Methods for Measuring Magnetic Flux Crosstalk Between Tunable Transmons

Blake R. Johnson; Colm A. Ryan; Deanna M. Abrams; Nicolas Didier; Shane A. Caldwell

REVIEW 2 major objections 4 minor 32 references

Methods for Measuring Magnetic Flux Crosstalk Between Tunable Transmons

T0 review · 2 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Flux crosstalk error in two-qubit gates is now predictable from a Ramsey measurement.

desk verdict Useful crosstalk-measurement toolkit with a sign error in the Appendix B infidelity derivation that flips the headline coefficient—fixable, but Eq. (6) should not be trusted as-is. read the letter →

arxiv 1908.11856 v4 pith:6OZLROAB submitted 2019-08-30 quant-ph

Deanna M. Abrams , Nicolas Didier , Shane A. Caldwell , Blake R. Johnson , Colm A. Ryan This is my paper · ORCID

classification quant-ph

keywords fluxcrosstalktunabletransmonparametricCZgatequantumprocesstomographyACsweetspotRamseymeasurementsuperconductingqubitfidelity

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

The paper tries to turn flux crosstalk between tunable transmons from a vague worry into a measurable specification. It presents three direct measurements—two for DC and one for AC flux crosstalk—with sensitivities as fine as about 0.001%, and defines crosstalk as a ratio of fluxes so values are comparable across devices. Its central theoretical result is an identity linking a Ramsey-measured average frequency shift to the process infidelity of a simultaneous parametrically activated CZ gate: $r = (27\pi^2/20)(\delta \bar{f}_{01}\tau)^2$. The paper argues that operating the gate at the AC sweet spot suppresses this error from quadratic to quartic order in crosstalk, keeping simultaneous gate fidelity above 99% for crosstalk below about 0.2%.

What carries the argument

The central identity is the crosstalk ratio $X_\Phi = d\Phi_A/d\Phi_B$ and the derived formula $r = (27\pi^2/20)(\delta \bar{f}_{01}\tau)^2$ for CZ infidelity. The ratio turns crosstalk into a device-comparable number, and the formula turns a Ramsey measurement of $\delta \bar{f}_{01}$ under a coherent adversarial pulse into a quantitative fidelity prediction without running two-qubit tomography. The argument runs through an effective interaction-picture Hamiltonian in which crosstalk adds an average-frequency-shift term $\delta\bar{\Delta}$ and a coupling shift $\delta g_{\text{eff}}$; leading-order infidelity follows from the trace overlap of the resulting evolution with the ideal CZ unitary. The AC sweet spot enters as the operating point where $\partial \bar{f}_{01}/\partial\Phi = 0$, making the leading frequency shift second-order in crosstalk and the infidelity quartic.

What would settle it

Run a CZ gate between two qubits while an adversarial flux pulse of fixed amplitude plays on a third qubit; measure the QPT process infidelity and the Ramsey-measured $\delta \bar{f}_{01}$, sweep $\tau$, and check whether the infidelity tracks $(27\pi^2/20)(\delta \bar{f}_{01}\tau)^2$ to within calibration errors. At the AC sweet spot, verify the infidelity scales quarticly with the adversarial amplitude; a persisting quadratic term or a mismatch with the Ramsey-based prediction would show the formula or the assumed dominance of the frequency-shift channel is wrong.

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Extended reading notes

Core claim

The central claim is that flux crosstalk between tunable transmons can be quantified directly with three low-level measurements, and that the AC version of those measurements predicts the fidelity of simultaneous two-qubit gates through a single formula. For a CZ gate of duration $\tau$ whose tunable qubit suffers an average frequency shift $\delta \bar{f}_{01}$ from an adversarial flux pulse, the leading-order process infidelity is $r = (27\pi^2/20)(\delta \bar{f}_{01}\tau)^2$. The paper derives this from an effective Hamiltonian in which crosstalk shifts both the average qubit frequency and the effective coupling, keeps the frequency-shift term after calibrating away local phase errors, and validates it with quantum process tomography of a CZ gate run while an adversarial pulse is played. At the AC sweet spot—the flux-pulse amplitude where the average frequency shift is stationary—the linear frequency shift vanishes, so the leading infidelity becomes quartic in crosstalk; the paper finds this operating point sustains 99% simultaneous gate fidelity for crosstalk below roughly 0.2%.

