson, P. N. Jepsen, Z. He, C. Duckering, C. Zhao, K.-H. Wu, J. Campo, K. Bagnall, M. Kwon et al., Experimental demonstration of logical magic state distillation, Nature (London) (2025), doi:10.1038/s41586-025-09367-3.
- B. W. Reichardt, A. Paetznick, D. Aasen, I. Basov, J. M. Bello-Rivas, P. Bonderson, R. Chao, W. van Dam, M. B. Hastings, A. Paz et al., Logical computation demonstrated with a neutral atom quantum processor, arXiv:2411.11822.
- M. Bedalov, M. Blakely, P. Buttler, C. Carnahan, F. T. Chong, W. C. Chung, D. C. Cole, P. Goiporia, P. Gokhale, B. Heim et al., Fault-tolerant operation and materials science with neutral atom logical qubits, arXiv:2412.07670.
- M.-T. Nguyen, J.-G. Liu, J. Wurtz, M. D. Lukin, S.-T. Wang, and H. Pichler, Quantum optimization with arbitrary connectivity using Rydberg atom arrays, PRX Quantum 4, 010316 (2023).
- M. Lanthaler, C. Dlaska, K. Ender, and W. Lechner, Rydberg-blockade-based parity quantum optimization, Phys. Rev. Lett. 130, 220601 (2023).
- S. Stastny, H. P. Büchler, and N. Lang, Functional completeness of planar Rydberg blockade structures, Phys. Rev. B 108, 085138 (2023).
- M. Lanthaler, K. Ender, C. Dlaska, and W. Lechner, Quantum optimization with globally driven neutral atom arrays, arXiv:2410.03902.
- A. Byun, S. Jeong, and J. Ahn, Programming higher-order interactions of Rydberg atoms, Phys. Rev. A 110, 042612 (2024).
- A. Cooper, J. P. Covey, I. S. Madjarov, S. G. Porsev, M. S. Safronova, and M. Endres, Alkaline-earth atoms in optical tweezers, Phys. Rev. X 8, 041055 (2018).
- A. Heinz, A. J. Park, N. Šantić, J. Trautmann, S. Porsev, M. Safronova, I. Bloch, and S. Blatt, State-dependent optical lattices for the strontium optical qubit, Phys. Rev. Lett. 124, 203201 (2020).
- R. Finkelstein, R. B.-S. Tsai, X. Sun, P. Scholl, S. Direkci, T. Gefen, J. Choi, A. L. Shaw, and M. Endres, Universal quantum operations and ancilla-based read-out for tweezer clocks, Nature (London) 634, 321 (2024).
- G. Unnikrishnan, P. Ilzhöfer, A. Scholz, C. Hölzl, A. Götzelmann, R. K. Gupta, J. Zhao, J. Krauter, S. Weber, N. Makki et al., Coherent control of the fine-structure qubit in a single alkaline-earth atom, Phys. Rev. Lett. 132, 150606 (2024).
- M. Ammenwerth, H. Timme, F. Gyger, R. Tao, I. Bloch, and J. Zeiher, Realization of a fast triple-magic all-optical qutrit in strontium-88, arXiv:2411.02869.
- A. L. Shaw, P. Scholl, R. Finkelstein, R. B.-S. Tsai, J. Choi, and M. Endres, Erasure cooling, control, and hyperentanglement of motion in optical tweezers, Science 388, 845 (2025).
- M. A. Norcia, A. W. Young, W. J. Eckner, E. Oelker, J. Ye, and A. M. Kaufman, Seconds-scale coherence on an optical clock transition in a tweezer array, Science 366, 93 (2019).
- A. W. Young, W. J. Eckner, W. R. Milner, D. Kedar, M. A. Norcia, E. Oelker, N. Schine, J. Ye, and A. M. Kaufman, Half-minute-scale atomic coherence and high relative stability in a tweezer clock, Nature (London) 588, 408 (2020).
- M. Takamoto, F.-L. Hong, R. Higashi, and H. Katori, An optical lattice clock, Nature (London) 435, 321 (2005).
