- Open Access
Entangling superconducting qubits via energy-selective local reservoirs
Phys. Rev. Research 8, 033175 – Published 11 August, 2026
DOI: https://doi.org/10.1103/mr1g-zqtq
Abstract
Engineered dissipation provides a powerful route to controlling and stabilizing quantum states in open systems. Superconducting circuits are particularly suited to this approach due to their tunable coupling to dissipative environments. Here, we realize programmable local reservoirs for superconducting qubits through parametrically driven couplings to readout resonators, creating energy-selective incoherent pump and loss. Using coupled superconducting qubits, we autonomously stabilize entangled single-excitation states with fidelity up to 90.8%. We probe the stabilization dynamics under varying initial conditions and bath parameters, and implement robust classical shadow estimation for accurate and scalable state characterization. Finally, we numerically study a configuration where the engineered pump and loss share a common dissipative mode, leading to reservoir-mediated interference and classically correlated steady states. Our results demonstrate a scalable and hardware-efficient framework for dissipative preparation and control of correlated many-body states in superconducting circuits.
Physics Subject Headings (PhySH)
Article Text
References (66)
- A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
- P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gustavsson, and W. D. Oliver, A quantum engineer's guide to superconducting qubits, Appl. Phys. Rev. 6, 021318 (2019).
- I. Carusotto, A. A. Houck, A. J. Kollár, P. Roushan, D. I. Schuster, and J. Simon, Photonic materials in circuit quantum electrodynamics, Nat. Phys. 16, 268 (2020).
- F. Verstraete, M. M. Wolf, and J. I. Cirac, Quantum computation and quantum-state engineering driven by dissipation, Nat. Phys. 5, 633 (2009).
- E. Kapit, The upside of noise: Engineered dissipation as a resource in superconducting circuits, Quantum Sci. Technol. 2, 033002 (2017).
- P. M. Harrington, E. J. Mueller, and K. W. Murch, Engineered dissipation for quantum information science, Nat. Rev. Phys. 4, 660 (2022).
- S. O. Valenzuela, W. D. Oliver, D. M. Berns, K. K. Berggren, L. S. Levitov, and T. P. Orlando, Microwave-induced cooling of a superconducting qubit, Science 314, 1589 (2006).
- K. Geerlings, Z. Leghtas, I. M. Pop, S. Shankar, L. Frunzio, R. J. Schoelkopf, M. Mirrahimi, and M. H. Devoret, Demonstrating a driven reset protocol for a superconducting qubit, Phys. Rev. Lett. 110, 120501 (2013).
- P. Magnard, P. Kurpiers, B. Royer, T. Walter, J.-C. Besse, S. Gasparinetti, M. Pechal, J. Heinsoo, S. Storz, A. Blais, and A. Wallraff, Fast and unconditional all-microwave reset of a superconducting qubit, Phys. Rev. Lett. 121, 060502 (2018).
- Y. Zhou, Z. Zhang, Z. Yin, S. Huai, X. Gu, X. Xu, J. Allcock, F. Liu, G. Xi, Q. Yu, H. Zhang, M. Zhang, H. Li, X. Song, Z. Wang, D. Zheng, S. An, Y. Zheng, and S. Zhang, Rapid and unconditional parametric reset protocol for tunable superconducting qubits, Nat. Commun. 12, 5924 (2021).
- X. Cao, M. Mucci, G. Liu, D. Pekker, and M. Hatridge, Engineering a multilevel bath for transmons with three-wave mixing and parametric drives, Phys. Rev. Lett. 135, 230403 (2025).
- R. Ma, B. Saxberg, C. Owens, N. Leung, Y. Lu, J. Simon, and D. I. Schuster, A dissipatively stabilized Mott insulator of photons, Nature (London) 566, 51 (2019).
- K. W. Murch, U. Vool, D. Zhou, S. J. Weber, S. M. Girvin, and I. Siddiqi, Cavity-assisted quantum bath engineering, Phys. Rev. Lett. 109, 183602 (2012).
- Y. Lu, S. Chakram, N. Leung, N. Earnest, R. K. Naik, Z. Huang, P. Groszkowski, E. Kapit, J. Koch, and D. I. Schuster, Universal stabilization of a parametrically coupled qubit, Phys. Rev. Lett. 119, 150502 (2017).
