High-contrast interaction between remote superconducting qubits mediated by multimode cable coupling

Dapeng Yu; Jiajian Zhang; Ji Chu; Jingjing Niu; Youpeng Zhong

REVIEW 2 major objections 6 minor 67 references

High-contrast interaction between remote superconducting qubits mediated by multimode cable coupling

T0 review · 2 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A multimode coaxial cable alone can deliver >99% simulated remote iSWAP and CZ gates via mode-sign interference.

desk verdict Genuinely new multi-mode interference mechanism for cable-mediated gates, but the >99% fidelity claim is not yet supported because the incoherent model omits pure dephasing. read the letter →

arxiv 2505.08606 v1 pith:MREYH3OC submitted 2025-05-13 quant-ph

Jiajian Zhang , Ji Chu , Jingjing Niu , Youpeng Zhong , Dapeng Yu This is my paper · ORCID

classification quant-ph PACS 85.25.Cp03.67.Lx

keywords superconductingqubitstransmonmultimodecoaxialcablecable-mediatedcouplingZZ-freeinteractioniSWAPgatecontrolled-Zdistributedquantumcomputing

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper aims to establish that a multimode superconducting cable between two transmon qubits can replace a tunable coupler. Because the coupling sign from each cable mode to the second qubit alternates as $(-1)^m$, every mode reinforces the useful $XX$ exchange interaction, while the parasitic $ZZ$ interaction cancels at a specific near-mode qubit frequency. That high-contrast working point lets spatially separated qubits perform direct iSWAP and controlled-Z gates by simply modulating qubit frequencies with square pulses. Numerical simulations with a 0.25 m cable, qubit $T_1 = 100\,\mu\mathrm{s}$, and cable-mode $T_1 = 10\,\mu\mathrm{s}$ predict fidelities above 99%, a level relevant for modular superconducting processors and distributed quantum error correction.

What carries the argument

The central object is the alternating-sign coupling pattern in the Hamiltonian $H = \sum_i[\omega_i a_i^\dagger a_i + \tfrac{\alpha_i}{2} a_i^\dagger a_i^\dagger a_i a_i] + \sum_m m\omega_{\mathrm{FSR}} c_m^\dagger c_m + \sum_m [g_{1,m}(a_1^\dagger c_m + c_m^\dagger a_1) + (-1)^m g_{2,m}(a_2^\dagger c_m + c_m^\dagger a_2)]$. Because qubit 2's coupling to mode $m$ carries $(-1)^m$, every mode adds constructively to the effective exchange strength $g_{\mathrm{eff}}$, while the fourth-order ZZ formula separates into negative repulsion terms from qubit second-excited states and positive repulsion terms from cable-mode second-excited states. The cancellation is captured by $\xi_{ZZ} \approx \sum_m g_{1,m}^2 g_{2,m}^2\,[-4/(\Delta_m^2\alpha) + 11/(2\Delta_m^3) + 8/(\Delta_m\alpha(\Sigma_m+\alpha)) - 2/(\Delta_m^2\Sigma_m)]$, with $\Delta_m = \omega - m\omega_{\mathrm{FSR}}$ and $\Sigma_m = \omega + m\omega_{\mathrm{FSR}}$, which the paper uses to locate the ZZ-free frequency and to compare against exact diagonalization.

What would settle it

Build the described 0.25 m cable-coupled transmon pair and measure the ZZ interaction strength versus qubit frequency: the mechanism is wrong if no ZZ-free point appears between modes $m=10$ and $m=11$ near the predicted frequency, or if the XX interaction vanishes at that point. A randomized-benchmarking experiment that includes dephasing would settle whether the total error stays below 1% once pure dephasing is added to the modeled relaxation.

Watch

Extended reading notes

Core claim

Two transmon qubits capacitively coupled to the ends of a half-wavelength coaxial cable feel a mode-dependent coupling sign: the coupling of qubit 2 to cable mode $m$ carries a factor $(-1)^m$ relative to qubit 1. As a result, the effective $XX$ coupling between the qubits, obtained by a Schrieffer-Wolff transformation, receives same-sign contributions from all cable modes, whereas the $ZZ$ interaction, computed to fourth order, receives opposite-sign contributions from the second excited states of the qubits and of the cable modes. At a specific qubit frequency between two cable modes these $ZZ$ contributions cancel, leaving a ZZ-free point where the $XX$ coupling is still several MHz strong: high on/off contrast without any added tunable coupler. Moving the qubits with square frequency pulses between a low-ZZ idle configuration and this interaction point yields a simulated 180 ns iSWAP gate and a 271 ns CZ gate, with coherent errors near 0.2% for both and total fidelities above 99% under the assumed relaxation times. The ZZ-free mechanism persists across realistic cable lengths and shifts predictably with coupling capacitance.

