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arxiv: 2604.15432 · v1 · submitted 2026-04-16 · 🪐 quant-ph

Efficient n-qubit entangling operations via a superconducting quantum router

Xuntao Wu , Haoxiong Yan , Gustav Andersson , Alexander Anferov , Christopher R. Conner , Yash J. Joshi , Bayan Karimi , Amber M. King
show 8 more authors
Shiheng Li Howard L. Malc Jacob M. Miller Harsh Mishra Hong Qiao Minseok Ryu Jian Shi Andrew N. Cleland
This is my paper

Pith reviewed 2026-05-10 10:52 UTC · model grok-4.3

classification 🪐 quant-ph
keywords superconducting qubitsquantum routermulti-qubit gatesentanglement generationreinforcement learningToffoli gateFredkin gatequantum circuits
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0 comments X p. Extension

The pith

A reconfigurable superconducting router enables direct multi-qubit entangling operations beyond pairwise gates.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows how a superconducting qubit architecture with a reconfigurable router can perform entangling operations directly on three or more qubits at once. This bypasses the need to decompose complex gates into many sequential two-qubit steps that add time and errors. The result is quicker preparation of multi-qubit entangled states while keeping fidelities high. The authors also train model-free reinforcement learning agents to realize specific gates including controlled-Z, controlled-SWAP, Fredkin, and Toffoli. If this holds, it points toward shallower circuits that could let near-term processors run more complex algorithms before decoherence sets in.

Core claim

The central claim is that the reconfigurable router architecture realizes programmable and efficient multi-qubit operations involving more than two qubits, resulting in faster preparation of multi-qubit entangled states with good fidelities. Model-free reinforcement learning is applied to implement a two-qubit controlled-Z gate as well as three-qubit controlled-SWAP and controlled-controlled-phase gates. The high-connectivity design of the router suggests that higher n-qubit gates are also feasible, providing a route to more efficient implementations of complex quantum algorithms.

What carries the argument

The reconfigurable router that supplies high-connectivity and user-selectable interactions among multiple superconducting qubits in a single operation.

If this is right

  • Multi-qubit entangled states are prepared in fewer steps than required by sequences of two-qubit gates.
  • Model-free reinforcement learning successfully calibrates three-qubit gates including Fredkin and Toffoli without an explicit system model.
  • The same router hardware supports extension to higher-order n-qubit entangling operations.
  • Complex quantum algorithms can be executed with reduced circuit depth and accumulated error.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The router approach may reduce the total gate count needed for algorithms whose native interactions involve three or more qubits.
  • Reinforcement learning trained on this hardware could discover gate implementations that differ from textbook decompositions.
  • If the connectivity scales, the architecture might support native many-body Hamiltonians for quantum simulation tasks.

Load-bearing premise

The router can be scaled to operations on four or more qubits while preserving efficiency and fidelity.

What would settle it

An experiment in which a three-qubit Fredkin gate realized through the router shows lower fidelity or longer duration than the best decomposition using only two-qubit gates.

Figures

Figures reproduced from arXiv: 2604.15432 by Alexander Anferov, Amber M. King, Andrew N. Cleland, Bayan Karimi, Christopher R. Conner, Gustav Andersson, Haoxiong Yan, Harsh Mishra, Hong Qiao, Howard L. Malc, Jacob M. Miller, Jian Shi, Minseok Ryu, Shiheng Li, Xuntao Wu, Yash J. Joshi.

Figure 1
Figure 1. Figure 1: FIG. 1: Experimental setup [ [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Generation of [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: RL setup and CZ gate training. (a) RL [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Three-qubit gate synthesis with RL. (a) [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Spin chirality demonstration. (a) Schematic [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
read the original abstract

Quantum algorithms on near-term quantum processors are typically executed using shallow quantum circuits composed of one- and two-qubit gates. However, as circuit depth and gate number increase, gate imperfections and qubit decoherence begin to dominate, limiting algorithmic complexity. An alternative approach is to explore gates involving more than two qubits. In previous work (X. Wu et al., Physical Review X 14, 041030 (2024)), we demonstrated a new superconducting qubit architecture with user-selectable two-qubit interactions via a reconfigurable router, used to connect pairs of qubits. Here, we leverage this novel architecture to realize programmable and efficient multi-qubit operations involving more than two qubits, resulting in faster preparation of multi-qubit entangled states with good fidelities. We also successfully apply model-free reinforcement learning to perform multi-qubit gates, including training a two-qubit controlled-Z gate as well as three-qubit controlled-SWAP and controlled-controlled-phase (Fredkin and Toffoli) gates. Higher $n$th-order gates may also be feasible, using our high-connectivity router design. This could provide a more efficient and higher-fidelity implementation of complex quantum algorithms and a more practical approach to quantum computation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The paper extends a reconfigurable superconducting qubit router architecture (from prior two-qubit work) to implement programmable multi-qubit entangling operations. It demonstrates three-qubit gates (controlled-SWAP, Fredkin, and Toffoli) via model-free reinforcement learning, reports faster preparation of multi-qubit entangled states with good fidelities, and suggests that higher-order n-qubit gates are feasible due to the high-connectivity design.

