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This paper proposes that two synchronously flux-tuned double-transmon couplers bridged by a 25 cm coaxial cable create a switchable nonlocal ZZ interaction between remote fixed-frequency transmon qubits, enabling a simulated remote CZ gate

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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A simulated scheme with synchronously tuned double-transmon couplers at both ends of a 25-cm cable is predicted to enable a high-fidelity remote controlled-Z gate between fixed-frequency qubits, with tunable nonlocal ZZ coupling.

T0 review reviewed 2026-08-02 challenge →

load-bearing objection A plausible simulation-based proposal for remote CZ gates that hinges on an unverified two-mode truncation of the cable; worth refereeing, but the headline numbers need a convergence check. the 3 major comments →

arxiv 2603.28526 v2 pith:X3PLWX6J submitted 2026-03-30 quant-ph

Tunable Nonlocal $ZZ$ Interaction for Remote Controlled-Z Gates Between Distributed Fixed-Frequency Qubits

Benzheng Yuan , Chaojie Zhang , Haoran He , Yangyang Fei , Chuanbing Han , Shuya Wang , Huihui Sun , Qing Mu
show 4 more authors
Bo Zhao Fudong Liu Weilong Wang Zheng Shan
This is my paper
classification quant-ph
keywords modular superconducting processorsfixed-frequency transmon qubitsdouble-transmon couplernonlocal ZZ interactionremote controlled-Z gatecoaxial cable interconnecttunable couplingcircuit QED
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

The paper aims to show that two fixed-frequency transmon qubits in separate packages can be entangled directly through a 25 cm superconducting cable, without a state-transfer protocol, by synchronously tuning a double-transmon coupler at each end. Each coupler mediates a flux-controlled cross-Kerr interaction between its local qubit and a cable mode; tuned together, the two couplers create a long-range ZZ coupling between distant qubits that can be switched from roughly 10^-5 MHz to above 10 MHz. The claimed payoff is a remote controlled-Z gate with a simulated 99.99% average closed-system fidelity, an on/off ratio exceeding 10^6, and no tunability or flux-noise burden on the fixed-frequency qubits themselves. If correct, this would give modular superconducting processors a gate-native interconnect and remove a significant scaling bottleneck.

Core claim

The central claim is that a double-transmon coupler (DTC)—a flux-threaded superconducting loop containing two transmon modes and a coupling Josephson junction—can serve as a gain-controlled tap between a fixed-frequency qubit and a multimode cable. In the local subsystem, the qubit–cable cross-Kerr strength is extracted from the energy combination ζ = E1100 − E0100 − E1000 + E0000; tuning the DTC flux near 0.3 (in units of the flux quantum) suppresses this coupling to about 10^-5 MHz, while flux near 0.5 maximizes it. Because structurally identical DTCs sit at opposite ends of the same cable, synchronously biasing both converts the two local qubit–cable couplings into a nonlocal qubit–qubit

What carries the argument

The load-bearing component is the double-transmon coupler (DTC): a superconducting loop containing two transmon modes and a coupling Josephson junction, threaded by external flux. Flux modulates both the coupler's nonlinearity and its coupling rate, so the same device can idle (qubit–cable ZZ ≈ 10^-5 MHz at flux 0.3) or activate (≳ 10 MHz at flux 0.5). The effective interaction strength is computed from the energy combination ζ = E1100 − E0100 − E1000 + E0000, and the global remote coupling emerges when identical DTCs at both cable ends are tuned synchronously. A second ingredient is the spatial parity of the retained cable modes: mode m=10 couples with the same sign to both ends, while mode

Load-bearing premise

The load-bearing premise, stated in the Distributed Circuit Architecture section, is that the 25 cm cable can be modeled as a lossless resonator with its spectrum truncated to the two modes (m=10 and m=11) closest to the qubit frequencies, and that all other cable modes, cable loss, connector parasitics, and impedance mismatches contribute below roughly 10^-4; if they leak or dephase at that level, the 99.99% fidelity and 10^6 on/off ratio would not hold.