Load-bearing premise

The quoted above-99% fidelities rest on an incoherent-error model that counts only relaxation (qubit $T_1 = 100\,\mu\mathrm{s}$, cable mode $T_1 = 10\,\mu\mathrm{s}$) and omits pure dephasing; if the flux-tuned transmons have realistic $T_2$ around 20–50 $\mu$s, the total error could climb above 1%.

Editorial extensions

If this is right

Two-qubit gates across a cable need no extra tunable coupler, so a distributed processor gains connectivity without additional circuit elements or their control lines.
The ZZ-free idle region (below 10 kHz in absolute coupling strength) lets qubits sit close to cable modes without accumulating parasitic phases, easing frequency allocation in larger modules.
Both iSWAP and CZ gates can be driven by simple square frequency pulses, so the same cable hardware supports two entangling gates with only pulse-shape changes; an optimized Slepian pulse reduces CZ coherent error to 0.03% at a longer 450 ns gate time.
Because a ZZ-free point also exists for qubits on opposite sides of a cable mode, controlled interactions can be arranged across a mode, supporting parallel gate operations on one cable.
Together with cable-mediated cross-resonance gates, the scheme makes direct cable-based two-qubit gates a practical route toward distributed quantum error correction and large-scale fault-tolerant superconducting processors.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Not claimed by the paper: the fidelity budget drops pure dephasing, so adding a realistic $T_2$ for flux-tuned transmons (roughly 20–50 $\mu$s) is the most direct unresolved test of whether the total error stays below 1%.
The supplement's cross-mode ZZ-free feature suggests a route the paper does not develop: using different cable-mode spacings for different qubit pairs could enable multiple simultaneous remote gates on a single cable, a testable multi-pair experiment.
The same alternating-sign mechanism could, by analogy, apply to other multimode quantum links whose mode functions have alternating parity at the coupling points; the paper does not examine these platforms.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Quick take: this is a genuinely new idea—using the alternating coupling signs of a multimode cable to get constructive XX and a ZZ-free idle point without any tunable coupler. The analytical derivation is backed by exact diagonalization, and the gate simulations are forward runs from stated parameters, so there is no fitting-to-target circularity. The core mechanism is solid.

What the paper does well: the Schrieffer-Wolff formula for geff and the fourth-order expression for ξZZ are checked against exact diagonalization in Fig. 2(c), and the ZZ-free frequency converges quickly with mode number. The supplemental scans over Cc and cable length show the effect is not a single-point accident, and the Slepian-pulse results give a nice alternative control path. The cross-mode ZZ feature in Fig. S4 is also a useful addition.

The soft spot that matters most is the incoherent error model. The fidelity budget uses only T1 relaxation (qubits 100 µs, cable modes 10 µs) and ignores pure dephasing. These are flux-tunable transmons, and during the square frequency pulses the dephasing rate is far from negligible. A 271 ns CZ gate with T2 of 20 µs contributes roughly 1.4% error by itself; even at 50 µs it's 0.5%, which pushes the reported 0.86% total above the claimed 1% threshold. So the 'above 99%' numbers are optimistic as written. Fixing this is straightforward—add a Tφ term and do a sensitivity sweep—but it should be done before the claim is used.

Two minor caveats: the square pulses are idealized, though the SM addresses pulse shaping; and Eq. (2) is an infinite sum over modes that does not obviously converge for the given coupling model. The paper effectively truncates to a few modes, and a referee should ask for a word on physical cutoff. Not a deal-breaker, but it deserves comment.

Bottom line: this is a solid, interesting theoretical proposal for modular architectures. It deserves a serious referee and a revision, not a desk reject. I'd bring it to our group meeting.

Referee Report

2 major / 6 minor

Summary. The manuscript proposes a scheme for implementing high-contrast two-qubit interactions between two transmon qubits connected by a multimode superconducting coaxial cable. The key idea is that the alternating signs of the qubit-cable coupling for odd and even cable modes lead to constructive interference of the effective XX coupling while allowing the ZZ interaction to vanish at a specific qubit frequency ('ZZ-free point') near a cable mode. Analytical formulas for the effective XX and ZZ couplings are derived via Schrieffer-Wolff and fourth-order perturbation theory and verified against exact diagonalization. The authors then simulate diabatic iSWAP and CZ gates using square qubit-frequency pulses, and report numerical fidelities above 99% for optimized idle and interaction frequencies, assuming qubit T1=100 µs and cable-mode T1=10 µs. The supplemental material provides additional error analysis and pulse-shaping options.