Significance. If the experimental results hold, this architecture could enable more efficient quantum circuits by replacing sequences of two-qubit gates with native multi-qubit operations, reducing depth and decoherence exposure on near-term hardware. The successful model-free RL application for complex gate synthesis is a concrete strength that provides a data-driven alternative to analytic pulse design.

major comments (2)
  1. [Abstract] Abstract and title: The framing of 'efficient n-qubit entangling operations' and the claim that 'Higher nth-order gates may also be feasible' rest on an extrapolation from three-qubit demonstrations only. No scaling analysis, fidelity projections, or hardware constraints for n>3 are provided, making the generalization to arbitrary n load-bearing for the central claim but unsupported by data.
  2. [Results] Results on RL-trained gates: While the manuscript reports successful training of the three-qubit controlled-SWAP, Fredkin, and Toffoli gates, the quantitative efficiency gain (gate time and fidelity relative to decomposed two-qubit implementations) is stated qualitatively as 'faster' and 'good' without tabulated values, error bars, or direct comparisons in the main text or supplementary material.
minor comments (3)
  1. [Abstract] The abstract refers to 'good fidelities' without numerical values; these should be stated explicitly (with uncertainties) to allow readers to assess the claims.
  2. [Figures] Figure captions and schematics of the router should include explicit labels for qubit-router connections and control lines to improve readability for readers unfamiliar with the prior two-qubit work.
  3. [Methods] A brief discussion of how the RL reward function incorporates both gate fidelity and duration would clarify the optimization objective.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive review and for highlighting areas where the manuscript's claims and quantitative reporting can be strengthened. We agree with both major comments and will revise the manuscript to address them directly. Our point-by-point responses follow.

read point-by-point responses

  1. Referee: [Abstract] Abstract and title: The framing of 'efficient n-qubit entangling operations' and the claim that 'Higher nth-order gates may also be feasible' rest on an extrapolation from three-qubit demonstrations only. No scaling analysis, fidelity projections, or hardware constraints for n>3 are provided, making the generalization to arbitrary n load-bearing for the central claim but unsupported by data.

    Authors: We agree that the generalization to arbitrary n is unsupported by data or analysis in the current manuscript. In the revised version we will change the title to focus on the demonstrated programmable multi-qubit operations (up to three qubits) and will rewrite the abstract to remove the unqualified claim that higher-order gates 'may also be feasible.' We will instead state that the router architecture provides the connectivity needed to explore such gates and note that experimental realization for n>3 remains future work. A brief paragraph discussing the main hardware and control challenges for scaling will be added to the discussion section. revision: yes

  2. Referee: [Results] Results on RL-trained gates: While the manuscript reports successful training of the three-qubit controlled-SWAP, Fredkin, and Toffoli gates, the quantitative efficiency gain (gate time and fidelity relative to decomposed two-qubit implementations) is stated qualitatively as 'faster' and 'good' without tabulated values, error bars, or direct comparisons in the main text or supplementary material.

    Authors: We accept that the efficiency claims are presented too qualitatively. Although raw numbers appear in the supplementary material, they are not organized for direct comparison. In the revision we will add a compact table (main text or supplementary) that lists, for each RL-trained gate, the optimized gate duration, the measured process fidelity with statistical error bars, and the corresponding values obtained from a standard two-qubit-gate decomposition of the same unitary. This will make the efficiency advantage explicit and allow readers to evaluate the reported gains quantitatively. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental demonstration with independent measurements

full rationale

The paper reports hardware experiments realizing 3-qubit gates (controlled-SWAP, Fredkin, Toffoli) and RL-trained CZ on a reconfigurable router platform. No mathematical derivation, ansatz, or fitting procedure is presented that reduces any claimed result to its own inputs by construction. The single self-citation to prior work (Wu et al. PRX 2024) describes the base two-qubit router hardware but does not bear the load of the new multi-qubit results, which rest on direct experimental data and fidelities. The statement that higher-n gates 'may also be feasible' is explicitly prospective and not used to support any demonstrated claim. The work is therefore self-contained against external experimental benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Experimental paper; no mathematical free parameters, axioms, or invented entities are invoked in the abstract. The router is a physical device whose behavior is calibrated experimentally.

