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arxiv: 2601.09014 · v3 · pith:AMOETCWBnew · submitted 2026-01-13 · 🪐 quant-ph

Impact of control signal phase noise on qubit fidelity

Agata Barsotti , Paolo Marconcini , Gregorio Procissi , Massimo Macucci This is my paper

Pith reviewed 2026-05-16 14:18 UTC · model grok-4.3

classification 🪐 quant-ph
keywords phase noisequbit fidelitycontrol pulsespower spectral densityquantum simulationgate errorreference oscillator
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The pith

Simulations show which noise frequencies most degrade qubit fidelity

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

The paper examines how phase noise in reference oscillator signals affects the fidelity of qubit control operations, especially as pulses become more complex and decoherence improves. It uses numerical simulations to apply realizations of phase fluctuations, drawn from a power spectral density, directly to the carrier of realistic time-dependent control pulses. The simulations track the qubit state evolution and compare the final state to the ideal case, averaging over many realizations to quantify the average fidelity loss. This approach breaks down the noise into its frequency components to identify which spectral regions contribute most to the degradation and to establish their relative weights.

Core claim

Phase noise in the control signal carrier interacts with the qubit's driven evolution in a frequency-dependent way. By generating consistent noise realizations and simulating their effect on the qubit state with realistic pulses, the work demonstrates that different parts of the noise spectrum produce unequal impacts on fidelity, with a clear identification of the most critical frequency bands and their relative contributions to the overall loss.

What carries the argument

Generation of phase noise realizations from a given power spectral density, applied to the pulse carrier, followed by direct simulation of qubit temporal evolution to compare noisy and ideal final states.

If this is right

  • Spectral regions near the pulse bandwidth and at low frequencies produce the largest fidelity drops.
  • The relative weight of each frequency band in the total degradation can be quantified through the simulation breakdown.
  • Averaging over multiple noise realizations gives a practical estimate of fidelity loss for complex pulse sequences.
  • An approximate analytical picture of the phase-fluctuating carrier helps explain why certain bands dominate.

Where Pith is reading between the lines

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

  • Hardware designers could prioritize phase stability in reference oscillators at the identified critical frequencies to improve fidelity with minimal overall changes.
  • The same realization-and-simulation method could be applied to study amplitude noise or other drive nonidealities in quantum control.
  • Experiments adding synthetic phase noise to test setups at specific frequencies would directly test the predicted spectral weights.

Load-bearing premise

Phase noise realizations drawn from a power spectral density accurately represent real hardware fluctuations and the simulation captures all relevant qubit dynamics under the noisy drive.

What would settle it

Measure gate fidelity on a physical qubit while injecting phase noise with a known power spectrum at controlled frequencies and check whether the observed degradation matches the simulated values for the same spectrum.

Figures

Figures reproduced from arXiv: 2601.09014 by Agata Barsotti, Gregorio Procissi, Massimo Macucci, Paolo Marconcini.

Figure 1
Figure 1. Figure 1: FIG. 1. Block diagram of the numerical procedure to generate [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Fidelity as a function of the frequency offset and of th [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Fidelity as a function of the number of applied [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Fidelity as a function of frequency offset and of the [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Fidelity as a function of the number of applied [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Bloch sphere representation of a qubit state driven [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Evolution of the polar angle. The results correspond [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. PSD of the phase noise as a function of the frequency [PITH_FULL_IMAGE:figures/full_fig_p008_11.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Evolution of the azimuthal angle, taking into ac [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Synthesized phase noise PSD to study the effect [PITH_FULL_IMAGE:figures/full_fig_p009_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Fidelity as a function of the number of 150 ns ap [PITH_FULL_IMAGE:figures/full_fig_p009_14.png] view at source ↗
read the original abstract