Significance. The scheme is conceptually attractive: it avoids tunable couplers and leverages the intrinsic multimode structure of the cable, with a ZZ-free point that is robust to the number of cable modes included. The analytical formulas (Eqs. 2, 4, 5) are cross-checked against exact diagonalization (Fig. 2c), and the gate simulations separate coherent error sources (leakage, ZZ error, iSWAP angle error) in a transparent way. The paper also provides clearly specified parameter choices and discusses alternative pulse shapes. If the fidelity claim can be made under a realistic decoherence model, the approach would be a valuable building block for modular quantum processors. However, as it stands the claim of 'realistic coherence' is not fully met because pure dephasing is omitted from the incoherent-error model, and the fidelity prediction is therefore not robust for flux-tunable devices.

major comments (2)

[Remote iSWAP and CZ gates, Fig. 4(c,f)] The incoherent-error model used to produce the fidelity estimates includes only T1 relaxation for qubits (100 µs) and cable modes (10 µs); no pure dephasing (T2) contribution is considered. Because the proposed gate operation relies on flux-frequency tuning of the transmons, the qubits are moved away from their sweet spots during the gate, where flux noise typically limits T2 to 20–50 µs. For a 271 ns CZ gate, a T2 of 20 µs contributes a dephasing error of approximately 1.4%, which alone exceeds the reported total error (0.86%) and would push the fidelity below 99%. The same holds for the iSWAP gate. The authors should include dephasing in the error model, or explicitly state that the 'realistic coherence' claim applies only to a T1-limited device and not to typical flux-tunable transmons.
[Remote iSWAP and CZ gates / Cable-mediated coupling (parameter set)] The fidelity results are computed for a single parameter point (Cc=5 fF, cable length 0.25 m, one optimized pair of idle/interaction frequencies). No sensitivity analysis is given for variations in the coupling capacitance, cable length, or qubit frequency calibration errors, all of which are unavoidable in practice. Since the ZZ-free condition arises from a delicate balance among mode-mediated level repulsions (Eq. 5), small parameter deviations could shift the ZZ-free frequency or change the residual ZZ, degrading the contrast and gate fidelity. The authors should either provide a robustness scan over realistic parameter spreads or temper the statement that the scheme is directly practical.

minor comments (6)

[Title and running text] The title contains 'mediate d' with a spacing error; it should read 'mediated'.
[Main text, error-estimation paragraph] The word 'intergrating' should be 'integrating' (it appears in the description of the incoherent-error estimation).
[Fig. 2 caption] The inset label 'ZZ off freq.' is ambiguous; please define it as 'ZZ-free frequency' for clarity.
[Eq. (2) and surrounding text] Equation (2) introduces the factor (-1)^m, but the preceding text explains the sign only for odd modes; please clarify that the mode index m starts at 1 and that all g_{i,m} are positive, so the (-1)^m factor encodes the alternating sign. Otherwise the sign convention is easy to misread.
[Main text, gate implementations] The term 'diabatic' is used without definition; consider replacing it with 'fast non-adiabatic' or defining it explicitly at first use.
[Supplemental Material, pulse optimization] The statement 'If qubit coherence permits, this optimized pulse is preferred' is vague; specify what coherence time is required for the 450 ns Slepian pulse to be beneficial.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the analytical XX/ZZ formulas are derived from the stated model Hamiltonian and cross-checked against exact diagonalization; the gate fidelities are forward simulations from stated parameters, not fitted outputs.