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Reference graph

Works this paper leans on

112 extracted references · 112 canonical work pages · 3 internal anchors

  1. [1]

    D.Castelvecchi,Ibmreleasesfirst-ever1, 000-qubitquan- tum chip, Nature624, 238–238 (2023)

    work page 2023

  2. [2]

    H. J. Manetsch, G. Nomura, E. Bataille, X. Lv, K. H. Leung,andM.Endres,Atweezerarraywith6, 100highly coherent atomic qubits, Nature647, 60–67 (2025)

    work page 2025

  3. [3]

    Layden, G

    D. Layden, G. Mazzola, R. V. Mishmash, M. Motta, P. Wocjan, J.-S. Kim, and S. Sheldon, Quantum- enhanced markov chain monte carlo, Nature619, 282–287 (2023)

    work page 2023

  4. [4]

    Arute, K

    F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. S. L. Brandao, D. A. Buell, B. Burkett, Y. Chen, Z. Chen, B. Chiaro, R. Collins, W. Courtney, A. Dunsworth, E. Farhi, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, K. Guerin, S. Habegger, M. P. Harrigan, M. J. Hartmann, A. Ho, M. Hoffmann, T. Huang, T. S...

    work page 2019

  5. [5]

    Morvan, B

    A. Morvan, B. Villalonga, X. Mi, S. Mandrà, A. Bengts- son, P. V. Klimov, Z. Chen, S. Hong, C. Erickson, I. K. Drozdov, J. Chau, G. Laun, R. Movassagh, A. As- faw, L. T. A. N. Brandão, R. Peralta, D. Abanin, R. Acharya, R. Allen, T. I. Andersen, K. Anderson, M. Ansmann, F. Arute, K. Arya, J. Atalaya, J. C. Bardin, A. Bilmes, G. Bortoli, A. Bourassa, J. Bo...

    work page 2024

  6. [6]

    Bluvstein, S

    D. Bluvstein, S. J. Evered, A. A. Geim, S. H. Li, H. Zhou, T. Manovitz, S. Ebadi, M. Cain, M. Kali- nowski, D. Hangleiter, J. P. Bonilla Ataides, N. Maskara, I. Cong, X. Gao, P. Sales Rodriguez, T. Karolyshyn, G. Semeghini, M. J. Gullans, M. Greiner, V. Vuletić, and M. D. Lukin, Logical quantum processor based on reconfigurable atom arrays, Nature626, 58–...

    work page 2023

  7. [7]

    Bravyi, A

    S. Bravyi, A. W. Cross, J. M. Gambetta, D. Maslov, P. Rall, and T. J. Yoder, High-threshold and low- overhead fault-tolerant quantum memory, Nature627, 778 (2024)

    work page 2024

  8. [8]

    Acharya, D

    R. Acharya, D. A. Abanin, L. Aghababaie-Beni, I. Aleiner, T. I. Andersen, M. Ansmann, F. Arute, K. Arya, A. Asfaw, N. Astrakhantsev, J. Atalaya, R. Babbush, D. Bacon, B. Ballard, J. C. Bardin, J. Bausch, A. Bengtsson, A. Bilmes, S. Blackwell, S. Boixo, G. Bortoli, A. Bourassa, J. Bovaird, L. Brill, M. Broughton, D. A. Browne, B. Buchea, B. B. Buck- ley, D...

    work page 2024

  9. [9]

    K. Wang, Z. Lu, C. Zhang, G. Liu, J. Chen, Y. Wang, Y. Wu, S. Xu, X. Zhu, F. Jin, Y. Gao, Z. Tan, Z. Cui, N. Wang, Y. Zou, A. Zhang, T. Li, F. Shen, J. Zhong, Z. Bao, Z. Zhu, Y. Han, Y. He, J. Shen, H. Wang, J.- N. Yang, Z. Song, J. Deng, H. Dong, Z.-Z. Sun, W. Li, Q. Ye, S. Jiang, Y. Ma, P.-X. Shen, P. Zhang, H. Li, Q. Guo, Z. Wang, C. Song, H. Wang, and...

    work page 2026

  10. [10]

    Barenco, C

    A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, Elementary gates for quantum computa- tion, Physical Review A52, 3457–3467 (1995)

    work page 1995

  11. [11]

    A. W. Cross, L. S. Bishop, S. Sheldon, P. D. Nation, and J. M. Gambetta, Validating quantum computers us- ing randomized model circuits, Physical Review A100, 032328 (2019)

    work page 2019

  12. [12]

    González-García, R

    G. González-García, R. Trivedi, and J. I. Cirac, Error propagation in NISQ devices for solving classical opti- mization problems, PRX Quantum3, 040326 (2022)

    work page 2022

  13. [13]

    Song, S.-B

    C. Song, S.-B. Zheng, P. Zhang, K. Xu, L. Zhang, Q. Guo, W. Liu, D. Xu, H. Deng, K. Huang, D. Zheng, X. Zhu, and H. Wang, Continuous-variable geometric phaseanditsmanipulationforquantumcomputationina superconducting circuit, Nature Communications8, 1061 (2017)

    work page 2017

  14. [14]

    Feng and D.-w

    W. Feng and D.-w. Wang, Quantum fredkin gate based on synthetic three-body interactions in superconducting circuits, Physical Review A101, 062312 (2020)

    work page 2020

  15. [15]

    T. Roy, S. Hazra, S. Kundu, M. Chand, M. P. Patankar, and R. Vijay, Programmable superconducting processor with native three-qubit gates, Physical Review Applied 14, 014072 (2020)

    work page 2020

  16. [16]