What would settle it

Run the simulation with the complete cable mode ladder and a lossy transmission-line model, or measure the qubit–cable ZZ on a single package across flux at the idle point; if leakage or dephasing from neglected modes, cable loss, or connector reflections appears at the 10^-4 level during a 350 ns gate, or if the measured idle ZZ is orders of magnitude above 10^-5 MHz, the predicted 99.99% fidelity and 10^6 on/off ratio are falsified.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Remote CZ gates can be executed directly between fixed-frequency qubits in separate packages, removing the overhead of converting a state-transfer protocol into a two-qubit gate.
  • The nonlocal ZZ interaction can be switched between residual coupling on the order of 10^-5 MHz and active coupling above 10 MHz, so the same cable link can idle almost silently and then perform a 350 ns entangling gate on demand.
  • The tunability lives entirely in the couplers, so the fixed-frequency qubits keep their coherence and control advantages while the architecture gains modular connectivity.
  • Under the paper's open-system noise model, endpoint-qubit decoherence is the largest infidelity source, with photon loss in the retained cable modes smaller but non-negligible—pointing future work at qubit coherence and cable loss.
  • The mode-parity sign structure (mode m=11 couples with opposite signs at the two ends) is part of what shapes the interaction, so gate performance is tied to the cable's mode spectrum and length.

Where Pith is reading between the lines

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

  • A natural next calculation is to add the full cable mode ladder and a lossy transmission-line model; if the neglected modes remain far from the qubit frequencies the scheme should survive, but the on/off ratio will be bounded by how well those modes are suppressed.
  • The same DTC-pair mechanism could be extended to a network of modules by adding switching or multiple couplers along the cable, turning the remote gate into a routing primitive for distributed quantum error correction.
  • Because the cable's free spectral range (about 440 MHz) and mode parities shift with cable length, the scheme may be adaptable to other inter-module distances, though each distance would require fresh optimization of flux points and mode assignment.
  • A single-module experiment measuring ζ versus flux on one DTC plus the cable would already test the core contrast claim before building a full two-module device.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The manuscript proposes a modular superconducting architecture in which two fixed-frequency transmon qubits in separate packages are connected through a 25-cm coaxial cable, with each qubit coupled to the cable via a double-transmon coupler (DTC). By synchronously flux-biasing the two DTCs, the authors claim to activate a tunable nonlocal ZZ interaction on demand while suppressing residual static coupling, yielding an on/off ratio exceeding 10^6. Using a circuit Hamiltonian truncated to two cable modes (m=10,11) and QuTiP time evolution, they report a remote controlled-Z gate with 99.99% average gate fidelity after optimizing a truncated Fourier flux pulse. The abstract additionally refers to open-system simulations showing qubit decoherence and cable photon loss contributions, but these results do not appear in the visible main text.

Significance. If the reported performance holds, this would be a valuable primitive for modular superconducting processors using fixed-frequency qubits: it avoids state-transfer overhead, retains fixed-frequency qubit advantages, and provides a gate-native interconnect with simulated fidelity above common error-correction thresholds. The work uses the full circuit Hamiltonian rather than a simplified effective model, and the time-evolution solver is a standard, reproducible tool. The strengths are the architectural concept, the synchronous dual-DTC control scheme, and the detailed numerical approach to pulse optimization. However, the headline quantitative claims—on/off ratio >10^6 and 99.99% fidelity—rest on a two-mode cable truncation that is not convergence-tested, and the abstract promises open-system results that are absent from the main text. These issues must be addressed before the claims can be regarded as demonstrated.