full rationale

The paper's derivation chain is self-contained. The Hamiltonian in Eq. (1) specifies a multimode cable with alternating coupling signs, and the effective XX interaction in Eq. (2) and ZZ interaction in Eqs. (4)-(5) are obtained by perturbative expansion from that Hamiltonian rather than assumed from the target behavior. The ZZ-free frequency is found by solving the analytical condition and is independently verified by exact diagonalization in Fig. 2(c), so it is not a parameter fitted to the later fidelity number. The iSWAP and CZ gate simulations evolve the model with fixed physical parameters (qubit T1 = 100 us, cable mode T1 = 10 us, Cc = 5 fF) and optimize the pulse frequencies within the model; the resulting fidelities are predictions, not inputs used to define the interaction formulas. Self-citations (e.g., refs. [57], [59]) appear only as background calculation details or supplemental methods and are not load-bearing for the central claim. The omission of pure dephasing from the incoherent error model is a modeling robustness concern, not a circularity: it does not make any predicted quantity equivalent to a fitted input by construction. Therefore no circular step is identified.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central claims depend on realistic device parameters (Cc, Cq, cable length, T1 values) and on modeling assumptions about the cable mode structure and qubit anharmonicities. No new physical entities are introduced. The main unstated simplifications are the neglect of dephasing and the ideal-mode description of the cable.

free parameters (5)

Coupling capacitance Cc = 5 fF
Chosen as a realistic capacitance giving g/2π ~ 11.5 MHz; the paper notes larger Cc enters the non-dispersive limit (Fig. S2(a)).
Qubit capacitance Cq = 90 fF (anharmonicity -216 MHz)
Sets the transmon anharmonicity α; Eq. (5) assumes α1=α2=α for the simplified ZZ formula.
Cable length / FSR = 0.25 m / 440 MHz
Defines the mode ladder; the supplement tests 0.12 m (917 MHz) and confirms ZZ freedom persists, but the main fidelity numbers use this length.
Qubit T1 = 100 µs
Assumed qubit relaxation time in the incoherent error estimate; directly affects the reported total errors.
Cable mode T1 = 10 µs
Assumed relaxation time for all cable modes; a single T1 for all modes is a simplification.

assumptions (5)

domain assumption The cable is an ideal linear multimode resonator with independent modes at integer multiples of FSR and qubit coupling signs alternating as (-1)^m.
Invoked in Eq. (1) and Fig. 1(b). Real cables have non-uniform impedance, mode mixing, and attenuation that could alter the intended interference pattern.
domain assumption The two transmon qubits have equal anharmonicity (α1=α2=α) and are modeled as weakly anharmonic Duffing oscillators.
Equation (5) for the simplified ZZ formula assumes α1=α2=α; the paper does not analyze sensitivity to anharmonicity mismatch between chips.
standard math Perturbative expansions (Schrieffer-Wolff for XX, fourth-order for ZZ) are valid in the near-mode regime.
Used to derive Eqs. (2) and (4). Exact diagonalization results in Fig. 2(c) validate the formulas for the chosen parameters.
ad hoc to paper Incoherent errors are dominated by T1 relaxation (qubit T1=100 µs, cable T1=10 µs); pure dephasing is negligible.
This assumption underlies the incoherent-error curves in Fig. 4(c,f) and the total errors (0.62% for iSWAP, 0.86% for CZ). Flux-tuned qubits typically have significant T2, which is not addressed.
domain assumption A finite number of cable modes is sufficient to capture ZZ and gate dynamics.
The inset of Fig. 2(c) shows ZZ converges with about two modes, but the gate simulations likely truncate the cable mode set; the effect of higher modes on gate leakage is not exhaustively shown.

how reviews work

0 comments

Cite this review

Pith. "Pith review of High-contrast interaction between remote superconducting qubits mediated by multimode cable coupling." pith.science (2026). https://pith.science/paper/MREYH3OC

@misc{pith2026250508606,
  author       = {Pith},
  title        = {Pith review of: High-contrast interaction between remote superconducting qubits mediated by multimode cable coupling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MREYH3OC}},
  note         = {Machine review of arXiv:2505.08606}
}

read the original abstract

Superconducting quantum processors offer a promising path towards practical quantum computing. However, building a fault-tolerant quantum computer with millions of superconducting qubits is hindered by wiring density, packaging constraints and fabrication yield. Interconnecting medium-scale processors via low-loss superconducting links provides a promising alternative. Yet, achieving high-fidelity two-qubit gates across such channels remains difficult. Here, we show that a multimode coaxial cable can mediate high-contrast interaction between spatially separated super-conducting qubits. Leveraging interference between cable modes, we can implement high-fidelity controlled-Z and ZZ-free iSWAP gates by simply modulating qubit frequencies. Numerical simulations under realistic coherence and coupling parameters predict fidelities above 99% for both gate schemes. Our approach provides a versatile building block for modular superconducting architectures and facilitates distributed quantum error correction and large-scale fault-tolerant quantum computing.

Figures

Figures reproduced from arXiv: 2505.08606 by the authors.

