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arxiv: 2604.08955 · v1 · submitted 2026-04-10 · 🪐 quant-ph

Impact of Pump Phase-Noise on Josephson Traveling-Wave Parametric Amplifiers

Daryoush Shiri , Likai Yang , Saesun Kim , Mohamed A. Hassan , Philip Krantz , Eric T. Holland This is my paper

Pith reviewed 2026-05-10 17:50 UTC · model grok-4.3

classification 🪐 quant-ph
keywords josephson traveling-wave parametric amplifierpump phase noisethree-wave mixingfour-wave mixingphase noisesuperconducting amplifiersparametric amplificationnonlinearity
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The pith

The three-wave mixing process in Josephson traveling-wave parametric amplifiers is more sensitive to pump phase noise than four-wave mixing due to higher-order even nonlinearities.

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

This paper investigates the effect of phase noise from the pump source on Josephson traveling-wave parametric amplifiers, which are used to boost signal-to-noise ratio in superconducting qubit readout. It establishes that the three-wave mixing process is more sensitive to this noise than the four-wave mixing process. The work identifies even-order nonlinearities of fourth order and above as the source of more than 10 dB extra phase noise at high frequency offsets when pump power increases. These results matter for maintaining low noise in quantum measurement chains. A polynomial model of the amplifier and analysis of the cyclo-stationary nature of phase noise support the simulation findings.

Core claim

Among the two amplification processes in Josephson traveling-wave parametric amplifiers, the three-wave mixing process is more sensitive to the pump phase noise than the four-wave mixing process. The even-order nonlinearity of fourth order and above in three-wave mixing is responsible for more than 10 dB increase of phase noise at high frequency offsets within the phase noise mask as the power of the pump increases. This is corroborated by a polynomial model of the amplifier and the cyclo-stationary property of phase noise.

What carries the argument

A polynomial model of the amplifier combined with harmonic balance periodic noise analysis and the Leeson phase noise model, used to simulate the differing impact of pump phase noise on the two mixing processes.

If this is right

  • Four-wave mixing offers greater resilience to pump phase noise than three-wave mixing in these amplifiers.
  • Raising pump power in three-wave mixing configurations produces larger phase noise increases at high offsets.
  • Even-order nonlinear terms drive phase noise in three-wave mixing more than in four-wave mixing.
  • Amplifier design can prioritize four-wave mixing when pump phase noise is a concern for qubit readout.

Where Pith is reading between the lines

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

  • Selecting four-wave mixing could reduce overall added noise in qubit readout systems that use noisy pump sources.
  • Physical device measurements are needed to test whether real fabrication variations change the simulated noise levels.
  • The mixing-process distinction may apply to noise performance in other superconducting parametric devices.

Load-bearing premise

The harmonic balance periodic noise analysis and Leeson model together with the polynomial model accurately represent the real amplifiers without missing physical effects or fabrication variations.

What would settle it

Direct measurement of the output phase noise spectrum on fabricated three-wave mixing and four-wave mixing Josephson traveling-wave parametric amplifiers at increasing pump powers, checking for the predicted 10 dB difference at high frequency offsets.

Figures

Figures reproduced from arXiv: 2604.08955 by Daryoush Shiri, Eric T. Holland, Likai Yang, Mohamed A. Hassan, Philip Krantz, Saesun Kim.

Figure 1
Figure 1. Figure 1: (a) Schematic of a JTWPA with 1000 unit cells made of a JJ (nonlinear [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Double side-band (DSB) phase noise power spectrum of a typical [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) SSB phase noise spectra at the input and output nodes of a 4WM [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The nonlinear transfer function implemented with SDD in Keysight [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Effect of even order nonlinearities at the output of the model amplifier. [PITH_FULL_IMAGE:figures/full_fig_p004_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Emergence of cyclo-stationary noise (and periodic correlation) in [PITH_FULL_IMAGE:figures/full_fig_p005_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: (a) Test of nonlinear amplifier output phase noise with large frequency [PITH_FULL_IMAGE:figures/full_fig_p005_8.png] view at source ↗
read the original abstract

Superconducting traveling-wave parametric amplifiers (TWPAs) are essential elements for enhancing the signal-to-noise ratio (SNR) and thus the read-out fidelity of superconducting qubits because of their high gain and near quantum-limited noise. However, the impact of the pump source, e.g., phase noise on these amplifiers, has not yet been studied. In this work, we show that among the two amplification processes in JTWPAs, the three-wave mixing (3WM) process is more sensitive to the pump phase noise than the four-wave mixing (4WM) process. We show that the even-order nonlinearity of 4th order and above in three-wave mixing is responsible for more than 10 dB increase of phase noise at high frequency offsets within the phase noise mask as the power of the pump increases. A polynomial model of the amplifier and cyclo-stationary property of phase noise also corroborate with the simulations. The Harmonic Balance (HB) periodic noise analysis tool and Leeson phase noise model in Keysight Advanced Design System (ADS) simulator were used in this study.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 1 minor

Summary. The manuscript presents a simulation-based study of pump phase noise effects on Josephson traveling-wave parametric amplifiers (JTWPAs). It claims that the three-wave mixing (3WM) process is more sensitive to pump phase noise than four-wave mixing (4WM), with even-order nonlinearities of 4th order and higher in 3WM responsible for more than 10 dB excess phase noise at high frequency offsets as pump power increases. The analysis relies on Harmonic Balance periodic noise simulations and the Leeson model in ADS, corroborated by a polynomial model of the amplifier.