Load-bearing premise

The prediction assumes that the average frequency shift measured with a Ramsey sequence while an adversarial pulse is played matches the average shift the qubit experiences during the simultaneous CZ gate, and that crosstalk infidelity is dominated by that frequency-shift term rather than by coupling changes, dephasing, or spurious resonances.

Editorial extensions

If this is right

A Ramsey measurement of $\delta \bar{f}_{01}$ plus the calibrated gate time $\tau$ gives a direct prediction of simultaneous CZ infidelity, replacing two-qubit tomography as a crosstalk diagnostic.
Operating parametrically activated CZ gates at the AC sweet spot reduces the crosstalk contribution to infidelity from quadratic to quartic order, so 99% simultaneous gate fidelity requires crosstalk below roughly 0.2% on this architecture.
The DC resonator and qubit methods agree to within about 0.1% across pairs and can be used to build chip-wide crosstalk matrices that expose asymmetric, non-local coupling between tunable qubits.
AC crosstalk varies strongly with modulation frequency for some qubit pairs, meaning simultaneous-gate error can be mitigated by choosing pulse frequencies where crosstalk is small.

Reading between the lines

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

If equation (6) survives further tests, the same Ramsey-interference measurement could serve as an acceptance test for chips: crosstalk below a specified $\delta \bar{f}_{01}$ at the operating pulse amplitude would guarantee simultaneous gate fidelity without process tomography.
A natural extension is to apply the phase-scan method to measure crosstalk from flux lines into fixed-frequency qubits or other circuit elements, using any frequency-dependent observable instead of $\bar{f}_{01}$.
The quartic sweet-spot suppression implies there may be an optimal trade-off between error from crosstalk and error from increased gate time or reduced coupling when moving to the sweet spot.

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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

First the useful part: the three methods are a genuine toolkit. The resonator phase-offset method and the qubit slope method are simple, the cross-check on Q0/Q12 agrees, and the AC phase-interference method gives clean sinusoids with a sensitivity table. The full pairwise matrices and the frequency dependence plots are exactly the kind of data an engineering team needs to decide whether crosstalk is a design problem or a control problem. These parts deserve to be published.

The theory section is where I have a problem. Eq. (B4) in Appendix B has a sign error in the cross term. I expanded |tr(U_CZ† U)|² using their displayed U and U11 from (B3), and the cross term is +(1/10)(δωτ)(δΔτ), not −. With their CZ02 relation δΔ=−δω, the infidelity becomes 11/80 (δωτ)², not 27/80. So Eq. (6) should be (11π²/20)(δf τ)² unless the gate is actually CZ20, in which case 27/80 is right but the paper mislabels it. Either way, the Appendix B derivation as written does not produce the headline coefficient. The 99% / 0.2% crosstalk threshold changes to roughly 0.31% in the 11/80 case.

This is fixable, but it is load-bearing because Eq. (6) is the quantitative bridge to gate error. The experimental validation in Fig. 6(c) cannot settle the sign: no error bars on the QPT points, the adversarial phase was not held at the worst-case value, and the paper itself notes extra dephasing. The agreement is qualitative, which is fine for a methods paper, but the abstract should not present it as a confirmed prediction.

Citation pattern is fine; the Bessel model and AC sweet spot come from the group's own published work, which is appropriate. No invented entities or hidden parameters beyond the standard voltage-to-flux conversions.

For whom: experimental groups working on tunable-transmon control, crosstalk mitigation, and simultaneous gate calibration. It deserves a serious referee; the measurements are valuable and the theory issue is fixable. I would ask the authors to show the expansion in Appendix B, state which CZ resonance was used, and either add error bars or soften the validation claim. Send to peer review.