- B. Bloom, T. Nicholson, J. Williams, S. Campbell, M. Bishof, X. Zhang, W. Zhang, S. Bromley, and J. Ye, An optical lattice clock with accuracy and stability at the level, Nature (London) 506, 71 (2014).
- I. S. Madjarov, A. Cooper, A. L. Shaw, J. P. Covey, V. Schkolnik, T. H. Yoon, J. R. Williams, and M. Endres, An atomic-array optical clock with single-atom readout, Phys. Rev. X 9, 041052 (2019).
- A. Aeppli, K. Kim, W. Warfield, M. S. Safronova, and J. Ye, Clock with systematic uncertainty, Phys. Rev. Lett. 133, 023401 (2024).
- N. Schine, A. W. Young, W. J. Eckner, M. J. Martin, and A. M. Kaufman, Long-lived Bell states in an array of optical clock qubits, Nat. Phys. 18, 1067 (2022).
- Z. Zhang, L. Van Damme, M. Rossignolo, L. Festa, M. Melchner, R. Eberhard, D. Tsevas, K. Mours, E. Reches, J. Zeiher et al., Recoil-free quantum gates with optical qubits, arXiv:2408.04622.
- A. Browaeys and T. Lahaye, Many-body physics with individually controlled Rydberg atoms, Nat. Phys. 16, 132 (2020).
- S. Weber, C. Tresp, H. Menke, A. Urvoy, O. Firstenberg, H. P. Büchler, and S. Hofferberth, Calculation of Rydberg interaction potentials, J. Phys. B: At. Mol. Opt. Phys. 50, 133001 (2017).
- A. Pagano, S. Weber, D. Jaschke, T. Pfau, F. Meinert, S. Montangero, and H. P. Büchler, Error budgeting for a controlled-phase gate with strontium-88 Rydberg atoms, Phys. Rev. Res. 4, 033019 (2022).
- J. Bradbury, R. Frostig, P. Hawkins, M. J. Johnson, C. Leary, D. Maclaurin, G. Necula, A. Paszke, J. VanderPlas, S. Wanderman-Milne, and Q. Zhang, JAX: Composable transformations of python+numpy programs, 2018, https://github.com/jax-ml/jax.
- J. H. Wesenberg, K. Mølmer, L. Rippe, and S. Kröll, Scalable designs for quantum computing with rare-earth-ion-doped crystals, Phys. Rev. A 75, 012304 (2007).
- C. Poole, T. M. Graham, M. A. Perlin, M. Otten, and M. Saffman, Architecture for fast implementation of quantum low-density parity-check codes with optimized Rydberg gates, Phys. Rev. A 111, 022433 (2025).
- I. S. Madjarov, J. P. Covey, A. L. Shaw, J. Choi, A. Kale, A. Cooper, H. Pichler, V. Schkolnik, J. R. Williams, and M. Endres, High-fidelity entanglement and detection of alkaline-earth Rydberg atoms, Nat. Phys. 16, 857 (2020).
- F. Robicheaux, T. Graham, and M. Saffman, Photon-recoil and laser-focusing limits to Rydberg gate fidelity, Phys. Rev. A 103, 022424 (2021).
- W. Li, C. Ates, and I. Lesanovsky, Nonadiabatic motional effects and dissipative blockade for Rydberg atoms excited from optical lattices or microtraps, Phys. Rev. Lett. 110, 213005 (2013).
- T. Keating, R. L. Cook, A. M. Hankin, Y.-Y. Jau, G. W. Biedermann, and I. H. Deutsch, Robust quantum logic in neutral atoms via adiabatic Rydberg dressing, Phys. Rev. A 91, 012337 (2015).
- P. Nandy, A. S. Matsoukas-Roubeas, P. Martínez-Azcona, A. Dymarsky, and A. del Campo, Quantum dynamics in krylov space: Methods and applications, Phys. Rep. 1125–1128, 1 (2025).
- Y. Chew, T. Tomita, T. P. Mahesh, S. Sugawa, S. de Léséleuc, and K. Ohmori, Ultrafast energy exchange between two single Rydberg atoms on a nanosecond timescale, Nat. Photon. 16, 724 (2022).
