The Pound-Drever-Hall Method for Superconducting-Qubit Readout

Alicia J. Koll\'ar; Ibukunoluwa Adisa; Kevin C. Cox; Won Chan Lee

REVIEW 2 major objections 5 minor 29 references

The Pound-Drever-Hall Method for Superconducting-Qubit Readout

T0 review · 2 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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

Pith's one-line read Pound-Drever-Hall readout makes transmon qubit state detection immune to microwave phase drift and tolerant of sidebands 28 dB above the carrier.

desk verdict Phase-stability demonstration is solid and worth citing; the 14 dB gain claim is a reasonable projection but not yet a measured result. read the letter →

arxiv 2512.03138 v3 pith:R4HD3DL4 submitted 2025-12-02 quant-ph

Ibukunoluwa Adisa , Won Chan Lee , Kevin C. Cox , Alicia J. Kollár This is my paper

classification quant-ph

keywords Pound-Drever-Hallsuperconductingqubittransmonreadoutdispersivephasestabilitymeasurement-inducedstatetransitionsheterodynegaincryogenicdetector

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

Pound-Drever-Hall (PDH) readout, a technique originally developed to lock lasers to optical cavities, can be applied to superconducting transmon qubits as a self-phase-referenced measurement. The PDH error signal is formed from the beat between a carrier tone and two sidebands that all share one source and one propagation path, so the readout depends only on differential phase — common-mode drift from generators, cables, and digitizers cancels. The paper demonstrates 0.73° RMS differential-phase stability over two hours, single-shot qubit-state discrimination even when the carrier phase wanders by hundreds of degrees, and a sideband-power tolerance of at least +28 dBc at detunings above 20 MHz, implying a possible 14 dB heterodyne-gain improvement in readout SNR. The current experiment reconstructs the PDH signal from room-temperature heterodyne detection of all three tones, so the phase-stability claim is directly demonstrated while the SNR gain remains a potential that would require a cryogenic square-law detector.

What carries the argument

The central object is the PDH error signal, the sum of the two carrier-sideband beat notes ε(ω) = E₊E₀e^{i(φ₀−φ₊)} + E₋E₀e^{i(φ₋−φ₀)}. It converts the qubit-state-dependent cavity frequency shift into a differential phase measurement that cancels common-mode phase errors because the three tones originate from one source and traverse the same path. The paper also introduces the scissors phase Σ = 2φ₀ − (φ₋ + φ₊), a linear combination orthogonal to both common-mode and differential-mode errors, which remains stable even when timing offsets rotate the standard PDH quadratures.

What would settle it

Run full three-tone PDH readout with a cryogenic square-law detector and measure the probability p(o|g) of jumping to a non-computational state as sideband power is increased while the carrier sits near resonance and the modulation frequency is 20 MHz. If p(o|g) rises measurably before the sideband reaches +28 dBc — or if two-tone spectroscopy reveals new transition lines attributable to carrier–sideband beats — the MIST-tolerance claim fails. A simpler Floquet calculation of quasienergies under the three-tone drive would also reveal whether the single-tone threshold is the right bound.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes that PDH readout of a transmon is intrinsically phase-stable and that strong off-resonant sidebands are free of measurement-induced state transitions (MIST). The stability follows because the qubit-state-dependent resonator frequency shift appears in the differential phases between carrier and sidebands, and any phase error that shifts all three tones equally drops out; errors that shift the sidebands oppositely are suppressed by the small ratio of modulation frequency to carrier frequency. The experimental signature is 0.73° RMS fluctuation of the differential phase over two hours while the raw carrier phase drifts about 400°, plus single-shot separat

Load-bearing premise

The claim that more than 14 dB of extra sideband power is safe for readout assumes that a single off-resonant probe tone's MIST-free behavior predicts the behavior of the full three-tone PDH interrogation; if carrier–sideband beating introduces extra transitions, the tolerated sideband power could be lower.