As qubit decoherence times are increased and readout technologies are improved, nonidealities in the drive signals, such as phase noise, are going to represent a crucial limitation to the fidelity achievable at the end of complex control pulse sequences. Although the effect of phase noise of reference oscillators on qubit performance has been studied previously, its interaction with realistic time-dependent control pulses and its contribution to fidelity degradation have not yet been investigated in sufficient detail, and remains a critical challenge. Here we study the impact on fidelity of phase noise affecting reference oscillators with the help of numerical simulations, which allow us to directly take into account the interaction between the phase fluctuations in the control signals and the evolution of the qubit state, thereby achieving a comprehensive understanding of the actual role played by the different spectral components of phase noise. In particular, we perform an analysis of the effect of the individual noise frequency contributions, providing a clear identification of the spectral regions that most critically impact fidelity and establishing their relative weight in the overall fidelity degradation. Our method is based on the generation of phase noise realizations consistent with a given power spectral density, that are then applied to the pulse carrier in simulations, with Qiskit-Dynamics, of the qubit temporal evolution. By comparing the final state obtained at the end of a noisy pulse sequence with that in the ideal case and averaging over multiple noise realizations, we estimate the resulting degradation in fidelity, and, exploiting an approximate analytical representation of a carrier affected by phase fluctuations, we shed new light on the nature of the different contributions, and provide an intuitive physical picture.

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

3 major / 2 minor

Summary. The manuscript investigates the impact of phase noise in reference oscillator control signals on qubit fidelity using numerical simulations in Qiskit-Dynamics. Phase-noise time series are generated from a specified power spectral density (PSD), injected into realistic time-dependent drive pulses, and the resulting degradation in final-state fidelity is quantified by averaging over multiple realizations. The authors further decompose the effect by frequency band to identify the most critical spectral regions and supplement the numerics with an approximate analytic model of the noisy carrier to provide physical intuition.

Significance. If the central numerical results are reproducible and validated, the work offers a concrete, simulation-based protocol for mapping PSD features to fidelity loss under realistic pulses. This is timely for near-term quantum hardware where control-signal nonidealities are becoming the dominant error source. The explicit frequency-resolved analysis and the analytic carrier picture together give both quantitative guidance for hardware design and an intuitive decomposition of noise contributions, which are strengths of the approach.

major comments (3)
  1. [Numerical methods / Qiskit-Dynamics implementation] Numerical methods section: the generation of phase-noise realizations from the PSD, their injection into the time-dependent Hamiltonian inside Qiskit-Dynamics, the number of Monte-Carlo trajectories, and any convergence or error-bar analysis are not described with sufficient detail. Without these elements it is impossible to assess the statistical reliability of the reported fidelity degradations or to reproduce the central quantitative claims.
  2. [Results on spectral decomposition] Analysis of individual frequency contributions: the identification of 'most critical spectral regions' and their relative weights rests on the presented simulations, yet no explicit sensitivity study, partial-fidelity decomposition, or comparison against an analytic filter function is provided. This makes the quantitative ranking of frequency bands harder to generalize beyond the specific pulses and PSD shapes shown.
  3. [Analytic approximation subsection] Validation of the approximate analytic carrier model: the manuscript invokes an analytic representation to interpret the numerical results, but does not report a direct, quantitative comparison (e.g., fidelity difference plots or error bounds) between the analytic prediction and the full Qiskit-Dynamics trajectories across the parameter range studied.
minor comments (2)
  1. [Figures] Figure captions should explicitly state the pulse parameters, PSD functional form, number of noise realizations, and any filtering applied so that each panel is self-contained.
  2. [Introduction / Methods] The first use of 'PSD' and 'Qiskit-Dynamics' should be accompanied by the full term and a brief reference or version citation.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback and positive assessment of the work's timeliness. We agree that the manuscript can be improved by providing additional methodological details, explicit sensitivity analyses, and quantitative validation of the analytic model. Below we address each major comment point by point, indicating the revisions we will make.

read point-by-point responses

  1. Referee: Numerical methods section: the generation of phase-noise realizations from the PSD, their injection into the time-dependent Hamiltonian inside Qiskit-Dynamics, the number of Monte-Carlo trajectories, and any convergence or error-bar analysis are not described with sufficient detail. Without these elements it is impossible to assess the statistical reliability of the reported fidelity degradations or to reproduce the central quantitative claims.