Referee Report

2 major / 4 minor

Summary. This manuscript addresses the problem of control crosstalk in flux-tunable transmon architectures. It defines a dimensionless crosstalk XΦ=dΦA/dΦB and presents three direct measurements: a resonator-spectroscopy DC method, a qubit-Ramsey DC method, and an AC method that measures the mean frequency shift of a qubit under a modulated flux pulse while an adversarial modulated pulse is applied to another qubit. The AC method is calibrated through a Bessel-function model of the average detuning. The paper then derives, in Appendix B, a leading-order expression r=(27π^2/20)(δf01 τ)^2 for the process infidelity of a parametrically activated CZ gate due to crosstalk, and uses quantum process tomography of a CZ gate in the presence of an adversarial pulse to test the prediction. It concludes that operating at the AC sweet spot suppresses crosstalk-induced infidelity to quartic order and that XΦ<0.2% is sufficient for 99% simultaneous gate fidelity.

Significance. If the central quantitative claim holds, the paper provides a practical and falsifiable bridge between a low-level crosstalk measurement and a high-level two-qubit gate fidelity: a Ramsey measurement of δf01 plus the calibrated gate time predicts an entangled-gate infidelity, and the AC sweet spot is identified as a design/operating principle for crosstalk robustness. The paper also contributes reproducible measurement methodologies—two independent DC methods that agree, a systematic AC crosstalk matrix, and frequency-dependent AC crosstalk data—with stated sensitivities. The Bessel-model fit for the AC calibration and the explicit Appendix B derivation are strengths; the derivation is independent of the fidelity data, and the comparison in Fig. 6(c) is not a fit to the theory.

major comments (2)

[Appendix B, Eq. (B4) and Eq. (6)] Re-expanding the displayed final unitary U(τ)=diag{1,e^{-iα},1,e^{-iα}U11} with U11 from Eq. (B3) directly yields r=(1/5)α²+(1/10)αβ+(3/80)β²+(1/5)γ² to second order in α=δωτ, β=δΔτ, γ=δgτ. This has a positive αβ cross term, while Eq. (B4) has a negative one. Consequently, inserting δΔ=−δω into the re-expanded formula gives r02=(11/80)(δωτ)² rather than (27/80)(δωτ)²; the factor 27/11 discrepancy propagates to Eq. (6) and raises the 99%-fidelity crosstalk threshold from 0.2% to about 0.31%. Because the physical sign of δΔ relative to δω is stated without derivation, the coefficient in Eq. (6) is not established; the authors should either correct the expansion or justify the sign convention that makes Eq. (B4) valid.
[Section V, Fig. 6(c)] The experimental validation cannot resolve the coefficient ambiguity. The measured fidelities are plotted without error bars, the phase between the CZ pulse and the adversarial pulse was not set to the worst-case value used in the theory lines, and the paper itself notes that additional dephasing from the adversarial pulse may contribute. The data demonstrate a qualitative decrease away from the sweet spot and greater robustness at low adversarial amplitude, but they do not quantitatively confirm the coefficient in Eq. (6).

minor comments (4)

[Section IV, Fig. 4(b)] The text says qubit A is modulated 'to the linear regime of its ¯Δ vs. flux amplitude curve,' but the figure shows a broad maximum; specify the numerical amplitude range used and how 'linear' is identified.
[Section V, Fig. 6(c)] The y-axis label 'Measured Fidelity (%)' and the legend entries in volts would be clearer if the adversarial amplitudes were converted to equivalent crosstalk XΦ using the calibration of Section IV, since the paper's metric is XΦ.
[Appendix B, Eq. (B1)] The first-order expansion in XΦ is written for the amplitude of the total flux; the paper should state explicitly that XΦ² terms are dropped and verify that this is negligible for the largest measured crosstalk values.
[Section VI, Conclusion] The conclusion repeats the 0.2% threshold without the conditions used in Section V (equal modulation frequencies, worst-case phase, and negligible δgeff); these caveats should accompany the quoted number.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: Eq. (6) is derived analytically in Appendix B and validated against independently measured frequency shifts, not fitted to gate fidelity data.