major comments (3)
  1. [Distributed Circuit Architecture (p.3, cable truncation)] The cable is truncated to two harmonic modes m=10 and m=11 with couplings J46=+25 MHz and J47=-25 MHz, and no convergence check is provided for neighboring modes m=9 and m=12, which lie only ~440 MHz away and have comparable 1/sqrt(m) coupling amplitudes. The idle-point ZZ suppression in Fig. 3(b) is computed within a subsystem containing only modes 10 and 11; omitted modes could contribute residual ZZ at the 10^-5 MHz level or higher, directly affecting the on/off ratio claim. Please provide a quantitative justification: e.g., include the nearest omitted modes in the spectrum and ZZ extraction, estimate their perturbative contribution, or argue from a symmetry that their cancellation is robust. This is load-bearing for the central claims.
  2. [Abstract vs. Performance of the Remote CZ Gate (p.5-6)] The abstract states that 'Open-system simulations further indicate that... endpoint-qubit decoherence is the largest contribution... photon loss in the retained cable modes remains smaller but non-negligible', but the main text contains no Lindblad master equation, no noise parameters, and no open-system fidelity results. The only fidelity reported in the main text is a closed-system coherent fidelity extracted from the projected unitary, yet the conclusion calls it 'average gate fidelity'. This conflates two different quantities. Either include the open-system analysis with the model and parameters, or clearly and consistently label the 99.99% as a coherent, closed-system fidelity and avoid the unsubstantiated open-system claims in the abstract and conclusion.
  3. [Eq. (7), fidelity definition] The average gate fidelity is computed from the actual evolution operator projected onto the computational subspace. If leakage is non-zero, the projected map is not trace-preserving and Eq. (7) can overestimate the process fidelity unless appropriately renormalized or supplemented with a leakage term. The paper reports leakage below 10^-4, but the formula as written does not show how leakage is included in the 99.99% number. Please specify how the projected U is normalized and whether leakage is treated as infidelity in Eq. (7), or use a process fidelity definition that includes leakage.
minor comments (5)
  1. [Eq. (3) and Fig. 2 caption] Eq. (3) defines the cross-Kerr shift for a single cable mode but the text and Fig. 2 refer to two cable modes (Cb1, Cb2); clarify how the individual ζ values are extracted from the multi-mode spectrum. The Fig. 2 caption has a typo: 'Cp1A and while Cp1B'.
  2. [Fig. 3(b), color scale] The colorbar in Fig. 3(b) spans values that appear inconsistent with the caption 'log10|ZZ|' and the quoted 10^-5 MHz idle value. Please check the scaling and labeling so that the on/off ratio is visually and numerically unambiguous.
  3. [Eq. (6), pulse definition] In the flux waveform, Φ_f is described as 'modulation amplitude' but the formula uses it as the final target flux. Define Φ_f explicitly and state the initial/final flux values used in the optimization.
  4. [Gate duration] The gate duration T=350 ns is presented as fixed. Is this an optimized parameter or an imposed duration? A sensitivity analysis of fidelity versus T would strengthen the claim that the pulse is robust.
  5. [References and notation] Several references to the experimental literature are appropriate, but the paper would benefit from a brief statement distinguishing the present scheme from the long-range ZZ interaction of Ref. [43] and the resonator-induced phase of Ref. [42], particularly regarding the role of the DTCs in achieving high on/off ratio.

Circularity Check

0 steps flagged

No significant circularity; the derivation is a self-contained numerical simulation with clearly labeled modeling assumptions.

full rationale

The paper's chain is: circuit Hamiltonian → subsystem decomposition → ZZ extracted from energy shifts → global 8-mode Hamiltonian → optimized flux pulses → computed gate fidelity. Each step is computed from the stated model and does not presuppose the conclusion. The idle point and operation point are identified from the spectrum of the same model, but that is standard design within a simulation, not a derivation of the result from the conclusion. The reported 99.99% coherent fidelity is evaluated in the same model used for pulse optimization, so it is a numerical self-consistency check rather than an independent experimental benchmark; however, the abstract and text explicitly label it as 'projected coherent fidelity' and the open-system results as 'within the representative Markovian noise model considered here.' The cable truncation to two modes and neglect of loss/parasitics are acknowledged modeling limitations and pose a correctness or robustness risk, but they are not circular reasoning. There is no load-bearing self-citation, no imported uniqueness theorem, and no fitted parameter renamed as a prediction. Therefore no significant circularity is present.

Axiom & Free-Parameter Ledger

5 free parameters · 4 axioms · 0 invented entities

The core simulation rests on a long list of hand-picked parameters, chosen flux operating points, optimized pulse coefficients, and a two-mode truncation of the cable. No independent experimental or formal verification is provided, so the reported 99.99% fidelity is a self-consistent model output rather than a benchmarked prediction.