- S. Shankar, M. Hatridge, Z. Leghtas, K. M. Sliwa, A. Narla, U. Vool, S. M. Girvin, L. Frunzio, M. Mirrahimi, and M. H. Devoret, Autonomously stabilized entanglement between two superconducting quantum bits, Nature (London) 504, 419 (2013).
- Z. Li, T. Roy, Y. Lu, E. Kapit, and D. I. Schuster, Autonomous stabilization with programmable stabilized state, Nat. Commun. 15, 6978 (2024).
- T. Brown, E. Doucet, D. Ristè, G. Ribeill, K. Cicak, J. Aumentado, R. Simmonds, L. Govia, A. Kamal, and L. Ranzani, Trade off-free entanglement stabilization in a superconducting qutrit-qubit system, Nat. Commun. 13, 3994 (2022).
- S. Hacohen-Gourgy, V. V. Ramasesh, C. De Grandi, I. Siddiqi, and S. M. Girvin, Cooling and autonomous feedback in a Bose-Hubbard chain with attractive interactions, Phys. Rev. Lett. 115, 240501 (2015).
- C. Chen, K. Tang, Y. Zhou, K. Yi, X. Zhang, X. Zhang, H. Guo, S. Liu, Y. Chen, T. Yan, and D. Yu, Hardware-efficient stabilization of entanglement via engineered dissipation in superconducting circuits, Phys. Rev. Res. 7, L022018 (2025).
- P. S. Shah, F. Yang, C. Joshi, and M. Mirhosseini, Stabilizing remote entanglement via waveguide dissipation, PRX Quantum 5, 030346 (2024).
- A. Grimm, N. E. Frattini, S. Puri, S. O. Mundhada, S. Touzard, M. Mirrahimi, S. M. Girvin, S. Shankar, and M. H. Devoret, Stabilization and operation of a Kerr-cat qubit, Nature (London) 584, 205 (2020).
- J. M. Gertler, B. Baker, J. Li, S. Shirol, J. Koch, and C. Wang, Protecting a bosonic qubit with autonomous quantum error correction, Nature (London) 590, 243 (2021).
- T. Thorbeck, A. McDonald, O. Lanes, J. Blair, G. Keefe, A. A. Stabile, B. Royer, L. C. Govia, and A. Blais, High-fidelity gates in a transmon using bath engineering for passive leakage reset, arXiv:2411.04101.
- J. Ding, Y. Li, H. Wang, G. Xue, T. Su, C. Wang, W. Sun, F. Li, Y. Zhang, Y. Gao, et al., Multipurpose architecture for fast reset and protective readout of superconducting qubits, Phys. Rev. Appl. 23, 014012 (2025).
- K. Y. Tan, M. Partanen, R. E. Lake, J. Govenius, S. Masuda, and M. Möttönen, Quantum-circuit refrigerator, Nat. Commun. 8, 15189 (2017).
- E. Kapit, M. Hafezi, and S. H. Simon, Induced self-stabilization in fractional quantum Hall states of light, Phys. Rev. X 4, 031039 (2014).
- M. Hafezi, P. Adhikari, and J. M. Taylor, Chemical potential for light by parametric coupling, Phys. Rev. B 92, 174305 (2015).
- J. Lebreuilly, A. Biella, F. Storme, D. Rossini, R. Fazio, C. Ciuti, and I. Carusotto, Stabilizing strongly correlated photon fluids with non-Markovian reservoirs, Phys. Rev. A 96, 033828 (2017).
- B. Du, R. Suresh, S. López, J. Cadiente, and R. Ma, Probing site-resolved current in strongly interacting superconducting circuit lattices, Phys. Rev. Lett. 133, 060601 (2024).
- B. Du, Q. Guo, S. López, and R. Ma, Tunneling spectroscopy in superconducting circuit lattices, Phys. Rev. Res. 7, L022038 (2025).
- M. A. Cazalilla, R. Citro, T. Giamarchi, E. Orignac, and M. Rigol, One dimensional bosons: From condensed matter systems to ultracold gases, Rev. Mod. Phys. 83, 1405 (2011).