full rationale

The claimed prediction chain is self-contained. Eq. (6) is obtained in Appendix B by writing the crosstalk-perturbed CZ Hamiltonian (B2), evolving it to U(τ)=diag{1,e^{-iδωτ},1,e^{-iδωτ}U11(τ)}, and expanding the standard average-infidelity expression r=(d^2−|tr(U_CZ†U)|^2)/(d^2+d) to leading order in δωτ, δΔτ, and δgτ; the coefficients 27/80 and 11/80 come from the stated relations δΔ=−δω for CZ02 and δΔ=+δω for CZ20, which follow from the energies of the |02> and |20> auxiliary levels relative to |11>. No parameter in this derivation is fitted to the QPT fidelity data. The experimental validation in Sec. V inputs the independently measured Ramsey frequency shift δf̄01 and the calibrated gate time τ into Eq. (6); the measured fidelities are outputs, not fit targets. The DC and AC crosstalk measurements similarly estimate crosstalk as ratios of measured frequency-response slopes (Eq. (2) and its AC analogue), using the voltage-to-flux conversion obtained from the analytic Bessel model of Ref. [28]; that model describes the single-qubit response to its own flux drive and does not encode the crosstalk ratio or the infidelity result. The self-citations to Ref. [28] and the AC sweet-spot concept are supporting tools, not the load-bearing target, and are not invoked as a uniqueness constraint. The skeptic's concern about the sign of the δω-δΔ cross term in Eq. (B4) is a possible algebraic/physics error that would change the coefficient of Eq. (6), but it is a correctness issue, not circularity; likewise, the paper's own caveats about non-worst-case phase and additional dephasing are limitations on the validation, not reductions of the prediction to its input.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claims rest on standard quantum circuit models, the linear crosstalk ratio assumption, and the Bessel-function modulation model from the authors' prior work. The only fitted numbers are calibration conversions between applied voltages or currents and flux quanta, which are necessary for converting measured frequency shifts into crosstalk ratios. No new physical entities are introduced.

free parameters (2)

Voltage-to-flux conversion rate in the AC reference scan = not reported numerically; extracted from fitting Eq. (3) to Ramsey detuning versus modulation amplitude
Section IV: the AC crosstalk ratio is obtained after converting top-of-fridge voltage to flux quanta using this fitted parameter; the reported AC crosstalk values and the 20 micro-Phi0 sensitivity inherit its uncertainty.
DC bias current-to-flux conversion per qubit = not reported; stated to be known to relative precision less than 0.5%
Section III: both DC crosstalk methods require converting applied bias current to flux quanta; the paper notes this conversion limits the relative uncertainty on the reported crosstalk values.

assumptions (5)

domain assumption Dispersive resonator-qubit Hamiltonian (Eq. 1) describes the undriven two-transmon system.
Used in Section III for the resonator method; the periodic resonator response is taken to inherit the qubit's flux dependence, and a phase offset is interpreted as crosstalk.
domain assumption Flux crosstalk is a linear ratio X_Phi = dPhi_A/dPhi_B, independent of bias point and pulse amplitude in the small-crosstalk limit.
Defined in the Introduction and used in Eq. (2) and Appendix B Eq. (B1) to convert measured frequency-slope ratios and amplitude changes into crosstalk values.
domain assumption The mean transmon frequency under modulation is given by the Bessel-function expansion Eq. (3) from Ref. [28].
Used in Section IV to fit the voltage-to-flux conversion and to interpret Ramsey-measured mean shifts; Ref. [28] is authored by a subset of the present authors.
domain assumption The interaction-picture Hamiltonian of Eq. (B2) captures CZ gate dynamics under crosstalk, with local Z rotations calibrated without crosstalk and decoherence and higher harmonics neglected.
The infidelity formula Eq. (6) is derived from this model in Appendix B; the paper states these simplifications explicitly.
ad hoc to paper Worst-case scenario of equal modulation frequencies and in-phase or anti-phase adversarial pulses is used for the numerical threshold.
Section V and Appendix B use this scenario to bound the infidelity and to derive the 0.2% crosstalk requirement for 99% fidelity; the experimental implementation does not control the on-chip phase to this worst case.