Editorial extensions

If this is right

PDH readout can remove the need for rolling phase calibration and reduce clocking precision requirements in superconducting-qubit experiments, lowering the per-channel cost of readout electronics.
Because the phase reference is intrinsic, single-shot readout remains viable even when generators and local oscillators are free-running or unlocked.
Off-resonant sidebands at detunings above 20 MHz can carry much more power than the carrier without inducing MIST, enabling faster or higher-SNR readout than conventional heterodyne at fixed resonant probe power.
A cryogenic square-law detector that mixes carrier and sidebands before amplification would realize the predicted more-than-14 dB heterodyne gain, motivating a new class of Josephson-junction detectors optimized for PDH beatnote detection.
The scissors phase offers a readout that survives simultaneous generator-phase and timing errors, which could be valuable in distributed or multiplexed measurement chains.

Reading between the lines

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

The 14 dB gain figure is an upper-bound estimate: the MIST measurement used a single probe tone, and a full three-tone PDH interrogation could in principle produce intermodulation or two-photon transitions at lower power; a direct three-tone MIST test would settle it.
The phase-stability advantage should extend naturally to frequency-multiplexed readout of many qubits, where a shared carrier and per-qubit sidebands could eliminate per-channel phase references — a scaling benefit the paper only gestures at.
The scissors phase could be applied beyond qubit readout, e.g., to precision resonator characterization or any microwave measurement where both source and digitizer timing are uncontrolled.
The synthetic-PDH reconstruction in this work demonstrates the signal but not the noise benefit; a testable extension is to compare the SNR of direct PDH readout (with a cryogenic square-law detector) against heterodyne readout at the same carrier power to verify the predicted gain.

Share X Bluesky LinkedIn Reddit HN

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

You should know two things about this paper. First, the phase-stability result is clean: 0.73° RMS differential phase over two hours while the raw carrier drifts by hundreds of degrees is a convincing demonstration of common-mode rejection. That part holds up. Second, the headline 14 dB heterodyne gain is not something they measured. It is an extrapolation from single-tone MIST thresholds to a three-tone PDH waveform they never actually applied with the carrier and sidebands simultaneously.

What is genuinely new: adapting PDH to single-shot transmon readout, the scissors phase Σ that stays robust even when differential-mode timing errors corrupt the standard PDH quadratures, and the MIST data at large detunings showing no transitions up to +28 dBc. They are also admirably honest about the main limitation: in S5 they say explicitly that the synthetic PDH reconstruction gives no SNR improvement over heterodyne, because all amplification happens before the carrier-sideband multiplication. The theory is standard PDH, but the application to qubit readout and the phase-stability benchmark are useful.

The soft spots are in proportion to how much weight the claims carry. The biggest one is the MIST extrapolation. The probe is applied alone between two heterodyne measurements; the qubit never sees the carrier plus sidebands together. In real PDH readout, the near-resonant carrier dresses the transmon and can generate intermodulation products or parametrically modulate the resonator, so the 28 dBc tolerance and the 14 dB gain are plausible but not demonstrated. This is not a fatal flaw, because the paper carefully says "potential" gain, but the abstract still leads with it. Second, what they built is a software reconstruction of PDH, not a true PDH receiver with a cryogenic square-law detector. That makes the phase-stability data a proof-of-principle rather than a full implementation of the method. It is fine for what it is, but readers should not confuse the synthetic reconstruction with the real thing. The state-assignment uses Gaussian fits with parameters taken from the reference data; that is standard practice, not circular.

The citation pattern is fine. They cite the prior microwave PDH resonator work, including the simultaneous independent work by Rath et al., and there is no self-citation loading.

Who gets value: people working on scalable readout architectures, especially anyone concerned with clock synchronization and rolling calibration for large qubit arrays. The paper deserves a serious referee. My recommendation: send it to peer review, and ask the authors to either validate the three-tone MIST scenario or tone down the 14 dB claim to what the single-tone data actually support. The phase-stability core is solid and the follow-up is clearly addressable.

