Sparse Non-Markovian Noise Modeling of Transmon-Based Multi-Qubit Operations

Gregory Quiroz; Kevin Schultz; Leigh Norris; Omar Shehab; Yasuo Oda

REVIEW 3 major objections 6 minor 2 cited by

Sparse Non-Markovian Noise Modeling of Transmon-Based Multi-Qubit Operations

T0 review · 3 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A sparse noise model built from a Lindblad master equation with only ten parameters per qubit predicts IBM transmon hardware dynamics to within 0.5% relative error, a sevenfold improvement over the platform's default noise model.

desk verdict Solid effective noise modeling paper with a strong out-of-sample core and an over-claimed VQE headline that needs error bars and repetition. read the letter →

arxiv 2412.16092 v1 pith:3QMJNVIA submitted 2024-12-20 quant-ph

Yasuo Oda , Kevin Schultz , Leigh Norris , Omar Shehab , Gregory Quiroz This is my paper · ORCID

classification quant-ph

keywords non-MarkoviannoisemodeltransmonqubitsLindbladmasterequationquantumspectroscopycross-resonancegatetwo-levelsystemsvariationaleigensolver

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 claims that a physically motivated noise model with only ten parameters per qubit and three per qubit pair can capture and predict both Markovian and non-Markovian noise in IBM transmon devices. The model is built from a Lindblad master equation extended with classical stochastic dephasing and control noise, plus quantum degrees of freedom for two-level systems and spectator-qubit crosstalk. From seven short characterization experiments, the learned parameters predict randomized benchmarking error rates, state-dependent dynamical decoupling decays, and a variational quantum eigensolver dissociation curve for H2. As a hardware proxy the model predicts expectation values within a relative error of 0.5%, a sevenfold improvement over the platform's default noise model. If correct, this offers a practical route to hardware-accurate circuit simulation without expensive tomographic characterization.

What carries the argument

The central object is the modified Lindblad master equation $$\dot{\rho}(t)=-i[H(t),\rho]+\sum_k \gamma_k (L_k \rho L_k^\dagger - \frac{1}{2}\{L_k^\dagger L_k,\rho\})$$ with Hamiltonian $H = H_C + H_N + H_{XT} + H_{TLS}$, where $H_C$ is single- and two-qubit control, $H_N(t)=\sum_j [\epsilon_j(t)H_C^{(j)}(t)+\beta_j(t)\sigma_z^{(j)}/2]$ is Gaussian wide-sense-stationary stochastic dephasing and control noise, $H_{XT}$ is ZZ crosstalk to spectator qubits, and $H_{TLS}$ couples each data qubit to one or more two-level systems initialized in the $|+\rangle$ state via a static ZZ coupling. The dissipator contains generalized amplitude damping, phase damping, and a bit-flip channel active during x-rotations. The argument is carried by (i) analytical Bloch-vector solutions of the LME for each characterization circuit, (ii) the filter-function formalism with fixed-total-time pulse sequences (FTTPS) to reconstruct the dephasing and control power spectral densities $S_\beta(\omega)$ and $S_\epsilon(\omega)$, and robust FTTPS (R-FTTPS) to isolate control noise, and (iii) a channel-reduced operator-sum representation for scalability.

What would settle it

Run the H2 VQE circuit on a qubit pair whose FTTPS shows a high-frequency resonance peak (as in the paper's Appendix G) and check whether the model still predicts the experimental expectation values within 0.5% relative error; a failure would show the static-ZZ, single-TLS ansatz is incomplete. A second direct test: calibrate on one qubit pair and apply the model to a different pair on the same device; if the 0.5% accuracy does not hold, the parameters are not context-stable.