**Figure 2.** Energy-level diagrams of the single-excitation (a) an [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** (a) Absolute ZZ interaction strength |ξZZ| versus Q1 and Q2 frequencies. The blue region indicates the qubit idling area where |ξZZ|/2π < 10 kHz. The red (green) dashed line marks interaction frequencies for iSWAP (CZ) gates. The red (green) curve with an arrow illustrates the frequency trajectory during the iSWAP (CZ) gate. Square pulses are used for qubit frequency modulations. (b) Simulated iSWAP gate length vers… view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Error analysis of remote iSWAP and CZ gates. (a) Coherent e [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

67 extracted references · 46 canonical work pages

[1]

The eﬀective XX interaction between two qubits mainly arises from second-order couplings me- diated by the two nearest cable modes

[57, 58]. The eﬀective XX interaction between two qubits mainly arises from second-order couplings me- diated by the two nearest cable modes. The two interac- tion paths add constructively due to the opposite (same) signs of the coupling strengths to the two qubits medi- ated by the odd (even) modes. Using the Schrieﬀer-Wolﬀ transformation, we obtain the ...

work page
[2]

P. W. Shor, in Proceedings 35th annual symposium on foundations of computer science (Ieee, 1994) pp. 124– 134

1994
[3]

For CZ gates, the qubit frequencies are tuned from the ZZ oﬀ region into |11, 00ð − |20, 00ð or |11, 00ð − |02, 00ð resonance, as indicated by the green dashed lines in Fig

62%, comprising 0.31% qubit loss, 0.12% cable mode loss, and 0.19% coherent errors. For CZ gates, the qubit frequencies are tuned from the ZZ oﬀ region into |11, 00ð − |20, 00ð or |11, 00ð − |02, 00ð resonance, as indicated by the green dashed lines in Fig. 3(a). Similar to the iSW AP gate, we optimize the idle frequencies of the qubits in Fig. 4(d) by ﬁx...

work page
[4]

M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information (Cambridge university press, 2010)

2010
[5]

arise from level repulsions associated with the second-excited states of the qubits and the cable modes, respectively. ZZ-free operation can be achieved at speciﬁc qubit frequencies where the neg- ative level repulsions from higher-frequency cable modes cancels out the positive contributions from other energy levels. Fig. 2(c) displays the calculated XX a...

work page
[6]

Gottesman, in Proceedings of Symposia in Applied Mathematics, Vol

D. Gottesman, in Proceedings of Symposia in Applied Mathematics, Vol. 58 (2002) pp. 221–236

work page 2002
[7]

I. M. Georgescu, S. Ashhab, and F. Nori, Rev. Mod. Phys. 86, 153 (2014)

2014
[8]

J. M. Gambetta, J. M. Chow, and M. Steﬀen, npj Quan- tum Inf. 3, 2 (2017)

work page 2017

Show all 67 references

[9]

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, et al., Nature 638, 920 (2024)

2024
[10]

A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Phys. Rev. A 86, 032324 (2012)

2012
[11]

Babbush, C

R. Babbush, C. Gidney, D. W. Berry, N. Wiebe, J. Mc- Clean, A. Paler, A. Fowler, and H. Neven, Phys. Rev. X 8, 041015 (2018)

2018
[12]

J. Lee, D. W. Berry, C. Gidney, W. J. Huggins, J. R. McClean, N. Wiebe, and R. Babbush, PRX Quantum 2, 030305 (2021)

2021
[13]

Huang, B

S. Huang, B. Lienhard, G. Calusine, A. Veps¨ al¨ ainen, J. Braum¨ uller, D. K. Kim, A. J. Melville, B. M. Niedziel- ski, J. L. Yoder, B. Kannan, et al. , PRX Quantum 2, 020306 (2021)

2021
[14]

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. , arXiv:2411.10406 [quant-ph]

arXiv
[15]

Bravyi, A

S. Bravyi, A. W. Cross, J. M. Gambetta, D. Maslov, P. Rall, and T. J. Yoder, Nature 627, 778 (2024)

2024
[16]

Vasmer and D

M. Vasmer and D. E. Browne, Phys. Rev. A 100, 012312 (2019)

2019
[17]

Jiang, J

L. Jiang, J. M. Taylor, A. S. Sørensen, and M. D. Lukin, Phys. Rev. A 76, 062323 (2007)

2007
[18]