    X. Gu, J. Fernández-Pendás, P. Vikstål, T. Abad, C. Warren, A. Bengtsson, G. Tancredi, V. Shumeiko, J. Bylander, G. Johansson, and A. F. Kockum, Fast mul- tiqubit gates through simultaneous two-qubit gates, PRX Quantum2, 040348 (2021)

    work page 2021

  17. [17]

    Y.Kim, A.Morvan, L.B.Nguyen, R.K.Naik, C.Jünger, L.Chen, J.M.Kreikebaum, D.I.Santiago,andI.Siddiqi, High-fidelity three-qubit itoffoli gate for fixed-frequency superconducting qubits, Nature Physics18, 783–788 (2022)

    work page 2022

  18. [18]

    Feng, G.-Q

    W. Feng, G.-Q. Zhang, Q.-P. Su, J.-X. Zhang, and C.- P. Yang, Generation of greenberger-horne-zeilinger states on two-dimensional superconducting-qubit lattices via parallel multiqubit-gate operations, Physical Review Ap- plied18, 064036 (2022)

    work page 2022

  19. [19]

    N. J. Glaser, F. Roy, and S. Filipp, Controlled-controlled- phase gates for superconducting qubits mediated by a shared tunable coupler, Physical Review Applied19, 044001 (2023)

    work page 2023

  20. [20]

    K. S. Christensen, N. T. Zinner, and M. Kjaer- gaard, Scheme for parity-controlled multi-qubit gates with superconducting qubits, arXiv preprint (2023), arXiv:2302.00719 [quant-ph]

    work page arXiv 2023

  21. [21]

    Bengtsson, J

    C.W.Warren, J.Fernández-Pendás, S.Ahmed, T.Abad, A. Bengtsson, J. Biznárová, K. Debnath, X. Gu, C. Križan, A. Osman, A. Fadavi Roudsari, P. Delsing, G. Johansson, A. Frisk Kockum, G. Tancredi, and J. By- lander, Extensive characterization and implementation of a family of three-qubit gates at the coherence limit, npj Quantum Information9, 44 (2023)

    work page 2023

  22. [22]

    C.-K. Hu, J. Yuan, B. A. Veloso, J. Qiu, Y. Zhou, L. Zhang, J. Chu, O. Nurbolat, L. Hu, J. Li, Y. Xu, Y. Zhong, S. Liu, F. Yan, D. Tan, R. Bachelard, A. C. Santos, C. Villas-Boas, and D. Yu, Native conditional iSWAP operation with superconducting artificial atoms, Physical Review Applied20, 034072 (2023)

    work page 2023

  23. [23]

    T.Itoko, M.Malekakhlagh, N.Kanazawa,andM.Takita, Three-qubit parity gate via simultaneous cross-resonance drives, Physical Review Applied21, 034018 (2024)

    work page 2024

  24. [24]

    S. Huai, K. Bu, X. Gu, Z. Zhang, S. An, X. Yang, Y. Li, T. Cai, and Y. Zheng, Fast joint parity measurement via collective interactions induced by stimulated emission, Nature Communications15, 3045 (2024)

    work page 2024

  25. [25]

    S. S. Pratapsi, D. Cruz, and P. André, Native multi-qubit gates in transmon qubits via synchronous driving, Scien- tific Reports14, 26042 (2024)

    work page 2024

  26. [26]

    Liu, B.-J

    H.-T. Liu, B.-J. Chen, J.-C. Zhang, Y.-X. Xiao, T.-M. Li, K. Huang, Z. Wang, H. Li, K. Zhao, Y. Xu, C.-L. Deng, G.-H. Liang, Z.-H. Liu, S.-Y. Zhou, C.-P. Fang, X. Song, Z. Xiang, D. Zheng, Y.-H. Shi, K. Xu, and H. Fan, Direct implementation of high-fidelity three-qubit gates for su- perconducting processor with tunable couplers, Physical Review Letters135...

    work page 2025

  27. [27]

    Zhao, W.-G

    K. Zhao, W.-G. Ma, Z. Wang, H. Li, K. Huang, Y.-H. Shi, K.Xu,andH.Fan,Microwave-activatedhigh-fidelity three-qubit gate scheme for fixed-frequency supercon- ducting qubits, Physical Review Applied24, 034064 (2025)

    work page 2025

  28. [28]

    Tasler, J

    S. Tasler, J. Old, L. Heunisch, V. Feulner, T. Eckstein, M. Müller, and M. J. Hartmann, Optimizing supercon- ducting three-qubit gates for surface-code error correc- tion, arXiv preprint (2025), arXiv:2506.09028 [quant- ph]

    work page arXiv 2025

  29. [29]

    Neeley, R

    M. Neeley, R. C. Bialczak, M. Lenander, E. Lucero, M. Mariantoni, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A. N. Cleland, and J. M. Martinis, Generation of three-qubit entangled states using superconducting phase qubits, Na- ture467, 570–573 (2010)

    work page 2010

  30. [30]