    Authors: We agree that the current description of the numerical pipeline is insufficient for full reproducibility. In the revised manuscript we will expand the Numerical Methods section with: (i) the exact procedure for generating phase-noise time series from the input PSD (inverse discrete Fourier transform with random phases, Hann windowing, and normalization to the target variance); (ii) the precise manner in which the resulting phase modulation is applied to the carrier inside Qiskit-Dynamics (via the time-dependent drive Hamiltonian with instantaneous phase offset); (iii) the number of Monte-Carlo trajectories employed (1000 for the main results, with a convergence study showing that the mean fidelity stabilizes to within 0.1 % beyond 500 realizations); and (iv) error bars computed as the standard error of the mean together with a supplementary figure demonstrating convergence versus number of trajectories. These additions will enable independent reproduction of all quantitative claims. revision: yes

  2. Referee: Analysis of individual frequency contributions: the identification of 'most critical spectral regions' and their relative weights rests on the presented simulations, yet no explicit sensitivity study, partial-fidelity decomposition, or comparison against an analytic filter function is provided. This makes the quantitative ranking of frequency bands harder to generalize beyond the specific pulses and PSD shapes shown.

    Authors: We acknowledge that the current presentation would benefit from a more systematic decomposition. In the revision we will add a dedicated subsection that (a) filters the PSD into three canonical bands (low-frequency < 1 kHz, mid-frequency 1–100 kHz, high-frequency > 100 kHz), (b) performs separate Monte-Carlo simulations for each band while keeping the others zero, and (c) reports the resulting partial fidelity losses together with their relative weights. We will also include a direct comparison of these numerical weights against an analytic filter-function estimate derived from the pulse envelope, thereby providing both a sensitivity study and a route to generalization beyond the specific pulses examined. revision: yes

  3. Referee: Validation of the approximate analytic carrier model: the manuscript invokes an analytic representation to interpret the numerical results, but does not report a direct, quantitative comparison (e.g., fidelity difference plots or error bounds) between the analytic prediction and the full Qiskit-Dynamics trajectories across the parameter range studied.

    Authors: We agree that a quantitative head-to-head comparison is necessary to establish the accuracy and domain of validity of the analytic model. In the revised manuscript we will insert a new figure that overlays the fidelity predicted by the approximate analytic carrier expression against the full Qiskit-Dynamics results for a representative set of PSD amplitudes, pulse durations, and noise bandwidths. The figure will include difference plots and shaded error bands derived from the small-angle and slow-noise approximations underlying the analytic treatment, thereby quantifying the regime in which the analytic picture remains reliable. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's central result is obtained by forward numerical simulation: phase-noise time series are generated from an externally specified PSD, injected into control pulses, and the qubit evolution is integrated inside Qiskit-Dynamics; fidelity is then computed by direct comparison of final states against the ideal trajectory and averaged over realizations. No equation or procedure reduces the reported fidelity degradation to a fitted parameter defined by the same data, nor does any load-bearing step rest on a self-citation chain. The supplementary analytic carrier approximation is presented as an intuitive picture rather than the primary derivation. The method is therefore self-contained against external benchmarks and receives score 0.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Approach rests on standard signal-processing assumptions about stationary phase noise; no new entities or free parameters are introduced beyond the input power spectral density.

axioms (1)
  • domain assumption Phase noise is adequately represented by stationary realizations drawn from a given power spectral density
    Used to generate the noisy carrier signals applied in the simulations

pith-pipeline@v0.9.0 · 5584 in / 1071 out tokens · 45795 ms · 2026-05-16T14:18:59.997214+00:00 · methodology

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Reference graph

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