A. Gold, J. Paquette, A. Stockklauser, M. J. Reagor, M. S. Alam, A. Bestwick, N. Didier, A. Nersisyan, F. Oruc, A. Razavi, et al. , npj Quantum Inf. 7, 142 (2021)

2021
[19]

J. Ang, G. Carini, Y. Chen, I. Chuang, M. Demarco, S. Economou, A. Eickbusch, A. Faraon, K.-M. Fu, S. Girvin, et al. , ACM Trans. Quantum Comput. 5, 1 (2024)

2024
[20]

Leung, Y

N. Leung, Y. Lu, S. Chakram, R. Naik, N. Earnest, R. Ma, K. Jacobs, A. Cleland, and D. Schuster, npj Quantum Inf. 5, 18 (2019)

2019
[21]

J. Niu, L. Zhang, Y. Liu, J. Qiu, W. Huang, J. Huang, H. Jia, J. Liu, Z. Tao, W. Wei, et al. , Nat. Electron. 6, 235 (2023)

2023
[22]

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, and A. N. Cleland, Nature 590, 571 (2021)

2021
[23]

C. J. Axline, L. D. Burkhart, W. Pfaﬀ, M. Zhang, K. Chou, P. Campagne-Ibarcq, P. Reinhold, L. Frun- zio, S. M. Girvin, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, Nat. Phys. 14, 705 (2018)

2018
[24]

L. D. Burkhart, J. D. Teoh, Y. Zhang, C. J. Ax- line, L. Frunzio, M. Devoret, L. Jiang, S. Girvin, and R. Schoelkopf, PRX Quantum 2, 030321 (2021)

2021
[25]

Kurpiers, P

P. Kurpiers, P. Magnard, T. Walter, B. Royer, M. Pechal, J. Heinsoo, Y. Salath´ e, A. Akin, S. Storz, J.-C. Besse, S. Gasparinetti, A. Blais, and A. Wallraﬀ, Nature 558, 264 (2018)

2018
[26]

J. Qiu, Y. Liu, L. Hu, Y. Wu, J. Niu, L. Zhang, W. Huang, Y. Chen, J. Li, S. Liu, Y. Zhong, L. Duan, and D. Yu, Sci. Bull. 70, 351 (2025)

2025
[27]

Majer, J

J. Majer, J. M. Chow, J. M. Gambetta, J. Koch, B. R. Johnson, J. A. Schreier, L. Frunzio, D. I. Schuster, A. A. Houck, A. Wallraﬀ, et al. , Nature 449, 443 (2007)

2007
[28]

M. A. Sillanp¨ a¨ a, J. I. Park, and R. W. Simmonds,Nature 449, 438 (2007)

2007
[29]

Filipp, M

S. Filipp, M. G¨ oppl, J. Fink, M. Baur, R. Bianchetti, L. Steﬀen, and A. Wallraﬀ, Phys. Rev. A 83, 063827 (2011)

2011
[30]

Lucero, R

E. Lucero, R. Barends, Y. Chen, J. Kelly, M. Mariantoni, A. Megrant, P. O’Malley, D. Sank, A. Vainsencher, J. Wenner, et al. , Nat. Phys. 8, 719 (2012)

2012
[31]

D. C. McKay, S. Filipp, A. Mezzacapo, E. Magesan, J. M. Chow, and J. M. Gambetta, Phys. Rev. Appl. 6, 064007 (2016)

2016
[32]

Takita, A

M. Takita, A. W. Cross, A. D. C´ orcoles, J. M. Chow, and J. M. Gambetta, Phys. Rev. Lett. 119, 180501 (2017)

2017
[33]

C. Song, K. Xu, W. Liu, C.-p. Yang, S.-B. Zheng, H. Deng, Q. Xie, K. Huang, Q. Guo, L. Zhang, et al. , Phys. Rev. Lett. 119, 180511 (2017)

2017
[34]

Cai, Q.-C

H. Cai, Q.-C. Liu, C.-H. Zhao, Y.-S. Zhang, J.-S. Liu, and W. Chen, Chin. Phys. B 27, 084207 (2018)

2018
[35]

C. Song, K. Xu, H. Li, Y.-R. Zhang, X. Zhang, W. Liu, Q. Guo, Z. Wang, W. Ren, J. Hao, et al. , Science 365, 574 (2019)

2019
[36]

D. C. McKay, R. Naik, P. Reinhold, L. S. Bishop, and D. I. Schuster, Phys. Rev. Lett. 114, 080501 (2015)

2015
[37]