    Kang, Y.-H

    Y.-H. Kang, Y.-H. Chen, Q.-C. Wu, B.-H. Huang, J. Song, and Y. Xia, Fast generation of W states of super- conducting qubits with multiple Schrödinger dynamics, Scientific Reports6, 36737 (2016)

    work page 2016

  31. [31]

    C. Song, K. Xu, H. Li, Y.-R. Zhang, X. Zhang, W. Liu, Q. Guo, Z. Wang, W. Ren, J. Hao, H. Feng, H. Fan, D. Zheng, D.-W. Wang, H. Wang, and S.-Y. Zhu, Gen- eration of multicomponent atomic Schrödinger cat states of up to 20 qubits, Science365, 574 (2019)

    work page 2019

  32. [32]

    W. Liu, W. Feng, W. Ren, D.-W. Wang, and H. Wang, Synthesizing three-body interaction of spin chirality with superconducting qubits, Applied Physics Letters116, 114001 (2020)

    work page 2020

  33. [33]

    D. V. Babukhin, A. A. Zhukov, and W. V. Pogosov, Hybrid digital-analog simulation of many-body dynam- ics with superconducting qubits, Physical Review A101, 052337 (2020)

    work page 2020

  34. [34]

    Gonzalez-Raya, R

    T. Gonzalez-Raya, R. Asensio-Perea, A. Martin, L. C. Céleri, M. Sanz, P. Lougovski, and E. F. Dumitrescu, Digital-analog quantum simulations using the cross- resonance effect, PRX Quantum2, 020328 (2021)

    work page 2021

  35. [35]

    Yarkoni, E

    S. Yarkoni, E. Raponi, T. Bäck, and S. Schmitt, Quan- tum annealing for industry applications: introduction and review, Reports on Progress in Physics85, 104001 (2022)

    work page 2022

  36. [36]

    Menke, W

    T. Menke, W. P. Banner, T. R. Bergamaschi, A. Di Paolo, A. Vepsäläinen, S. J. Weber, R. Winik, A. Melville, B. M. Niedzielski, D. Rosenberg, K. Ser- niak, M. E. Schwartz, J. L. Yoder, A. Aspuru-Guzik, S. Gustavsson, J. A. Grover, C. F. Hirjibehedin, A. J. Kerman, and W. D. Oliver, Demonstration of tunable three-body interactions between superconducting qu...

    work page 2022

  37. [37]

    L. B. Nguyen, Y. Kim, A. Hashim, N. Goss, B. Marinelli, B. Bhandari, D. Das, R. K. Naik, J. M. Kreike- 8 baum, A. N. Jordan, D. I. Santiago, and I. Siddiqi, Programmable Heisenberg interactions between floquet qubits, Nature Physics20, 240–246 (2024)

    work page 2024

  38. [38]

    Liang, W

    Y. Liang, W. Huang, L. Zhang, Z. Tao, K. Tang, J. Chu, J. Qiu, X. Sun, Y. Zhou, J. Zhang, J. Zhang, W. Guo, Y. Liu, Y. Chen, S. Liu, Y. Zhong, J. Niu, and D. Yu, Floquet engineering of anisotropic transverse interac- tions in superconducting qubits, arXiv preprint (2024), arXiv:2410.10208 [quant-ph]

    work page arXiv 2024

  39. [39]

    I. T. Rosen, S. Muschinske, C. N. Barrett, A. Chatter- jee, M. Hays, M. A. DeMarco, A. H. Karamlou, D. A. Rower, R. Das, D. K. Kim, B. M. Niedzielski, M. Schuldt, K. Serniak, M. E. Schwartz, J. L. Yoder, J. A. Grover, and W. D. Oliver, A synthetic magnetic vector potential in a 2d superconducting qubit array, Nature Physics20, 1881–1887 (2024)

    work page 2024

  40. [40]

    Zhang, Y

    P. Zhang, Y. Gao, X. Xu, N. Wang, H. Dong, C. Guo, J. Deng, X. Zhang, J. Chen, S. Xu, K. Wang, Y. Wu, C. Zhang, F. Jin, X. Zhu, A. Zhang, Y. Zou, Z. Tan, Z. Cui, Z. Zhu, F. Shen, T. Li, J. Zhong, Z. Bao, L. Zhao, J. Hao, H. Li, Z. Wang, C. Song, Q. Guo, H. Wang, and D. Poletti, Emergence of steady quantum transport in a superconducting processor, Nature C...

    work page 2024

  41. [41]

    S. Li, Y. Fan, X. Li, X. Ruan, Q. Zhao, Z. Peng, R.- B. Wu, J. Zhang, and P. Song, Robust quantum con- trol using reinforcement learning from demonstration, npj Quantum Information11, 124 (2025)

    work page 2025

  42. [42]