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Cite this review

Pith. "Pith review of Methods for Measuring Magnetic Flux Crosstalk Between Tunable Transmons." pith.science (2026). https://pith.science/paper/6OZLROAB

@misc{pith2026190811856,
  author       = {Pith},
  title        = {Pith review of: Methods for Measuring Magnetic Flux Crosstalk Between Tunable Transmons},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6OZLROAB}},
  note         = {Machine review of arXiv:1908.11856}
}

read the original abstract

In the gate model of quantum computing, a program is typically decomposed into a sequence of 1- and 2-qubit gates that are realized as control pulses acting on the system. A key requirement for a scalable control system is that the qubits are addressable - that control pulses act only on the targeted qubits. The presence of control crosstalk makes this addressability requirement difficult to meet. In order to provide metrics that can drive requirements for decreasing crosstalk, we present three measurements that directly quantify the DC and AC flux crosstalk present between tunable transmons, with sensitivities as fine as 0.001%. We develop the theory to connect AC flux crosstalk measures to the infidelity of a parametrically activated two-qubit gate. We employ quantum process tomography in the presence of crosstalk to provide an empirical study of the effects of crosstalk on two-qubit gate fidelity.

Figures

Figures reproduced from arXiv: 1908.11856 by the authors.

**Figure 2.** FIG. 2. DC crosstalk via resonator spectroscopy. (a) Shows [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3. Matrix of DC crosstalk as measured by the qubit [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 5.** Figure 5: FIG. 5. Examples of the variety of observed frequency depen [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

**Figure 4.** Figure 4: FIG. 4. (a) Pulse sequence for measuring AC flux crosstalk. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 6.** Figure 6: FIG. 6. (a) Tomography of a CZ gate between qubits 1 and [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

**Figure 7.** Figure 7: FIG. 7. Histogram comparing the results of the two DC [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

**Figure 8.** Figure 8: FIG. 8. AC flux crosstalk between pairs of tunable qubits across the chip. AC crosstalk values are marked as blue dots, while [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]

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Works this paper leans on

32 extracted references · 28 canonical work pages

[1]

Demonstration of a Parametrically-Activated Entangling Gate Protected from Flux Noise

Sabrina S. Hong, Alexander T. Papageorge, Prasahnt Sivarajah, Genya Crossman, Nicolas Dider, Anthony M. Polloreno, Eyob A. Sete, Stefan W. Turkowski, Marcus P. 8 da Silva, and Blake R. Johnson, “Demonstration of a Parametrically-Activated Entangling Gate Protected from Flux Noise,” arXiv e-prints , arXiv:1901.08035 (2019), arXiv:1901.08035 [quant-ph]

work page Pith review arXiv 2019
[2]

Entanglement stabilization using ancilla- based parity detection and real-time feedback in super- conducting circuits,

Christian Kraglund Andersen, Ants Remm, Stefania Lazar, Sebastian Krinner, Johannes Heinsoo, Jean-Claude Besse, Mihai Gabureac, Andreas Wallraﬀ, and Christo- pher Eichler, “Entanglement stabilization using ancilla- based parity detection and real-time feedback in super- conducting circuits,” npj Quantum Information 5, 69 (2019)

work page 2019
[3]

Quantum devices & simulators,

“Quantum devices & simulators,” (2018)

work page 2018
[4]

Superconducting quantum circuits at the surface code threshold for fault tolerance,

R. Barends, J. Kelly, A. Megrant, A. Veitia, D. Sank, E. Jeﬀrey, T. C. White, J. Mutus, A. G. Fowler, B. Camp- bell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, C. Neill, P. O’Malley, P. Roushan, A. Vainsencher, J. Wenner, A. N. Korotkov, A. N. Cleland, and John M. Marti- nis, “Superconducting quantum circuits at the surface code threshold for fault tolera...

arXiv 2014
[5]

Procedure for systematically tuning up cross-talk in the cross-resonance gate,

Sarah Sheldon, Easwar Magesan, Jerry M. Chow, and Jay M. Gambetta, “Procedure for systematically tuning up cross-talk in the cross-resonance gate,” Phys. Rev. A 93, 060302(R) (2016)

work page 2016
[6]

Diabatic gates for frequency-tunable superconducting qubits

R. Barends, C. M. Quintana, A. G. Petukhov, Yu Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graﬀ, T. Huang, E. Jeﬀrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mu...

work page Pith review arXiv 2019
[7]

Quantum supremacy using a programmable superconducting processor,

Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando G. S. L. Brandao, David A. Buell, Brian Burkett, Yu Chen, Zijun Chen, Ben Chiaro, Roberto Collins, William Courtney, Andrew Dunsworth, Ed- ward Farhi, Brooks Foxen, Austin Fowler, Craig Gidney, Marissa Giustina, Rob Graﬀ, Keith Guerin, S...