Kandala, K

A. Kandala, K. X. Wei, S. Srinivasan, E. Magesan, S. Carnevale, G. Keefe, D. Klaus, O. Dial, and D. McKay, Phys. Rev. Lett. 127, 130501 (2021)

2021
[38]

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, npj Quantum Inf. 9 (2023)

2023
[39]

K. Heya, T. Phung, M. Malekakhlagh, R. Steiner, M. Turchetti, W. Shanks, J. Mamin, W.-S. Lu, Y. P. Kandel, N. Sundaresan, and J. Orcutt, arXiv:2502.15034 [quant-ph]
[40]

Barends, J

R. Barends, J. Kelly, A. Megrant, A. Veitia, D. Sank, E. Jeﬀrey, T. C. White, J. Mutus, A. G. Fowler, B. Campbell, et al. , Nature 508, 500 (2014)

2014
[41]

Krinner, S

S. Krinner, S. Lazar, A. Remm, C. K. Andersen, N. Lacroix, G. J. Norris, C. Hellings, M. Gabureac, C. Eichler, and A. Wallraﬀ, Phys. Rev. Applied 14, 024042 (2020)

2020
[42]

P. Zhao, P. Xu, D. Lan, J. Chu, X. Tan, H. Yu, and Y. Yu, Phys. Rev. Lett. 125, 200503 (2020)

2020
[43]

Y. Chen, C. Neill, P. Roushan, N. Leung, M. Fang, R. Barends, J. Kelly, B. Campbell, Z. Chen, B. Chiaro, et al. , Phys. Rev. Lett. 113, 220502 (2014)

2014
[44]

F. Yan, P. Krantz, Y. Sung, M. Kjaergaard, D. L. Camp- bell, T. P. Orlando, S. Gustavsson, and W. D. Oliver, Phys. Rev. Appl. 10, 054062 (2018)

2018
[45]

Goto, Phys

H. Goto, Phys. Rev. Appl. 18, 034038 (2022)

2022
[46]

Foxen, C

B. Foxen, C. Neill, A. Dunsworth, P. Roushan, B. Chiaro, 7 A. Megrant, J. Kelly, Z. Chen, K. Satzinger, R. Barends, et al. , Phys. Rev. Lett. 125, 120504 (2020)

2020
[47]

Y. Xu, J. Chu, J. Yuan, J. Qiu, Y. Zhou, L. Zhang, X. Tan, Y. Yu, S. Liu, J. Li, F. Yan, and D. Yu, Phys. Rev. Lett. 125, 240503 (2020)

2020
[48]

Y. Sung, L. Ding, J. Braum¨ uller, A. Veps¨ al¨ ainen, B. Kan- nan, M. Kjaergaard, A. Greene, G. O. Samach, C. Mc- Nally, D. Kim, et al. , Phys. Rev. X 11, 021058 (2021)

2021
[49]

Stehlik, D

J. Stehlik, D. Zajac, D. Underwood, T. Phung, J. Blair, S. Carnevale, D. Klaus, G. Keefe, A. Carniol, M. Kumph, M. Steﬀen, and O. Dial, Phys. Rev. Lett. 127, 080505 (2021)

2021
[50]

Li, K.-M

H.-K. Li, K.-M. Li, H. Dong, Q.-J. Guo, W.-X. Liu, Z. Wang, H.-H. Wang, and D.-N. Zheng, Chin. Phys. B 28, 080305 (2019)

2019
[51]

P. Zhao, Y. Zhang, G. Xue, Y. Jin, and H. Yu, Appl. Phys. Lett. 121 (2022)

2022
[52]

Marxer, A

F. Marxer, A. Veps¨ al¨ ainen, S. W. Jolin, J. Tuorila, A. Landra, C. Ockeloen-Korppi, W. Liu, O. Ahonen, A. Auer, L. Belzane, et al. , PRX Quantum 4, 010314 (2023)

2023
[53]

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, Phys. Rev. X 14, 041030 (2024)

2024
[54]

G. J. Norris, K. Dalton, D. C. Zanuz, A. Rom- mens, A. Flasby, M. B. Panah, F. Swiadek, C. Scarato, C. Hellings, J.-C. Besse, and A. Wall- raﬀ, arXiv:2503.12603 [quant-ph]

arXiv
[55]

Renger, J

M. Renger, J. Verjauw, N. Wurz, A. Hosseinkhani, C. Ockeloen-Korppi, W. Liu, A. Rath, M. J. Thapa, F. Vigneau, E. Wybo, et al. , arXiv:2503.10903 [quant- ph]
[56]