Referee Report

2 major / 5 minor

Summary. The manuscript proposes a Pound-Drever-Hall-style multi-tone readout for superconducting transmon qubits. Because the three tones are generated from a single source and travel the same path, the detected differential phase between carrier and sidebands is largely immune to common-mode microwave phase drift. Since a suitable cryogenic square-law detector is not available, the authors implement a 'synthetic' PDH receiver: all three tones are simultaneously downconverted and digitized, and the PDH error signal is reconstructed digitally. They report 0.73° RMS differential-phase stability over 2 h (compared with roughly 400° carrier phase drift), single-shot state discrimination with free-running generators, and a 'scissors phase' Σ = 2ϕ0 − (ϕ− + ϕ+) robust to modulation and digitizer timing errors. A separate MIST benchmark, using a single probe tone applied between two heterodyne measurements, shows no added transitions at detunings ≥20 MHz up to +28 dBc probe power; the authors interpret this as permitting 14 dB of intrinsic heterodyne gain for a future PDH implementation with a cryogenic |E|^2 detector.

Significance. If the phase-stability result holds, the work is a useful step toward self-referenced microwave readout and reduces the need for phase-locked references and rolling calibration. The 2-hour differential-phase data are direct and convincing, and the paper is transparent that the reconstruction itself provides no SNR gain (Appendix S5) and that the 14 dB figure is a projection contingent on future hardware. The MIST measurement is carefully designed with a two-measurement protocol and Gaussian state assignment. The principal weakness is that the headline gain claim extrapolates single-tone MIST results to the three-tone PDH waveform, where carrier dressing and intermodulation could alter thresholds; this specific concern is not addressed by the data. The paper is therefore scientifically sound in its demonstrated claims but overstates the certainty of the quantitative gain projection.

major comments (2)

[Main text, Fig. 4; Appendix S7] The 'at least 28 dBc' sideband-tolerance claim is an extrapolation from a single-tone MIST measurement. In the protocol of Appendix S7, the probe is applied alone between two heterodyne measurements, with the readout carrier absent. In a real PDH interrogation the near-resonant carrier and both sidebands arrive simultaneously; the carrier ac-Stark dresses the transmon, the Josephson nonlinearity can generate intermodulation products (e.g., 2ω0−ω±, ω−+ω0−ω+), and the 20–30 MHz beat itself may parametrically modulate the resonator. None of these channels is probed by the single-tone measurement. The statement 'the PDH readout scheme can tolerate at least 28 dBc more power in the sideband at large detunings' should be restricted to the single-probe test unless a three-tone MIST measurement or a quantitative estimate of these multi-tone processes is provided. Since the 14 dB potential gain c
[Appendix S5; main text 'Intrinsic Heterodyne Gain'] The 14 dB improvement is not realized by the reported receiver. Appendix S5 states explicitly that the reconstructed PDH signal inherits all heterodyne detection noise and shows no SNR improvement; the gain requires a cryogenic square-law detector that does not yet exist. The paper does disclose this, but the abstract and concluding paragraphs present the 14 dB figure as a property of 'the PDH readout scheme' rather than as a prediction conditional on (i) a new detector and (ii) the three-tone MIST assumption of Comment 1. Please clearly separate measured results from projections, e.g., by labeling the 14 dB number as a predicted bound for a future hardware implementation.

minor comments (5)