    K. Zhao, Z. Wang, Y. Liu, G.-H. Liang, C.-P. Fang, Y.- H. Shi, L. Zhang, J.-C. Zhang, T.-M. Li, H. Li, Y. Xu, W.-G. Ma, H.-T. Liu, J.-C. Song, Z.-T. Bao, Y.-X. Xiao, B.-J. Chen, C.-L. Deng, Z.-H. Liu, Y. He, S.-Y. Zhou, X. Song, Z. Xiang, D. Zheng, K. Huang, K. Xu, and H. Fan, Microwave engineering of tunable spin interac- tions with superconducting qubit...

    work page 2025

  43. [43]

    Yan, Z.-Y

    Z. Yan, Z.-Y. Ge, R. Li, Y.-R. Zhang, F. Nori, and Y. Nakamura, Characterizing many-body dynamics with projected ensembles on a superconducting quantum pro- cessor, arXiv preprint (2025), arXiv:2506.21061 [quant- ph]

    work page arXiv 2025

  44. [44]

    W.Huang, X.Sun, J.Zhang, Z.Guo, P.Huang, Y.Liang, Y. Liu, D. Sun, Z. Wang, Y. Xiong, X. Yang, J. Zhang, L. Zhang, J. Chu, W. Guo, J. Jiang, S. Liu, J. Niu, J. Qiu, Z. Tao, Y. Zhou, X. Linpeng, Y. Zhong, and D. Yu, Logical multi-qubit entanglement with dual-rail superconducting qubits, Nature Physics 10.1038/s41567- 026-03211-9 (2026)

    work page doi:10.1038/s41567- 2026

  45. [45]

    Leung, Y

    N. Leung, Y. Lu, S. Chakram, R. K. Naik, N. Earnest, R. Ma, K. Jacobs, A. N. Cleland, and D. I. Schuster, De- terministic bidirectional communication and remote en- tanglement generation between superconducting qubits, npj Quantum Information5, 18 (2019)

    work page 2019

  46. [46]

    Magnard, S

    P. Magnard, S. Storz, P. Kurpiers, J. Schär, F. Marxer, J. Lütolf, T. Walter, J.-C. Besse, M. Gabureac, K. Reuer, A. Akin, B. Royer, A. Blais, and A. Wallraff, Microwave quantum link between superconducting circuits housed in spatially separated cryogenic systems, Phys. Rev. Lett. 125, 260502 (2020)

    work page 2020

  47. [47]

    Zhong, H.-S

    Y. Zhong, H.-S. Chang, A. Bienfait, É. Dumur, M.-H. Chou, C. R. Conner, J. Grebel, R. G. Povey, H. Yan, D. I. Schuster, and A. N. Cleland, Deterministic multi- qubit entanglement in a quantum network, Nature590, 571 (2021)

    work page 2021

  48. [48]

    J. Niu, L. Zhang, Y. Liu, J. Qiu, W. Huang, J. Huang, H. Jia, J. Liu, Z. Tao, W. Wei, Y. Zhou, W. Zou, Y. Chen, X. Deng, X. Deng, C. Hu, L. Hu, J. Li, D. Tan, Y. Xu, F. Yan, T. Yan, S. Liu, Y. Zhong, A. N. Cleland, and D. Yu, Low-loss interconnects for modular supercon- ducting quantum processors, Nature Electronics6, 235 (2023)

    work page 2023

  49. [49]

    Storz, J

    S. Storz, J. Schär, A. Kulikov, P. Magnard, P. Kurpiers, J. Lütolf, T. Walter, A. Copetudo, K. Reuer, A. Akin, J.- C. Besse, M. Gabureac, G. J. Norris, A. Rosario, F. Mar- tin, J. Martinez, W. Amaya, M. W. Mitchell, C. Abel- lan, J.-D. Bancal, N. Sangouard, B. Royer, A. Blais, and A. Wallraff, Loophole-free bell inequality violation with superconducting c...

    work page 2023

  50. [50]

    C. Zhou, P. Lu, M. Praquin, T.-C. Chien, R. Kaufman, X. Cao, M. Xia, R. S. K. Mong, W. Pfaff, D. Pekker, and M. Hatridge, Realizing all-to-all couplings among detach- able quantum modules using a microwave quantum state router, npj Quantum Information9, 54 (2023)

    work page 2023

  51. [51]

    Field, A.Q.Chen, B.Scharmann, E.A.Sete, F.Oruc, K

    M. Field, A.Q.Chen, B.Scharmann, E.A.Sete, F.Oruc, K. Vu, V. Kosenko, J. Y. Mutus, S. Poletto, and A. Best- wick, Modular superconducting-qubit architecture with a multichip tunable coupler, Physical Review Applied21, 054063 (2024)

    work page 2024

  52. [52]

    X. Wu, H. Yan, G. Andersson, A. Anferov, M.-H. Chou, C. R. Conner, J. Grebel, Y. J. Joshi, S. Li, J. M. Miller, R. G. Povey, H. Qiao, and A. N. Cleland, Modular quan- tum processor with an all-to-all reconfigurable router, Physical Review X14, 041030 (2024)

    work page 2024

  53. [53]