work page 2019
[8]

Parallel entangling operations on a universal ion-trap quantum computer,

C. Figgatt, A. Ostrander, N. M. Linke, K. A. Landsman, D. Zhu, D. Maslov, and C. Monroe, “Parallel entangling operations on a universal ion-trap quantum computer,” Nature 572, 368–372 (2019)

work page 2019

Show all 32 references

[9]

Probing context-dependent errors in quantum processors,

Kenneth Rudinger, Timothy Proctor, Dylan Langharst, Mohan Sarovar, Kevin Young, and Robin Blume-Kohout, “Probing context-dependent errors in quantum processors,” Phys. Rev. X 9, 021045 (2019)

2019
[10]

Suppression of Qubit Crosstalk in a Tunable Coupling Superconducting Circuit,

Gengyan Zhang, Pranav S. Mundada, and Andrew A. Houck, “Suppression of Qubit Crosstalk in a Tunable Coupling Superconducting Circuit,” arXiv e-prints , arXiv:1810.04182 (2018), arXiv:1810.04182 [quant-ph]

2018 arXiv
[11]

Direct randomized benchmarking for multiqubit devices,

Timothy J. Proctor, Arnaud Carignan-Dugas, Kenneth Rudinger, Erik Nielsen, Robin Blume-Kohout, and Kevin Young, “Direct randomized benchmarking for multiqubit devices,” Phys. Rev. Lett. 123, 030503 (2019)

2019
[12]

10-Qubit Entanglement and Parallel Logic Operations with a Superconducting Circuit,

Chao Song, Kai Xu, Wuxin Liu, Chui-Ping Yang, Shi-Biao Zheng, Hui Deng, Qiwei Xie, Keqiang Huang, Qiujiang Guo, Libo Zhang, Pengfei Zhang, Da Xu, Dongning Zheng, Xiaobo Zhu, H. Wang, Y. A. Chen, C. Y. Lu, Siyuan Han, and Jian-Wei Pan, “10-Qubit Entanglement and Parallel Logic ...

2017 arXiv
[13]

Characterization of address- ability by simultaneous randomized benchmarking,

Jay M. Gambetta, A. D. C´ orcoles, S. T. Merkel, B. R. Johnson, John A. Smolin, Jerry M. Chow, Colm A. Ryan, Chad Rigetti, S. Poletto, Thomas A. Ohki, Mark B. Ketchen, and M. Steﬀen, “Characterization of address- ability by simultaneous randomized benchmarking,” Phys. Rev. Let...

2012
[14]

Three-qubit randomized benchmarking,

David C. McKay, Sarah Sheldon, John A. Smolin, Jerry M. Chow, and Jay M. Gambetta, “Three-qubit randomized benchmarking,” Phys. Rev. Lett. 122, 200502 (2019)

2019
[15]

Characterizing large-scale quan- tum computers via cycle benchmarking,

Alexander Erhard, Joel James Wallman, Lukas Postler, Michael Meth, Roman Stricker, Esteban Adrian Mar- tinez, Philipp Schindler, Thomas Monz, Joseph Emer- son, and Rainer Blatt, “Characterizing large-scale quan- tum computers via cycle benchmarking,” arXiv e-prints , arXiv:190...

2019 arXiv
[16]

Maximally Sensitive Sets of States,

Daniel Gottesman, “Maximally Sensitive Sets of States,” arXiv e-prints , arXiv:1907.05950 (2019), arXiv:1907.05950 [quant-ph]

2019 arXiv
[17]

Bounding quantum gate error rate based on reported av- erage ﬁdelity,

Yuval R Sanders, Joel J Wallman, and Barry C Sanders, “Bounding quantum gate error rate based on reported av- erage ﬁdelity,” New Journal of Physics 18, 012002 (2015)

2015
[18]

Crosstalk error correction through dy- namical decoupling of single-qubit gates in capacitively coupled singlet-triplet semiconductor spin qubits,

Donovan Buterakos, Robert E. Throckmorton, and S. Das Sarma, “Crosstalk error correction through dy- namical decoupling of single-qubit gates in capacitively coupled singlet-triplet semiconductor spin qubits,” Phys. Rev. B 97, 045431 (2018)