[Abstract and Fig. 3] The claim 'capable of single-shot readout' is not supported by a quantitative assignment fidelity or confusion matrix. The heatmaps in Fig. 3 and Fig. S4 show separation, but a number (e.g., single-shot readout fidelity with and without induced phase errors) would make the claim precise and testable.
[Appendix S7, Fig. S10 caption] 'pump power' appears where 'probe power' is meant. Please correct.
[Fig. 2 caption] Typo: 'A verage' should be 'Average'.
[Appendix S5 and S7] Typos: 'carruer' should be 'carrier' in Appendix S5; 'signitures' should be 'signatures' in Appendix S7; 'repectively' should be 'respectively' in Appendix S3.
[Eq. (3) and Eq. (S16)] The connection between the main-text PDH signal (Eq. 3) and the complex error signal ϵ(ω) defined in Eq. (S16) should be stated explicitly. The sign convention for the lower sideband differs from standard optical notation, and the reader currently has to infer the relation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the phase-stability result is a direct measurement of the differential phase, and the MIST/heterodyne-gain claims rest on measured thresholds and algebraic scaling rather than fitted inputs.

full rationale

The paper's central claims are either measured directly or follow algebraically from the definition of the PDH observable. The phase-stability result (Fig. 2 and S5) is a direct measurement of the differential phase φ0−φ−; the cancellation of common-mode drift is explicitly shown in S2D (φ0'−φ±' = φ0−φ±), so it is a consequence of the method, not a hidden fitted prediction. The 14 dB heterodyne-gain claim rests on measured MIST thresholds in Fig. 4/S10, where a single off-resonant probe at large detunings shows no transitions up to +28 dBc, and on the algebraic scaling ϵQ ∝ E0E±. No parameter is fitted to the claimed outcome. S5 explicitly concedes that the synthetic reconstruction gives no SNR improvement and that the gain projection requires a future cryogenic square-law detector; this is a validity/extrapolation caveat, not circularity. The state-assignment procedure in S6 uses the MIST reference itself to locate the |o⟩ cluster, which is self-referential but not load-bearing: the MIST threshold is determined by the power dependence of p(o|j), not by the calibration. The scissors phase Σ = 2φ0−(φ−+φ+) is defined and shown invariant under common/differential errors by direct substitution; this is again definitional rather than circular. No load-bearing self-citations or imported uniqueness theorems appear. Overall, the derivation chain is self-contained against the measured data and the explicit equations, with no circular step identified.

Assumptions & free parameters 3 free parameters · 5 assumptions · 1 invented entities

The central claims rest on standard dispersive-cQED physics, a phase-error decomposition model, and three experiment-specific assumptions: Gaussian state assignment, single-tone MIST extrapolation, and the hanger-transmission equivalence. The main human-chosen parameters are the state-assignment boundaries, sideband precompensation, and measurement frequency. No new physical entity is invented; the scissors phase is a signal-processing construction.

free parameters (3)

State-assignment Gaussian parameters = Not stated numerically; fitted to reference probe data
Centers, widths, and decision boundaries for |g>, |e>, and |o> are obtained from Gaussian fits to reference IQ histograms (S6). All MIST probabilities and the thresholds that support the 14 dB claim inherit these fitted classifications.
Sideband phase precompensation offsets = Not stated numerically
Fixed phase offsets are applied to the sideband tones to enforce equal-and-opposite phase relative to the carrier at the detector (S4, S8). These are chosen from an initial dispersion measurement and affect the reconstructed PDH and scissors phases.
Measurement carrier frequency = 6.7717 GHz
Chosen near the resonator frequency for the qubit in |e> to provide optimal distinguishability between |g>, |e>, and |o> (S6). The MIST thresholds and phase-separation figures depend on this hand-chosen operating point.

assumptions (5)