J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Phys. Rev. A 76, 042319 (2007)

2007
[57]

Ohfuchi and S

M. Ohfuchi and S. Sato, Quantum Sci. Technol. 9, 035014 (2024)

2024
[58]

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, arXiv:2407.20338 [quant-ph]

arXiv
[60]

Chu and F

J. Chu and F. Yan, Phys. Rev. Appl. 16, 054020 (2021)

2021
[61]

R. Li, K. Kubo, Y. Ho, Z. Yan, Y. Nakamura, and H. Goto, Phys. Rev. X 14, 041050 (2024)

2024
[62]

See Supplemental Material at [url] for the simulation de- tails
[63]

Kueng, D

R. Kueng, D. M. Long, A. C. Doherty, and S. T. Flam- mia, Phys. Rev. Lett. 117, 170502 (2016)

2016
[64]

Eickbusch, M

A. Eickbusch, M. McEwen, V. Sivak, A. Bourassa, J. Atalaya, J. Claes, D. Kafri, C. Gidney, C. W. War- ren, J. Gross, et al. , arXiv:2412.14360 [quant-ph]

arXiv
[65]

High-contrast interaction between remote superconducting qubits mediated by multimode cable coupling

J. M. Martinis and M. R. Geller, Phys. Rev. A 90, 022307 (2014). Supplemental Material for “High-contrast interaction between remote superconducting qubits mediated by multimode cable coupling” CONTENTS I. Full energy spectrum 2 II. ZZ interaction 3 III. Pulse optimization for...

2014
[66]

Mollenhauer, A

M. Mollenhauer, A. Irfan, X. Cao, S. Mandal, and W. Pfaﬀ, arXiv:2407.16743 [quant-ph]

arXiv
[67]

J. M. Martinis and M. R. Geller, Phys. Rev. A 90, 022307 (2014)

2014
[68]

Y. Sung, L. Ding, J. Braum¨ uller, A. Veps¨ al¨ ainen, B. Kannan, M. Kjaergaard, A. Greene, G. O. Samach, C. McNally, D. Kim, et al. , Phys. Rev. X 11, 021058 (2021) . 6

2021

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

The eﬀective XX interaction between two qubits mainly arises from second-order couplings me- diated by the two nearest cable modes

[57, 58]. The eﬀective XX interaction between two qubits mainly arises from second-order couplings me- diated by the two nearest cable modes. The two interac- tion paths add constructively due to the opposite (same) signs of the coupling strengths to the two qubits medi- ated by the odd (even) modes. Using the Schrieﬀer-Wolﬀ transformation, we obtain the ...

work page

[2] [2]

P. W. Shor, in Proceedings 35th annual symposium on foundations of computer science (Ieee, 1994) pp. 124– 134

1994

[3] [3]

For CZ gates, the qubit frequencies are tuned from the ZZ oﬀ region into |11, 00ð − |20, 00ð or |11, 00ð − |02, 00ð resonance, as indicated by the green dashed lines in Fig

62%, comprising 0.31% qubit loss, 0.12% cable mode loss, and 0.19% coherent errors. For CZ gates, the qubit frequencies are tuned from the ZZ oﬀ region into |11, 00ð − |20, 00ð or |11, 00ð − |02, 00ð resonance, as indicated by the green dashed lines in Fig. 3(a). Similar to the iSW AP gate, we optimize the idle frequencies of the qubits in Fig. 4(d) by ﬁx...

work page

[4] [4]

M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information (Cambridge university press, 2010)

2010

[5] [5]

arise from level repulsions associated with the second-excited states of the qubits and the cable modes, respectively. ZZ-free operation can be achieved at speciﬁc qubit frequencies where the neg- ative level repulsions from higher-frequency cable modes cancels out the positive contributions from other energy levels. Fig. 2(c) displays the calculated XX a...

work page

[6] [6]

Gottesman, in Proceedings of Symposia in Applied Mathematics, Vol

D. Gottesman, in Proceedings of Symposia in Applied Mathematics, Vol. 58 (2002) pp. 221–236

work page 2002

[7] [7]

I. M. Georgescu, S. Ashhab, and F. Nori, Rev. Mod. Phys. 86, 153 (2014)

2014

[8] [8]

J. M. Gambetta, J. M. Chow, and M. Steﬀen, npj Quan- tum Inf. 3, 2 (2017)

work page 2017