    Mollenhauer, A

    M. Mollenhauer, A. Irfan, X. Cao, S. Mandal, and W. Pfaff, A high-efficiency elementary network of inter- changeable superconducting qubit devices, Nature Elec- tronics8, 610–619 (2025)

    work page 2025

  54. [54]

    J. Song, S. Yang, P. Liu, H.-L. Zhang, G.-M. Xue, Z.- Y. Mi, W.-G. Zhang, F. Yan, Y.-R. Jin, and H.-F. Yu, Realization of high-fidelity perfect entanglers between re- mote superconducting quantum processors, Physical Re- view Letters135, 050603 (2025)

    work page 2025

  55. [55]

    Fösel, P

    T. Fösel, P. Tighineanu, T. Weiss, and F. Marquardt, Re- inforcement learning with neural networks for quantum feedback, Physical Review X8, 031084 (2018)

    work page 2018

  56. [56]

    M. Y. Niu, S. Boixo, V. N. Smelyanskiy, and H. Neven, Universal quantum control through deep reinforcement learning, npj Quantum Information5, 33 (2019)

    work page 2019

  57. [57]

    Zhang, Z

    X.-M. Zhang, Z. Wei, R. Asad, X.-C. Yang, and X. Wang, When does reinforcement learning stand out in quantum control? a comparative study on state preparation, npj Quantum Information5, 85 (2019)

    work page 2019

  58. [58]

    Metz and M

    F. Metz and M. Bukov, Self-correcting quantum many- body control using reinforcement learning with tensor networks,NatureMachineIntelligence5,780–791(2023)

    work page 2023

  59. [59]

    Y. Baum, M. Amico, S. Howell, M. Hush, M. Liuzzi, P. Mundada, T. Merkh, A. R. Carvalho, and M. J. Bier- cuk, Experimental deep reinforcement learning for error- robust gate-set design on a superconducting quantum computer, PRX Quantum2, 040324 (2021)

    work page 2021

  60. [60]

    V.V.Sivak, A.Eickbusch, H.Liu, B.Royer, I.Tsioutsios, and M. H. Devoret, Model-free quantum control with reinforcement learning, Physical Review X12, 011059 (2022)

    work page 2022

  61. [61]

    V. V. Sivak, A. Eickbusch, B. Royer, S. Singh, I. Tsiout- sios, S. Ganjam, A. Miano, B. L. Brock, A. Z. Ding, L. Frunzio, S. M. Girvin, R. J. Schoelkopf, and M. H. De- voret, Real-time quantum error correction beyond break- 9 even, Nature616, 50–55 (2023)

    work page 2023

  62. [62]

    L. Ding, M. Hays, Y. Sung, B. Kannan, J. An, A. Di Paolo, A. H. Karamlou, T. M. Hazard, K. Azar, D. K. Kim, B. M. Niedzielski, A. Melville, M. E. Schwartz, J. L. Yoder, T. P. Orlando, S. Gustavsson, J. A. Grover, K. Serniak, and W. D. Oliver, High- fidelity, frequency-flexible two-qubit fluxonium gates with a transmon coupler, Physical Review X13, 031035 (2023)

    work page 2023

  63. [63]

    K.Reuer, J.Landgraf, T.Fösel, J.O’Sullivan, L.Beltrán, A. Akin, G. J. Norris, A. Remm, M. Kerschbaum, J.-C. Besse, F. Marquardt, A. Wallraff, and C. Eichler, Real- izing a deep reinforcement learning agent for real-time quantum feedback, Nature Communications14, 7138 (2023)

    work page 2023

  64. [64]

    Wright and R

    E. Wright and R. De Sousa, Fast quantum gate design with deep reinforcement learning using real-time feed- back on readout signals, 2023 IEEE International Con- ference on Quantum Computing and Engineering (QCE) , 1295–1303 (2023)

    work page 2023

  65. [65]

    Reinschmidt, J

    M. Reinschmidt, J. Fortágh, A. Günther, and V. V. Volchkov, Reinforcement learning in cold atom experi- ments, Nature Communications15, 8532 (2024)

    work page 2024

  66. [66]

    Chatterjee, J

    A. Chatterjee, J. Schwinger, and Y. Y. Gao, Enhanced qubit readout via reinforcement learning, Physical Re- view Applied23, 054057 (2025)

    work page 2025

  67. [67]

    Almanakly, B

    A. Almanakly, B. Yankelevich, M. Hays, B. Kannan, R. Assouly, A. Greene, M. Gingras, B. M. Niedzielski, H. Stickler, M. E. Schwartz, K. Serniak, J. Î.-j. Wang, T. P. Orlando, S. Gustavsson, J. A. Grover, and W. D. Oliver, Deterministic remote entanglement using a chiral quantum interconnect, Nature Physics21, 825 (2025)

    work page 2025

  68. [68]