domain assumption The transmon is treated as a two-level system coupled to the resonator in the dispersive regime (S2A).
All readout-signal derivations start from the Jaynes-Cummings Hamiltonian and retain only the dispersive two-level term, neglecting higher transmon levels except in the empirical |o> category.
standard math Phase errors decompose into a common-mode part α(1,1,1) and a differential part β(-1,0,1); PDH is sensitive only to β (S2D).
This decomposition underlies the central phase-stability argument. It is mathematically clean, but its applicability to every real drift channel (path length, digitizer timing, generator phase) is asserted rather than proven.
domain assumption Measurement outcomes are dominated by Gaussian noise, so state assignment via Gaussian fits and linear decision boundaries is valid (S6).
The MIST probabilities and all |o> classifications rely on this Gaussian assumption; non-Gaussian tails would change the derived thresholds.
ad hoc to paper A single off-resonant probe tone replicates the effect of a PDH sideband in the full three-tone configuration (Fig. 4, S7).
This is the load-bearing extrapolation behind the 14 dB gain claim. The paper does not test the actual carrier-plus-two-sidebands waveform for MIST, so multi-tone effects are uncharacterized.
domain assumption S21 transmission through the hanger-coupled resonator is equivalent to reflection in an optical PDH scheme (S8).
The experiment treats the hanger geometry as a reflection-like PDH measurement without a circulator; if the transmission-phase response differs from the assumed scattering model, the error-signal interpretation would shift.

invented entities (1)

Scissors phase Σ
purpose: A new phase combination Σ = 2ϕ0 - (ϕ- + ϕ+) claimed to reject both common-mode and differential-mode phase errors.
Not a physical entity; it is a derived observable demonstrated within this paper. No external falsifiable handle is provided beyond the paper's own data.

how reviews work

0 comments

Cite this review

Pith. "Pith review of The Pound-Drever-Hall Method for Superconducting-Qubit Readout." pith.science (2026). https://pith.science/paper/R4HD3DL4

@misc{pith2026251203138,
  author       = {Pith},
  title        = {Pith review of: The Pound-Drever-Hall Method for Superconducting-Qubit Readout},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/R4HD3DL4}},
  note         = {Machine review of arXiv:2512.03138}
}

abstract

Scaling quantum computers to large sizes requires the implementation of many parallel qubit readouts. Here we present an ultrastable superconducting-qubit readout method using the multi-tone self-phase-referenced Pound-Drever-Hall (PDH) technique, originally developed for use with optical cavities. In this work, we benchmark PDH readout of a single transmon qubit, using room-temperature heterodyne detection of all tones to reconstruct the PDH signal. We demonstrate that PDH qubit readout is insensitive to microwave phase drift, displaying $0.73^\circ$ phase stability over 2 hours, and capable of single-shot readout in the presence of phase errors exceeding the phase shift induced by the qubit state. We show that the PDH sideband tones do not cause unwanted measurement-induced state transitions for a transmon qubit, leading to a potential signal enhancement of at least $14$~dB.

Figures

Figures reproduced from arXiv: 2512.03138 by the authors.

**Figure 1.** Schematic of drift sensitivities for conventional and PDH readout of transmon qubits. Schematic IQ-plane representation of measurement outcomes corresponding to the ground (blue) and the excited states (orange) of a transmon. (a) For heterodyne readout, the measurement signals are sensitive to both the power (red arrow) and the phase (blue arrow) of the measurement tone. (b) In self phase-referenced PDH readout, th… view at source ↗

**Figure 2.** Long-term phase stability of PDH readout. Average carrier and sideband phases over 1000 consecutive single shots are monitored over a period of 2 hours for sideband detunings from 5 − 30 MHz. (a) Raw carrier phase ϕ0, showing roughly 400◦ drift due to a frequency offset between the carrier and the LO. (b) Non-linear residual fluctuations ϕ˜0 after subtracting the linear drift observed in (a). (c) Fluctuations of the… view at source ↗

**Figure 3.** Single-shot phase stability of PDH readout. (a) PDH readout with free running generators for the qubit prepared either in |g⟩ or |e⟩. (a-i) Heterodyne IQ distribution for the carrier. Loss of phase coherence collapses the two states into overlapping IQ distributions. The color map indicates ϑe, the fraction of events corresponding to preparation in |e⟩. Transparency is reduced for pixels with less than 10 counts, w… view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: MIST in PDH readout. MIST due to additional tones during readout is diagnosed using two sequential measurements with a probe tone applied in between (a-inset). Outcomes for each measurement are classified as ground |g⟩, excited |e⟩, or other |o⟩. (a) Conditional probab…