free parameters (5)
  • Flux idle/working points Φ_idle≈0.3, Φ_work≈0.5 = 0.3 and 0.5 (in units of Φ0)
    Chosen by hand from the computed ZZ landscape to define off/on states; the entire gate protocol depends on these operating points.
  • Pulse coefficients λ_k (truncated Fourier series) = optimized numerically
    Free parameters optimized to suppress leakage and enforce the π conditional phase; any reported fidelity is conditional on this optimization.
  • Cable-mode coupling amplitudes J46^(m=11)=+25 MHz, J47^(m=11)=-25 MHz = ±25 MHz
    Assigned 'to reflect this spatial difference' rather than derived from a specific physical layout; sign and magnitude are inputs to the simulation.
  • Gate duration T = 350 ns
    Chosen/optimized so that the conditional phase converges to π; longer or shorter durations would change the fidelity.
  • Device parameters in Table S1 (ECi, EJi, ELi, Jlk) = not listed in visible main text
    Hand-selected 'experimentally relevant parameters'; without these values the simulation cannot be reproduced from the main text alone.
axioms (4)
  • standard math Circuit quantization of Josephson-junction networks (Eq. 1) is valid.
    The Hamiltonian with charging, Josephson, and capacitive coupling terms is assumed to describe the circuit.
  • domain assumption Double-transmon couplers behave as described in Refs. [44-48].
    The paper relies on prior DTC theory and experiments for the coupler's physics and residual-coupling suppression; no independent derivation is given.
  • ad hoc to paper The cable can be truncated to two harmonic modes m=10 and m=11 with no other modes affecting the computational subspace.
    A tractability assumption; no convergence check against including more modes is presented.
  • domain assumption A Markovian noise model with endpoint qubit decoherence and cable photon loss is representative.
    The open-system results are claimed in the abstract but not described in the visible main text; the noise model is a representative assumption.

reviewed 2026-08-02 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Tunable Nonlocal $ZZ$ Interaction for Remote Controlled-Z Gates Between Distributed Fixed-Frequency Qubits." pith.science (2026). https://pith.science/paper/X3PLWX6J

@misc{pith2026260328526,
  author       = {Pith},
  title        = {Pith review of: Tunable Nonlocal $ZZ$ Interaction for Remote Controlled-Z Gates Between Distributed Fixed-Frequency Qubits},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/X3PLWX6J}},
  note         = {Machine review of arXiv:2603.28526}
}
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abstract

Scaling superconducting quantum processors toward fault-tolerant operation will likely require architectures that extend beyond monolithic chips. Modular processors connected by low-loss superconducting links provide a promising route, but implementing entangling gates between remote fixed-frequency qubits remains challenging. Here we propose a distributed architecture in which two synchronously controlled double-transmon couplers mediate the interaction between fixed-frequency transmons in separate packages connected by a 25-cm coaxial cable. The scheme activates a tunable nonlocal $ZZ$ interaction on demand while suppressing residual static coupling, allowing the superconducting link to function as a gate-native interconnect rather than solely as a state-transfer channel. Circuit-level simulations show an on/off ratio exceeding $10^6$ and a remote controlled-Z gate with a projected coherent fidelity of $99.99\%$ under experimentally relevant parameters. Open-system simulations further indicate that, within the representative Markovian noise model considered here, endpoint-qubit decoherence is the largest contribution to gate infidelity, while photon loss in the retained cable modes remains smaller but non-negligible. These results identify DTC-mediated tunable nonlocal coupling as a promising gate primitive for modular superconducting processors based on fixed-frequency qubits.

Figures

Figures reproduced from arXiv: 2603.28526 by Benzheng Yuan, Bo Zhao, Chaojie Zhang, Chuanbing Han, FuDong Liu, Haoran He, Huihui Sun, Qing Mu, Shuya Wang, Weilong Wang, Yangyang Fei, Zheng Shan.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of the distributed architecture for coupling remote fixed-frequency transmon qubits. (a) Schematic of the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Energy spectrum and effective [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. System spectrum and DTC-mediated effective non [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: Specifically, the coupling for DTC2 is effectively switched off at a flux bias of Φ(2) ext ≈ 0.3 (idle point) and reaches its maximum magnitude at Φ(2) ext ≈ 0.5. Building upon the precise characterization of the localized subsystems, we construct a comprehen￾sive global Hamiltonian encompassing eight domi￾nant modes: two qubits, four coupler modes (two per DTC), and two retained cable modes. The global ei… view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Dynamics of the remote CZ gate. (a) Simultane [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

discussion (0)

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Forward citations

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Reference graph

Works this paper leans on

51 extracted references · 1 linked inside Pith · cited by 2 Pith papers

  1. [1]

    R. P. Feynman, Simulating physics with computers, in Feynman and computation(cRc Press, 2018) pp. 133– 153

    2018

  2. [2]

    Bluvstein, S

    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, Nature626, 58 (2024)

    2024

  3. [3]