2018
[19]

A blueprint for demonstrating quantum supremacy with supercon- ducting qubits,

Charles Neill, Pedran Roushan, K Kechedzhi, Sergio Boixo, Sergei V Isakov, V Smelyanskiy, A Megrant, B Chiaro, A Dunsworth, K Arya, et al. , “A blueprint for demonstrating quantum supremacy with supercon- ducting qubits,” Science 360, 195–199 (2018)

2018
[20]

Charge-insensitive qubit design derived from the cooper pair box,

Jens Koch, Terri M. Yu, Jay Gambetta, A. A. Houck, D. I. Schuster, J. Majer, Alexandre Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Charge-insensitive qubit design derived from the cooper pair box,” Phys. Rev. A 76, 042319 (2007)

2007
[21]

Demon- stration of two-qubit algorithms with a superconducting quantum processor,

Leonardo DiCarlo, Jerry M Chow, Jay M Gambetta, Lev S Bishop, Blake R Johnson, DI Schuster, J Majer, Alexandre Blais, L Frunzio, SM Girvin, et al. , “Demon- stration of two-qubit algorithms with a superconducting quantum processor,” Nature 460, 240 (2009)

2009
[22]

Realization of three-qubit quantum error cor- rection with superconducting circuits,

Matthew D Reed, Leonardo DiCarlo, Simon E Nigg, Luyan Sun, Luigi Frunzio, Steven M Girvin, and Robert J 9 Schoelkopf, “Realization of three-qubit quantum error cor- rection with superconducting circuits,” Nature 482, 382 (2012)

2012
[23]

Entanglement and quantum error correction with superconducting qubits,

Matthew David Reed, “Entanglement and quantum error correction with superconducting qubits,” arXiv preprint arXiv:1311.6759 (2013)

2013 arXiv
[24]

Flux qubits and readout device with two independent ﬂux lines,

B. L. T. Plourde, T. L. Robertson, P. A. Reichardt, T. Hime, S. Linzen, C.-E. Wu, and John Clarke, “Flux qubits and readout device with two independent ﬂux lines,” Phys. Rev. B 72, 060506(R) (2005)

2005
[25]

State preservation by repetitive error detection in a supercon- ducting quantum circuit,

Julian Kelly, Rami Barends, Austin G Fowler, Anthony Megrant, Evan Jeﬀrey, Theodore C White, Daniel Sank, Josh Y Mutus, Brooks Campbell, Yu Chen, et al. , “State preservation by repetitive error detection in a supercon- ducting quantum circuit,” Nature 519, 66 (2015), see supp...

2015
[26]

Detecting bit-ﬂip errors in a logical qubit using stabilizer measurements,

Diego Riste, Stefano Poletto, M-Z Huang, Alessandro Bruno, Visa Vesterinen, O-P Saira, and Leonardo Di- Carlo, “Detecting bit-ﬂip errors in a logical qubit using stabilizer measurements,” Nature communications 6, 6983 (2015)

2015
[27]

Tuneable hopping and nonlinear cross-kerr interactions in a high-coherence superconducting circuit,

M. Kounalakis, C. Dickel, A. Bruno, N. K. Langford, and G. A. Steele, “Tuneable hopping and nonlinear cross-kerr interactions in a high-coherence superconducting circuit,” npj Quantum Information 4, 38 (2018)

2018
[28]

Analytical modeling of parametrically modulated transmon qubits,

Nicolas Didier, Eyob A. Sete, Marcus P. da Silva, and Chad Rigetti, “Analytical modeling of parametrically modulated transmon qubits,” Physical Review A 97, 022330 (2018), arXiv:1706.06566 [quant-ph]

2018 arXiv
[29]

Parametrically activated entangling gates using transmon qubits,

SA Caldwell, N Didier, CA Ryan, EA Sete, A Hudson, P Karalekas, R Manenti, MP da Silva, R Sinclair, E Acala, et al. , “Parametrically activated entangling gates using transmon qubits,” Physical Review Applied 10, 034050 (2018)

2018
[30]

Demonstration of universal paramet- ric entangling gates on a multi-qubit lattice,

Matthew Reagor, Christopher B Osborn, Nikolas Tezak, Alexa Staley, Guenevere Prawiroatmodjo, Michael Scheer, Nasser Alidoust, Eyob A Sete, Nicolas Didier, Marcus P da Silva, et al. , “Demonstration of universal paramet- ric entangling gates on a multi-qubit lattice,” Science a...