- Z. Yan, Y.-R. Zhang, M. Gong, Y. Wu, Y. Zheng, S. Li, C. Wang, F. Liang, J. Lin, Y. Xu, et al., Strongly correlated quantum walks with a 12-qubit superconducting processor, Science 364, 753 (2019).
- A. H. Karamlou, I. T. Rosen, S. E. Muschinske, C. N. Barrett, A. Di Paolo, L. Ding, P. M. Harrington, M. Hays, R. Das, D. K. Kim, B. M. Niedzielski, M. Schuldt, K. Serniak, M. E. Schwartz, J. L. Yoder, S. Gustavsson, Y. Yanay, J. A. Grover, and W. D. Oliver, Probing entanglement in a 2D hard-core Bose-Hubbard lattice, Nature (London) 629, 561 (2024).
- H.-Y. Huang, R. Kueng, and J. Preskill, Predicting many properties of a quantum system from very few measurements, Nat. Phys. 16, 1050 (2020).
- S. Chen, W. Yu, P. Zeng, and S. T. Flammia, Robust shadow estimation, PRX Quantum 2, 030348 (2021).
- B. Vermersch, A. Rath, B. Sundar, C. Branciard, J. Preskill, and A. Elben, Enhanced estimation of quantum properties with common randomized measurements, PRX Quantum 5, 010352 (2024).
- V. Vitale, A. Rath, P. Jurcevic, A. Elben, C. Branciard, and B. Vermersch, Robust estimation of the quantum Fisher information on a quantum processor, PRX Quantum 5, 030338 (2024).
- W. K. Wootters, Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett. 80, 2245 (1998).
- H. Levine, A. Haim, J. S. C. Hung, N. Alidoust, M. Kalaee, L. DeLorenzo, E. A. Wollack, P. Arrangoiz-Arriola, A. Khalajhedayati, R. Sanil, et al., Demonstrating a long-coherence dual-rail erasure qubit using tunable transmons, Phys. Rev. X 14, 011051 (2024).
- J.-H. Yeh, J. LeFebvre, S. Premaratne, F. Wellstood, and B. Palmer, Microwave attenuators for use with quantum devices below 100 mK, J. Appl. Phys. 121, 224501 (2017).
- Z. Wang, S. Shankar, Z. K. Minev, P. Campagne-Ibarcq, A. Narla, and M. H. Devoret, Cavity attenuators for superconducting qubits, Phys. Rev. Appl. 11, 014031 (2019).
- S. Krinner, S. Storz, P. Kurpiers, P. Magnard, J. Heinsoo, R. Keller, J. Luetolf, C. Eichler, and A. Wallraff, Engineering cryogenic setups for 100-qubit scale superconducting circuit systems, EPJ Quantum Technol. 6, 2 (2019).
- A. P. Place, L. V. Rodgers, P. Mundada, B. M. Smitham, M. Fitzpatrick, Z. Leng, A. Premkumar, J. Bryon, A. Vrajitoarea, S. Sussman, et al., New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds, Nat. Commun. 12, 1779 (2021).
- C. Wang, X. Li, H. Xu, Z. Li, J. Wang, Z. Yang, Z. Mi, X. Liang, T. Su, C. Yang, et al., Towards practical quantum computers: Transmon qubit with a lifetime approaching 0.5 milliseconds, npj Quantum Inf. 8, 3 (2022).
- E. Jeffrey, D. Sank, J. Y. Mutus, T. C. White, J. Kelly, R. Barends, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. Megrant, P. J. J. O’Malley, C. Neill, P. Roushan, A. Vainsencher, J. Wenner, A. N. Cleland, and J. M. Martinis, Fast accurate state measurement with superconducting qubits, Phys. Rev. Lett. 112, 190504 (2014).
- A. Chu, M. Mamaev, M. Koppenhöfer, M. Yuan, and A. A. Clerk, Reconfigurable dissipative entanglement between many spin ensembles: From robust quantum sensing to many-body state engineering, Phys. Rev. X 16, 021047 (2026).
- J. Guo, O. Hart, C.-F. Chen, A. J. Friedman, and A. Lucas, Designing open quantum systems with known steady states: Davies generators and beyond, Quantum 9, 1612 (2025).