    L. S. Madsen, F. Laudenbach, M. F. Askarani, F. Ror- tais, T. Vincent, J. F. Bulmer, F. M. Miatto, L. Neuhaus, L. G. Helt, M. J. Collins,et al., Quantum computational advantage with a programmable photonic processor, Na- ture606, 75 (2022)

    2022

  4. [4]

    S. G. Philips, M. T. Madzik, S. V. Amitonov, S. L. de Snoo, M. Russ, N. Kalhor, C. Volk, W. I. Lawrie, D. Brousse, L. Tryputen,et al., Universal control of a six-qubit quantum processor in silicon, Nature609, 919 (2022)

    2022

  5. [5]

    S. A. Moses, C. H. Baldwin, M. S. Allman, R. Ancona, L. Ascarrunz, C. Barnes, J. Bartolotta, B. Bjork, P. Blan- chard, M. Bohn,et al., A race-track trapped-ion quantum processor, Physical Review X13, 041052 (2023)

    2023

  6. [6]

    Nakamura, Y

    Y. Nakamura, Y. A. Pashkin, and J. Tsai, Coherent con- trol of macroscopic quantum states in a single-cooper- pair box, nature398, 786 (1999)

    1999

  7. [7]

    Blais, A

    A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wall- raff, Circuit quantum electrodynamics, Reviews of Mod- ern Physics93, 025005 (2021)

    2021

  8. [8]

    Arute, K

    F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. Brandao, D. A. Buell,et al., Quantum supremacy using a programmable superconducting processor, nature574, 505 (2019)

    2019

  9. [9]

    Y. Kim, A. Eddins, S. Anand, K. X. Wei, E. Van Den Berg, S. Rosenblatt, H. Nayfeh, Y. Wu, M. Zale- tel, K. Temme,et al., Evidence for the utility of quan- tum computing before fault tolerance, Nature618, 500 (2023)

    2023

  10. [10]

    Morvan, B

    A. Morvan, B. Villalonga, X. Mi, S. Mandr` a, A. Bengts- son, P. Klimov, Z. Chen, S. Hong, C. Erickson, I. Droz- dov,et al., Phase transitions in random circuit sampling, Nature634, 328 (2024)

    2024

  11. [11]

    P. W. Shor, Polynomial-time algorithms for prime factor- ization and discrete logarithms on a quantum computer, SIAM review41, 303 (1999)

    1999

  12. [12]

    N. P. De Leon, K. M. Itoh, D. Kim, K. K. Mehta, T. E. Northup, H. Paik, B. Palmer, N. Samarth, S. Sangtawesin, and D. W. Steuerman, Materials chal- lenges and opportunities for quantum computing hard- ware, Science372, eabb2823 (2021)

    2021

  13. [13]

    McEwen, L

    M. McEwen, L. Faoro, K. Arya, A. Dunsworth, T. Huang, S. Kim, B. Burkett, A. Fowler, F. Arute, J. C. Bardin,et al., Resolving catastrophic error bursts from cosmic rays in large arrays of superconducting qubits, Nature Physics18, 107 (2022)

    2022

  14. [14]

    Suzuki, S

    Y. Suzuki, S. Endo, K. Fujii, and Y. Tokunaga, Quantum 7 error mitigation as a universal error reduction technique: Applications from the nisq to the fault-tolerant quantum computing eras, PRX quantum3, 010345 (2022)

    2022

  15. [15]

    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)

    2024

  16. [16]

    H. Zhou, C. Zhao, M. Cain, D. Bluvstein, N. Maskara, C. Duckering, H.-Y. Hu, S.-T. Wang, A. Kubica, and M. D. Lukin, Low-overhead transversal fault tolerance for universal quantum computation, Nature646, 303 (2025)

    2025

  17. [17]

    Chamberland, K

    C. Chamberland, K. Noh, P. Arrangoiz-Arriola, E. T. Campbell, C. T. Hann, J. Iverson, H. Putterman, T. C. Bohdanowicz, S. T. Flammia, A. Keller,et al., Building a fault-tolerant quantum computer using concatenated cat codes, PRX Quantum3, 010329 (2022)

    2022

  18. [18]

    Suppressing quantum errors by scaling a surface code log- ical qubit, Nature614, 676 (2023)

    2023

  19. [19]