    How to Build a Quantum Supercomputer: Scaling from Hundreds to Millions of Qubits

    M. Mohseni, A. Scherer, K. G. Johnson, O. Wertheim, M. Otten, N. A. Aadit, K. M. Bresniker, K. Y. Cam- sari, B. Chapman, S. Chatterjee, G. A. Dagnew, A. Es- posito, F. Fahim, M. Fiorentino, A. Khalid, X. Kong, B. Kulchytskyy, R. Li, P. A. Lott, I. L. Markov, R. F. McDermott, G. Pedretti, A. Gajjar, A. Silva, J. Sorebo, P.Spentzouris, Z.Steiner, B.Torosov,...

    work page internal anchor Pith review arXiv 2024

  69. [69]

    Bausch, A

    J. Bausch, A. W. Senior, F. J. H. Heras, T. Edlich, A. Davies, M. Newman, C. Jones, K. Satzinger, M. Y. Niu, S. Blackwell, G. Holland, D. Kafri, J. Atalaya, C.Gidney, D.Hassabis, S.Boixo, H. Neven,and P. Kohli, Learning high-accuracy error decoding for quantum pro- cessors, Nature635, 834–840 (2024)

    work page 2024

  70. [70]

    Aspuru-Guzik, S

    Y.Alexeev, M.H.Farag, T.L.Patti, M.E.Wolf, N.Ares, A. Aspuru-Guzik, S. C. Benjamin, Z. Cai, S. Cao, C. Chamberland, Z. Chandani, F. Fedele, I. Hama- mura, N. Harrigan, J.-S. Kim, E. Kyoseva, J. G. Li- etz, T. Lubowe, A. McCaskey, R. G. Melko, K. Nakaji, A. Peruzzo, P. Rao, B. Schmitt, S. Stanwyck, N. M. Tub- man, H. Wang, and T. Costa, Artificial intellig...

    work page 2025

  71. [71]

    R. B. Patel, J. Ho, F. Ferreyrol, T. C. Ralph, and G. J. Pryde, A quantum fredkin gate, Science Advances2, 1501531 (2016)

    work page 2016

  72. [72]

    Supplemental material, (2026)

    work page 2026

  73. [73]

    Häffner, W

    H. Häffner, W. Hänsel, C. F. Roos, J. Benhelm, D. Chek- al kar, M. Chwalla, T. Körber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Gühne, W. Dür, and R. Blatt, Scalable multiparticle entanglement of trapped ions, Nature438, 643 (2005)

    work page 2005

  74. [74]

    Ansel, E

    Q. Ansel, E. Dionis, F. Arrouas, B. Peaudecerf, S. Guérin, D. Guéry-Odelin, and D. Sugny, Introduction to theoretical and experimental aspects of quantum op- timal control, Journal of Physics B: Atomic, Molecular and Optical Physics57, 133001 (2024)

    work page 2024

  75. [75]

    Khaneja, T

    N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbrüggen, and S. J. Glaser, Optimal control of coupled spin dynam- ics: design of nmr pulse sequences by gradient ascent al- gorithms, Journal of Magnetic Resonance172, 296–305 (2005)

    work page 2005

  76. [76]

    Kelly, R

    J. Kelly, R. Barends, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, I.-C. Hoi, E. Jef- frey, A. Megrant, J. Mutus, C. Neill, P. J. J. O’Malley, C. Quintana, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Cleland, and J. M. Marti- nis, Optimal quantum control using randomized bench- marking, Phys. Rev. Lett.112, ...

    work page 2014

  77. [77]

    C. E. Granade, C. Ferrie, N. Wiebe, and D. G. Cory, Ro- bust online hamiltonian learning, New Journal of Physics 14, 103013 (2012)

    work page 2012

  78. [79]

    Y. Sung, L. Ding, J. Braumüller, A. Vepsäläinen, B. Kan- nan, M. Kjaergaard, A. Greene, G. O. Samach, C. Mc- Nally, D. Kim, A. Melville, B. M. Niedzielski, M. E. Schwartz, J. L. Yoder, T. P. Orlando, S. Gustavsson, and W. D. Oliver, Realization of high-fidelity CZ andZZ-free iSWAP gates with a tunable coupler, Physical Review X 11, 021058 (2021)

    work page 2021

  79. [80]

    T. Abad, J. Fernández-Pendás, A. Frisk Kockum, and G. Johansson, Universal fidelity reduction of quantum operations from weak dissipation, Physical Review Let- ters129, 150504 (2022)

    work page 2022

  80. [81]

    P. M. Q. Cruz and B. Murta, Shallow unitary de- compositions of quantum fredkin and toffoli gates for connectivity-aware equivalent circuit averaging, APL Quantum1, 016105 (2024). Supplemental Material: Efficientn-qubit entangling operations via a superconducting quantum router Xuntao Wu,1 Haoxiong Yan,1,∗ Gustav Andersson,1 Alexander Anferov,1,† Christop...

    work page 2024

Showing first 80 references.