Significance. If the simulation results accurately reflect physical JTWPAs, the findings would be significant for optimizing low-noise amplifiers in superconducting qubit readout systems. By quantifying the relative sensitivity of 3WM versus 4WM and linking excess noise to higher-order even nonlinearities, the work could guide pump source specifications and process selection to improve signal-to-noise performance in quantum information applications. The use of standard tools (HB periodic noise, Leeson model) and a corroborating polynomial model provides a reproducible framework for further analysis.

major comments (1)
  1. [Abstract] Abstract: The central quantitative claim that even-order nonlinearity of 4th order and above in 3WM causes more than 10 dB increase of phase noise at high offsets is presented without experimental data, device parameters, or error analysis. This leaves the 3WM/4WM sensitivity ranking and the 10 dB figure dependent on the unvalidated fidelity of the polynomial nonlinearity model and Harmonic Balance cyclo-stationary noise propagation, which is load-bearing for the main conclusion.
minor comments (1)
  1. The abstract uses the term 'phase noise mask' without defining its frequency range, power levels, or how it is constructed from the Leeson model.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for their careful and constructive review of our manuscript. The comment correctly identifies that the work is simulation-based and highlights the need for clearer presentation of parameters and model limitations. We have revised the manuscript to include explicit device parameters, additional discussion of model assumptions and error sources, and a qualified statement of the 10 dB figure as simulation-derived. Our point-by-point response follows.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central quantitative claim that even-order nonlinearity of 4th order and above in 3WM causes more than 10 dB increase of phase noise at high offsets is presented without experimental data, device parameters, or error analysis. This leaves the 3WM/4WM sensitivity ranking and the 10 dB figure dependent on the unvalidated fidelity of the polynomial nonlinearity model and Harmonic Balance cyclo-stationary noise propagation, which is load-bearing for the main conclusion.

    Authors: We agree that the abstract and main text would benefit from more explicit details. The study is entirely simulation-based using the Harmonic Balance periodic noise analysis and Leeson model in ADS, cross-checked against an independent polynomial nonlinearity model. In the revised manuscript we have added the specific device parameters (Josephson junction critical current, transmission line length, dispersion parameters) employed in the simulations, together with a dedicated subsection discussing the assumptions of the cyclo-stationary noise propagation and potential discrepancies with physical devices. The 10 dB excess phase-noise figure is now qualified as obtained under the simulated pump-power sweep and within the phase-noise mask. While we cannot supply experimental validation data, the use of standard commercial tools and the polynomial corroboration provide a reproducible framework for the reported sensitivity ranking between 3WM and 4WM. revision: partial

standing simulated objections not resolved
  • Absence of experimental measurements to validate the simulation results against fabricated JTWPAs.

Circularity Check

0 steps flagged

No circularity: claims rest on external simulator outputs and standard models

full rationale

The paper derives its central claims (3WM more sensitive than 4WM to pump phase noise, with even-order nonlinearities causing >10 dB excess at high offsets) exclusively from Harmonic Balance periodic-noise simulations in ADS using the Leeson model plus a polynomial nonlinearity model. These are standard external tools and a conventional Josephson-junction expansion; the text gives no indication that any parameter was fitted to the same output quantities later presented as results, nor any self-citation chain, self-definition, or ansatz smuggled from prior author work. The derivation chain is therefore the forward execution of an independent model rather than a tautology that reduces to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are identifiable from the provided text. The work assumes standard models of nonlinearity and phase noise.

pith-pipeline@v0.9.0 · 5506 in / 1119 out tokens · 48048 ms · 2026-05-10T17:50:35.392341+00:00 · methodology

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Reference graph

Works this paper leans on

3 extracted references · 3 canonical work pages

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    Model- ing Josephson traveling-wave parametric amplifiers with electromagnetic and circuit co-simulation,

    10 Yang, L., Wang, J., Hassan, M. A., Krantz, P., and O’Brien, K. P., “Model- ing Josephson traveling-wave parametric amplifiers with electromagnetic and circuit co-simulation,” in2025 IEEE/MTT-S International Microwave Symposium - IMS 2025, 2025, pp. 65–68. 11 Armstrong, J. A., Bloembergen, N., Ducuing, J., and Pershan, P. S., “Interactions between light...

    work page 2025

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    X-parameter based design and simulation of Josephson traveling-wave parametric amplifiers for quantum computing applications,

    20 Peng, K., Poore, R., Krantz, P., Root, D. E., and O’Brien, K. P., “X-parameter based design and simulation of Josephson traveling-wave parametric amplifiers for quantum computing applications,”2022 IEEE In- ternational Conference on Quantum Computing and Engineering (QCE), pp. 331–340, Sept

    work page 2022

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    The role of master clock stability in quantum information processing,

    21 Ball, H., Oliver, W. D., and Biercuk, M. J., “The role of master clock stability in quantum information processing,”npj Quantum Information, vol. 2, no. 1, p. 16033, 2016

    work page 2016