    V. V. Sivak, A. Eickbusch, B. Royer, S. Singh, I. Tsiout- sios, S. Ganjam, A. Miano, B. L. Brock, A. Z. Ding, L. Frunzio,et al., Real-time quantum error correction beyond break-even, Nature616, 50 (2023)

    2023

  20. [20]

    Quantum error correction below the surface code thresh- old, Nature638, 920 (2025)

    2025

  21. [21]

    E. T. Campbell, B. M. Terhal, and C. Vuillot, Roads towards fault-tolerant universal quantum computation, Nature549, 172 (2017)

    2017

  22. [22]

    Gidney and M

    C. Gidney and M. Eker ˚ a, How to factor 2048 bit rsa in- tegers in 8 hours using 20 million noisy qubits, Quantum 5, 433 (2021)

    2048

  23. [23]

    Bravyi, O

    S. Bravyi, O. Dial, J. M. Gambetta, D. Gil, and Z. Nazario, The future of quantum computing with su- perconducting qubits, Journal of Applied Physics132 (2022)

    2022

  24. [24]

    Mohseni, A

    M. Mohseni, A. Scherer, K. G. Johnson, O. Wertheim, M. Otten, N. A. Aadit, Y. Alexeev, K. M. Bresniker, K. Y. Camsari, B. Chapman,et al., How to build a quan- tum supercomputer: Scaling from hundreds to millions of qubits, arXiv preprint arXiv:2411.10406 (2024)

    Pith/arXiv arXiv 2024

  25. [25]

    D. D. Awschalom, H. Bernien, R. Hanson, W. D. Oliver, and J. Vuˇ ckovi´ c, Challenges and opportunities for quan- tum information hardware, Science390, 1004 (2025)

    2025

  26. [26]

    A. Gold, J. Paquette, A. Stockklauser, M. J. Reagor, M. S. Alam, A. Bestwick, N. Didier, A. Nersisyan, F. Oruc, A. Razavi,et al., Entanglement across separate silicon dies in a modular superconducting qubit device, npj Quantum Information7, 142 (2021)

    2021

  27. [27]

    Field, A

    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)

    2024

  28. [28]

    G. J. Norris, K. Dalton, D. Colao Zanuz, A. Rommens, A. Flasby, M. Bahrami Panah, F. Swiadek, C. Scarato, C. Hellings, J.-C. Besse,et al., Performance characteri- zation of a multi-module quantum processor with static inter-chip couplers, EPJ Quantum Technology (2026)

    2026

  29. [29]

    Krinner, S

    S. Krinner, S. Storz, P. Kurpiers, P. Magnard, J. Hein- soo, R. Keller, J. Luetolf, C. Eichler, and A. Wallraff, Engineering cryogenic setups for 100-qubit scale super- conducting circuit systems, EPJ Quantum Technology 6, 2 (2019)

    2019

  30. [30]

    Zhong, H.-S

    Y. Zhong, H.-S. Chang, K. Satzinger, M.-H. Chou, A. Bienfait, C. Conner, ´E. Dumur, J. Grebel, G. A. Peairs, R. G. Povey,et al., Violating bell’s inequality with remotely connected superconducting qubits, Nature Physics15, 741 (2019)

    2019

  31. [31]

    Zhong, H.-S

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

    2021

  32. [32]

    Storz, J

    S. Storz, J. Sch¨ ar, A. Kulikov, P. Magnard, P. Kurpiers, J. L¨ utolf, T. Walter, A. Copetudo, K. Reuer, A. Akin, et al., Loophole-free bell inequality violation with super- conducting circuits, Nature617, 265 (2023)

    2023

  33. [33]

    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 (2025)

    2025

  34. [34]

    Kurpiers, P

    P. Kurpiers, P. Magnard, T. Walter, B. Royer, M. Pechal, J. Heinsoo, Y. Salath´ e, A. Akin, S. Storz, J.-C. Besse, et al., Deterministic quantum state transfer and remote entanglement using microwave photons, Nature558, 264 (2018)

    2018

  35. [35]

    C. J. Axline, L. D. Burkhart, W. Pfaff, M. Zhang, K. Chou, P. Campagne-Ibarcq, P. Reinhold, L. Frunzio, S. Girvin, L. Jiang,et al., On-demand quantum state transfer and entanglement between remote microwave cavity memories, Nature Physics14, 705 (2018)

    2018

  36. [36]