2018
[31]

Limitations of quantum process tomography,

Lynden K. Shalm, Morgan Mitchell, and Aephraim Stein- berg, “Limitations of quantum process tomography,” Pro- ceedings of SPIE - The International Society for Optical Engineering 5631 (2005), 10.1117/12.583241

2005 doi
[32]

Self-consistent quantum process tomography,

Seth T. Merkel, Jay M. Gambetta, John A. Smolin, Ste- fano Poletto, Antonio D. C´ orcoles, Blake R. Johnson, Colm A. Ryan, and Matthias Steﬀen, “Self-consistent quantum process tomography,” Phys. Rev. A 87, 062119 (2013), arXiv:1211.0322 [quant-ph]. Appendix A: Comparison of M...

2013 arXiv

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Demonstration of a Parametrically-Activated Entangling Gate Protected from Flux Noise

Sabrina S. Hong, Alexander T. Papageorge, Prasahnt Sivarajah, Genya Crossman, Nicolas Dider, Anthony M. Polloreno, Eyob A. Sete, Stefan W. Turkowski, Marcus P. 8 da Silva, and Blake R. Johnson, “Demonstration of a Parametrically-Activated Entangling Gate Protected from Flux Noise,” arXiv e-prints , arXiv:1901.08035 (2019), arXiv:1901.08035 [quant-ph]

work page Pith review arXiv 2019

[2] [2]

Entanglement stabilization using ancilla- based parity detection and real-time feedback in super- conducting circuits,

Christian Kraglund Andersen, Ants Remm, Stefania Lazar, Sebastian Krinner, Johannes Heinsoo, Jean-Claude Besse, Mihai Gabureac, Andreas Wallraﬀ, and Christo- pher Eichler, “Entanglement stabilization using ancilla- based parity detection and real-time feedback in super- conducting circuits,” npj Quantum Information 5, 69 (2019)

work page 2019

[3] [3]

Quantum devices & simulators,

“Quantum devices & simulators,” (2018)

work page 2018

[4] [4]

Superconducting quantum circuits at the surface code threshold for fault tolerance,

R. Barends, J. Kelly, A. Megrant, A. Veitia, D. Sank, E. Jeﬀrey, T. C. White, J. Mutus, A. G. Fowler, B. Camp- bell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, C. Neill, P. O’Malley, P. Roushan, A. Vainsencher, J. Wenner, A. N. Korotkov, A. N. Cleland, and John M. Marti- nis, “Superconducting quantum circuits at the surface code threshold for fault tolera...

arXiv 2014

[5] [5]

Procedure for systematically tuning up cross-talk in the cross-resonance gate,

Sarah Sheldon, Easwar Magesan, Jerry M. Chow, and Jay M. Gambetta, “Procedure for systematically tuning up cross-talk in the cross-resonance gate,” Phys. Rev. A 93, 060302(R) (2016)

work page 2016

[6] [6]

Diabatic gates for frequency-tunable superconducting qubits

R. Barends, C. M. Quintana, A. G. Petukhov, Yu Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graﬀ, T. Huang, E. Jeﬀrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mu...

work page Pith review arXiv 2019

[7] [7]

Quantum supremacy using a programmable superconducting processor,

Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando G. S. L. Brandao, David A. Buell, Brian Burkett, Yu Chen, Zijun Chen, Ben Chiaro, Roberto Collins, William Courtney, Andrew Dunsworth, Ed- ward Farhi, Brooks Foxen, Austin Fowler, Craig Gidney, Marissa Giustina, Rob Graﬀ, Keith Guerin, S...

work page 2019

[8] [8]

Parallel entangling operations on a universal ion-trap quantum computer,

C. Figgatt, A. Ostrander, N. M. Linke, K. A. Landsman, D. Zhu, D. Maslov, and C. Monroe, “Parallel entangling operations on a universal ion-trap quantum computer,” Nature 572, 368–372 (2019)

work page 2019