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

29 extracted references · 2 linked inside Pith

[10]

Swiadek, R

F. Swiadek, R. Shillito, P. Magnard, A. Remm, C. Hellings, N. Lacroix, Q. Ficheux, D. C. Zanuz, G. J. Norris, A. Blais, et al. , PRX Quantum 5, 040326 (2024)

2024
[11]

P. A. Spring, L. Milanovic, Y. Sunada, S. Wang, A. F. Van Loo, S. Tamate, and Y. Nakamura, PRX Quantum 6, 020345 (2025)

2025
[12]

Walter, P

T. Walter, P. Kurpiers, S. Gasparinetti, P. Mag- nard, A. Potočnik, Y. Salathé, M. Pechal, M. Mondal, M. Oppliger, C. Eichler, and A. Wallraﬀ, Phys. Rev. Appl. 7, 054020 (2017)

2017
[13]

Krantz, M

P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gus- tavsson, and W. D. Oliver, Appl. Phys. Rev. 6, 021318 (2019)

2019
[16]

P. D. Kurilovich, T. Connolly, C. G. Bøttcher, D. K. Weiss, S. Hazra, V. R. Joshi, A. Z. Ding, H. Nho, S. Diamond, V. D. Kurilovich, et al. , arXiv preprint arXiv:2501.09161 (2025)

arXiv 2025
[18]

Khezri, A

M. Khezri, A. Opremcak, Z. Chen, K. C. Miao, M. McEwen, A. Bengtsson, T. White, O. Naaman, D. Sank, A. N. Korotkov, et al. , Physical Review Ap- plied 20, 054008 (2023)

2023
[20]

Y. Y. Gao, M. A. Rol, S. Touzard, and C. Wang, PRX quantum 2, 040202 (2021)

2021
[23]

Blais, A

A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraﬀ, Rev. Mod. Phys. 93, 025005 (2021)

2021

Show all 29 references

[24]

Wallraﬀ, D

A. Wallraﬀ, D. I. Schuster, A. Blais, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Physical review letters 95, 060501 (2005)

2005
[25]

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
[26]

Blais, R.-S

A. Blais, R.-S. Huang, A. Wallraﬀ, S. M. Girvin, and R. J. Schoelkopf, Phys. Rev. A 69, 062320 (2004)

2004
[27]

Krantz, M

P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gustavsson, and W. D. Oliver, Appl. Phys. Rev. 6, 021318 (2019)

2019
[28]

R. V. Pound, Review of Scientiﬁc Instruments 17, 490 (1946)

1946
[29]

R. W. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, Applied Physics B 31, 97 (1983)

1983
[30]

E. D. Black, American journal of physics 69, 79 (2001)

2001
[31]

Lindström, J

T. Lindström, J. Burnett, M. Oxborrow, and A. Y. Tzalenchuk, Review of Scientiﬁc Instruments 82, 104706 (2011)

2011
[32]

S. E. de Graaf, A. Danilov, and S. Kubatkin, IEEE Transactions on Applied Superconductivity 24, 1 (2014)

2014
[33]

Kedar, Z

D. Kedar, Z. Yao, I. Ryger, J. L. Hall, and J. Ye, Optica 11, 58 (2024)

2024
[34]

P. K. Rath, J. D. Philips, T. Yoon, K. R. Shirer, A. Fereidouni, and J. Pollanen, arXiv preprint arXiv:2512.06289 (2025)

2025
[35]

Haroche and J.-M

S. Haroche and J.-M. Raimond, Exploring the quantum: atoms, cavities, and photons (Oxford university press, 2006)

2006
[36]

M. F. Dumas, B. Groleau-Paré, A. McDonald, M. H. Muñoz Arias, C. Lledó, B. D’Anjou, and A. Blais, Phys. Rev. X 14, 041023 (2024)

2024
[37]