- T. G. Walker and M. Saffman, Consequences of Zeeman degeneracy for the van der Waals blockade between Rydberg atoms, Phys. Rev. A 77, 032723 (2008).
- S. Jandura and G. Pupillo, Time-optimal two- and three-qubit gates for Rydberg atoms, Quantum 6, 712 (2022).
- S. Jandura, J. D. Thompson, and G. Pupillo, Optimizing Rydberg gates for logical-qubit performance, PRX Quantum 4, 020336 (2023).
- A. N. Korotkov, Error matrices in quantum process tomography, arXiv:1309.6405.
- K. Sahay, J. Jin, J. Claes, J. D. Thompson, and S. Puri, High-threshold codes for neutral-atom qubits with biased erasure errors, Phys. Rev. X 13, 041013 (2023).
- K. Tiurev, C. Goeller, L. Stenzel, P. Schnabl, A. Messinger, M. Fellner, and W. Lechner, Optimal decoder for the error correcting parity code, arXiv:2505.05210.
- J. P. Bonilla Ataides, D. K. Tuckett, S. D. Bartlett, S. T. Flammia, and B. J. Brown, The XZZX surface code, Nat. Commun. 12, 2172 (2021).
- J. Roffe, L. Z. Cohen, A. O. Quintavalle, D. Chandra, and E. T. Campbell, Bias-tailored quantum LDPC codes, Quantum 7, 1005 (2023).
- K. Tiurev, P.-J. H. S. Derks, J. Roffe, J. Eisert, and J.-M. Reiner, Correcting non-independent and non-identically distributed errors with surface codes, Quantum 7, 1123 (2023).
- E. Huang, A. Pesah, C. T. Chubb, M. Vasmer, and A. Dua, Tailoring three-dimensional topological codes for biased noise, PRX Quantum 4, 030338 (2023).
- K. Brechtelsbauer, F. Butt, D. F. Locher, S. H. Quintero, S. Weber, M. Müller, and H. P. Büchler, Measurement-free quantum error correction optimized for biased noise, arXiv:2505.15669.
- S. Ma, G. Liu, P. Peng, B. Zhang, S. Jandura, J. Claes, A. P. Burgers, G. Pupillo, S. Puri, and J. D. Thompson, High-fidelity gates and mid-circuit erasure conversion in an atomic qubit, Nature (London) 622, 279 (2023).
- R. Tao, O. Lib, F. Gyger, H. Timme, M. Ammenwerth, I. Bloch, and J. Zeiher, Universal gates for a metastable qubit in strontium-88, arXiv:2506.10714.
- L. H. Pedersen, N. M. Møller, and K. Mølmer, Fidelity of quantum operations, Phys. Lett. A 367, 47 (2007).
- C. Fromonteil, D. Bluvstein, and H. Pichler, Protocols for Rydberg entangling gates featuring robustness against quasistatic errors, PRX Quantum 4, 020335 (2023).
- S. Anand, C. E. Bradley, R. White, V. Ramesh, K. Singh, and H. Bernien, A dual-species Rydberg array, Nat. Phys. 20, 1744 (2024).
- J. Emerson, R. Alicki, and K. Zyczkowski, Scalable noise estimation with random unitary operators, J. Opt. B: Quantum Semiclassical Opt. 7, S347 (2005).
- M. R. Geller and Z. Zhou, Efficient error models for fault-tolerant architectures and the Pauli twirling approximation, Phys. Rev. A 88, 012314 (2013).
- T. Abad, Y. Schattner, A. F. Kockum, and G. Johansson, Impact of decoherence on the fidelity of quantum gates leaving the computational subspace, Quantum 9, 1684 (2025).
- C. J. Wood and J. M. Gambetta, Quantification and characterization of leakage errors, Phys. Rev. A 97, 032306 (2018).
- R. De Keijzer, J. Snijders, A. Carvalho, and S. Kokkelmans, Pulse family optimization for parameterized quantum gates using spectral clustering, Acad. Quantum 1 (2024).
- D. Layden, B. Mitchell, and K. Siva, Theory of quantum error mitigation for non-Clifford gates, arXiv:2403.18793.