- X. Mi, A. A. Michailidis, S. Shabani, K. C. Miao, P. V. Klimov, J. Lloyd, E. Rosenberg, R. Acharya, I. Aleiner, T. I. Andersen, et al., Stable quantum-correlated many-body states through engineered dissipation, Science 383, 1332 (2024).
- Y. Zhan, Z. Ding, J. Huhn, J. Gray, J. Preskill, G. K.-L. Chan, and L. Lin, Rapid quantum ground state preparation via dissipative dynamics, Phys. Rev. X 16, 011004 (2026).
- D. Marcos, A. Tomadin, S. Diehl, and P. Rabl, Photon condensation in circuit quantum electrodynamics by engineered dissipation, New J. Phys. 14, 055005 (2012).
- J. Lebreuilly, M. Wouters, and I. Carusotto, Towards strongly correlated photons in arrays of dissipative nonlinear cavities under a frequency-dependent incoherent pumping, C. R. Phys. 17, 836 (2016).
- R. Ma, C. Owens, A. Houck, D. I. Schuster, and J. Simon, Autonomous stabilizer for incompressible photon fluids and solids, Phys. Rev. A 95, 043811 (2017).
- P. Kurilovich, V. D. Kurilovich, J. Lebreuilly, and S. Girvin, Stabilizing the Laughlin state of light: Dynamics of hole fractionalization, SciPost Phys. 13, 107 (2022).
- A. Shabani and H. Neven, Artificial quantum thermal bath: Engineering temperature for a many-body quantum system, Phys. Rev. A 94, 052301 (2016).
- R. J. Lewis-Swan, A. Safavi-Naini, A. M. Kaufman, and A. M. Rey, Dynamics of quantum information, Nat. Rev. Phys. 1, 627 (2019).
- Y. Yanay and A. A. Clerk, Reservoir engineering with localized dissipation: Dynamics and prethermalization, Phys. Rev. Res. 2, 023177 (2020).
- F. Ares, P. Calabrese, and S. Murciano, The quantum Mpemba effects, Nat. Rev. Phys. 7, 451 (2025).
- S. Campbell, I. D’Amico, M. A. Ciampini, J. Anders, N. Ares, S. Artini, A. Auffèves, L. B. Oftelie, L. P. Bettmann, M. V. S. Bonança, et al., Roadmap on quantum thermodynamics, Quantum Sci. Technol. 11, 012501 (2026).
- M. A. Aamir, P. Jamet Suria, J. A. Marín Guzmán, C. Castillo-Moreno, J. M. Epstein, N. Yunger Halpern, and S. Gasparinetti, Thermally driven quantum refrigerator autonomously resets a superconducting qubit, Nat. Phys. 21, 318 (2025).
- T. Uusnäkki, T. Mörstedt, W. Teixeira, M. Rasola, and M. Möttönen, Initial demonstration of a quantum heat engine based on dissipation-engineered superconducting circuits, Nat. Commun. 17, 6054 (2026).
- Q. Guo, B. Du, and R. Ma, Data and simulation code for “Entangling superconducting qubits via energy-selective local reservoirs”, Zenodo, 2026, http://doi.org/10.5281/zenodo.20190733.
- S. S. Elder, C. S. Wang, P. Reinhold, C. T. Hann, K. S. Chou, B. J. Lester, S. Rosenblum, L. Frunzio, L. Jiang, and R. J. Schoelkopf, High-fidelity measurement of qubits encoded in multilevel superconducting circuits, Phys. Rev. X 10, 011001 (2020).
- X. Y. Jin, A. Kamal, A. P. Sears, T. Gudmundsen, D. Hover, J. Miloshi, R. Slattery, F. Yan, J. Yoder, T. P. Orlando, S. Gustavsson, and W. D. Oliver, Thermal and residual excited-state population in a 3D transmon qubit, Phys. Rev. Lett. 114, 240501 (2015).
- B. Du, Q. Guo, and R. Ma, Programmable superradiance in an interacting qubit array, arXiv:2605.12442.
- A. Elben and B. Vermersch, RandomMeas.jl: A Julia package for randomized measurements in quantum devices, Quantum 10, 2086 (2026).
- J. A. Smolin, J. M. Gambetta, and G. Smith, Efficient method for computing the maximum-likelihood quantum state from measurements with additive Gaussian noise, Phys. Rev. Lett. 108, 070502 (2012).