Shillito, A

R. Shillito, A. Petrescu, J. Cohen, J. Beall, M. Hauru, M. Ganahl, A. G. Lewis, G. Vidal, and A. Blais, Physical Review Applied 18, 034031 (2022)

2022
[38]

Connolly, P

T. Connolly, P. D. Kurilovich, V. D. Kurilovich, C. G. Bøttcher, S. Hazra, W. Dai, A. Z. Ding, V. R. Joshi, H. Nho, S. Diamond, et al. , arXiv preprint arXiv:2506.05306 (2025). 20 300 K 50 K 20 kHz LPF 20 kHz LPF 20 kHz LPF 20 kHz LPF 20 kHz LPF -1dB Magnet FBL 1 In FBL 2 In J...

2025 arXiv
[39]

D. Sank, Z. Chen, M. Khezri, J. Kelly, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. Fowler, et al. , Physical review letters 117, 190503 (2016)

2016
[40]

Lloyd, IEEE Transactions on Information Theory 28, 129 (1982)

S. Lloyd, IEEE Transactions on Information Theory 28, 129 (1982)

1982
[41]

Gambetta, W

J. Gambetta, W. Braﬀ, A. Wallraﬀ, S. Girvin, and R. Schoelkopf, Physical Review A—Atomic, Molecular, and Optical Physics 76, 012325 (2007)

2007
[42]

Magesan, J

E. Magesan, J. M. Gambetta, A. D. Córcoles, and J. M. Chow, Phys. Rev. Lett. 114, 200501 (2015)

2015
[43]

P. J. Rousseeuw, Journal of Computational and Applied Mathematics 20, 53 (1987)

1987
[44]

Bista, M

A. Bista, M. Thibodeau, K. Nie, K. Chow, B. K. Clark, and A. Kou, arXiv preprint arXiv:2501.17807 (2025). [25] M. Khezri, A. Opremcak, Z. Chen, K. C. Miao, M. McEwen, A. Bengtsson, T. White, O. Naaman, D. Sank, A. N. Korotkov, et al. , Physical Review Applied 20, 054008 (2023)

2025

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.

[1] [10]

Swiadek, R

F. Swiadek, R. Shillito, P. Magnard, A. Remm, C. Hellings, N. Lacroix, Q. Ficheux, D. C. Zanuz, G. J. Norris, A. Blais, et al. , PRX Quantum 5, 040326 (2024)

2024

[2] [11]

P. A. Spring, L. Milanovic, Y. Sunada, S. Wang, A. F. Van Loo, S. Tamate, and Y. Nakamura, PRX Quantum 6, 020345 (2025)

2025

[3] [12]

Walter, P

T. Walter, P. Kurpiers, S. Gasparinetti, P. Mag- nard, A. Potočnik, Y. Salathé, M. Pechal, M. Mondal, M. Oppliger, C. Eichler, and A. Wallraﬀ, Phys. Rev. Appl. 7, 054020 (2017)

2017

[4] [13]

Krantz, M

P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gus- tavsson, and W. D. Oliver, Appl. Phys. Rev. 6, 021318 (2019)

2019

[5] [16]

P. D. Kurilovich, T. Connolly, C. G. Bøttcher, D. K. Weiss, S. Hazra, V. R. Joshi, A. Z. Ding, H. Nho, S. Diamond, V. D. Kurilovich, et al. , arXiv preprint arXiv:2501.09161 (2025)

arXiv 2025

[6] [18]

Khezri, A

M. Khezri, A. Opremcak, Z. Chen, K. C. Miao, M. McEwen, A. Bengtsson, T. White, O. Naaman, D. Sank, A. N. Korotkov, et al. , Physical Review Ap- plied 20, 054008 (2023)

2023

[7] [20]

Y. Y. Gao, M. A. Rol, S. Touzard, and C. Wang, PRX quantum 2, 040202 (2021)

2021

[8] [23]

Blais, A

A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraﬀ, Rev. Mod. Phys. 93, 025005 (2021)

2021