    J. Niu, L. Zhang, Y. Liu, J. Qiu, W. Huang, J. Huang, H. Jia, J. Liu, Z. Tao, W. Wei,et al., Low-loss intercon- nects for modular superconducting quantum processors, Nature Electronics6, 235 (2023)

    2023

  37. [37]

    M. R. Geller, E. Donate, Y. Chen, M. T. Fang, N. Leung, C. Neill, P. Roushan, and J. M. Martinis, Tunable coupler for superconducting xmon qubits: Perturbative nonlinear model, Physical Review A92, 012320 (2015)

    2015

  38. [38]

    Y. Chen, C. Neill, P. Roushan, N. Leung, M. Fang, R. Barends, J. Kelly, B. Campbell, Z. Chen, B. Chiaro, et al., Qubit architecture with high coherence and fast tunable coupling, Physical review letters113, 220502 (2014)

    2014

  39. [39]

    Foxen, C

    B. Foxen, C. Neill, A. Dunsworth, P. Roushan, B. Chiaro, A. Megrant, J. Kelly, Z. Chen, K. Satzinger, R. Barends, et al., Demonstrating a continuous set of two-qubit gates for near-term quantum algorithms, Physical Review Let- ters125, 120504 (2020)

    2020

  40. [40]

    Sheldon, E

    S. Sheldon, E. Magesan, J. M. Chow, and J. M. Gam- betta, Procedure for systematically tuning up cross- talk in the cross-resonance gate, Physical Review A93, 060302 (2016)

    2016

  41. [41]

    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)

    2025

  42. [42]

    X. Deng, W. Zheng, X. Liao, H. Zhou, Y. Ge, J. Zhao, D. Lan, X. Tan, Y. Zhang, S. Li,et al., Long-range zz in- teraction via resonator-induced phase in superconducting qubits, Physical Review Letters134, 020801 (2025)

    2025

  43. [43]

    Zhang, J

    J. Zhang, J. Chu, J. Niu, Y. Zhong, and D. Yu, High- contrast interaction between remote superconducting qubits mediated by multimode cable coupling, Applied Physics Letters127(2025)

    2025

  44. [44]

    Goto, Double-transmon coupler: Fast two-qubit gate with no residual coupling for highly detuned super- 8 conducting qubits, Physical review applied18, 034038 (2022)

    H. Goto, Double-transmon coupler: Fast two-qubit gate with no residual coupling for highly detuned super- 8 conducting qubits, Physical review applied18, 034038 (2022)

    2022

  45. [45]

    D. L. Campbell, A. Kamal, L. Ranzani, M. Senatore, and M. D. LaHaye, Modular tunable coupler for super- conducting circuits, Physical Review Applied19, 064043 (2023)

    2023

  46. [46]

    K. Kubo, Y. Ho, and H. Goto, High-performance mul- tiqubit system with double-transmon couplers: Toward scalable superconducting quantum computers, Physical Review Applied22, 024057 (2024)

    2024

  47. [47]

    R. Li, K. Kubo, Y. Ho, Z. Yan, Y. Nakamura, and H. Goto, Realization of high-fidelity cz gate based on a double-transmon coupler, Physical Review X14, 041050 (2024)

    2024

  48. [48]

    R. Li, K. Kubo, Y. Ho, Z. Yan, S. Inoue, Y. Nakamura, and H. Goto, Capacitively shunted double-transmon cou- pler realizing bias-free idling and a high-fidelity cz gate, Physical Review Applied23, 064069 (2025)

    2025

  49. [49]

    K. Heya, T. Phung, M. Malekakhlagh, R. Steiner, M. Turchetti, W. Shanks, J. Mamin, W.-S. Lu, Y. P. Kandel, N. Sundaresan,et al., Randomized benchmark- ing of a remote cnot gate via a meter-scale microwave link, Physical Review Letters135, 200801 (2025)

    2025

  50. [50]

    J. R. Johansson, P. D. Nation, and F. Nori, Qutip: An open-source python framework for the dynamics of open quantum systems, Computer physics communica- tions183, 1760 (2012)

    2012

  51. [51]

    L. H. Pedersen, N. M. Moller, and K. Mølmer, Fidelity of quantum operations, Physics Letters A367, 47 (2007)

    2007

This paper was first reviewed by deepseek-v4-flash on August 2, 2026.