Watch

Extended reading notes

Core claim

The authors establish that a hybrid noise model—local Markovian dissipation (generalized amplitude damping, phase damping, and a control bit-flip channel) plus extended Markovian degrees of freedom (ZZ crosstalk to spectator qubits and ZZ-coupled two-level systems initialized in the |+> state) plus Gaussian wide-sense-stationary stochastic dephasing and control noise—captures and predicts a wide range of single- and two-qubit behaviors on IBM transmon devices. The model's parameters are learned from seven noise-amplification experiments (T1, T2 Hahn echo, Ramsey, SPAM, fixed-total-time pulse sequences, finite-pulse-width sequences, crosstalk, and cross-resonance gates). The learned model predicts error-per-Clifford rates in randomized benchmarking, state-dependent decays under multi-qubit XY4 dynamical decoupling, and the H2 dissociation curve from a variational quantum eigensolver. The headline quantitative claim is that, as a training proxy for hardware, the model predicts expectation values within a relative error of 0.5%, a 7x improvement over the platform's default noise model; replacing the correlated-dephasing term with a Markovian phase-damping channel degrades the accuracy to about 3.8%, showing the non-Markovian terms carry the improvement.

Load-bearing premise

The model assumes every relevant noise process on the studied devices belongs to one parameterized family—local damping and bit-flip, static detuning, ZZ crosstalk, two-level systems with static coupling, and Gaussian wide-sense-stationary dephasing and control noise—and that parameters learned from short calibration circuits transfer to arbitrary circuits for the duration of an experiment.

Editorial extensions

If this is right

For the 64% of qubits that are purely Markovian, the model provides a full error description from a handful of short experiments, predicting randomized benchmarking error rates without running RB.
For qubits with correlated dephasing (26%), the model predicts how much fidelity improves with dynamical decoupling pulse number, identifying which qubits will benefit most from DD.
The VQE result implies variational algorithms can be trained offline against a faithful noise model, saving quantum hardware time and enabling noise-aware ansatz selection before submitting circuits.
The operator-sum channel reduction extends the model beyond a few qubits, so hardware-accurate simulation may scale to larger devices by composing per-qubit and per-pair channels.
Two-qubit ECR gates require no two-qubit dissipative terms; single-qubit dissipation plus coherent Hamiltonian corrections suffice, simplifying future multi-qubit characterization.

Reading between the lines

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

If the predictive accuracy generalizes to larger systems, it suggests a physics-informed sparse ansatz can outperform generic dense noise models in the few-qubit regime, because the dominant error mechanisms in fixed-frequency transmons are already captured by this small parameter set.
The framework—Markovian dissipators plus classical stochastic noise plus a few quantum TLS/spectator degrees of freedom—should transfer to other qubit modalities where dephasing and TLS coupling dominate, though the paper only demonstrates it on IBM fixed-frequency transmons.
The Gaussian wide-sense-stationary assumption could be tested by measuring higher-order noise cumulants (e.g., via spin-locking or higher-order QNS); if TLS telegraph switching contributes appreciably, the model would need non-Gaussian extensions.
A practical test of the method's value: calibrate the model on one device generation and apply it to another; if characterization transfer fails, the model's usefulness as a universal hardware proxy is limited.

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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

Dear colleague,

Here is my read on arXiv:2412.16092. The paper proposes a sparse Lindblad noise model for transmon qubits, extended with TLSs, crosstalk, and stochastic dephasing/control noise. The main thing to know: the model itself is a sensible integration of known ingredients, and the out-of-sample validation is mostly genuine, but the headline VQE claim (0.5% relative error, 7x improvement) is the softest part of the paper and should not be taken at face value.

What is actually new is the specific 10+3 parameter model, the R-FTTPS sequence for isolating correlated control noise, and the systematic characterization across 39 qubits on seven IBM devices. The paper is unusually thorough analytically: the Bloch-vector solutions for all the characterization circuits are derived in the appendices and validated against numerical simulation. The RB prediction is a true out-of-sample test, and the CPMG predictions use PSDs reconstructed from a different experiment class (FTTPS), which is the right experimental logic. The multi-qubit DD results are also genuinely predictive.

The soft spots. The VQE result is a single experimental point at one bond length, with no repeated runs, no error bars, and no sensitivity analysis. The comparison to the IBM default model is also confounded by calibration age: the default model used properties collected roughly 9 hours before the experiment, while the proposed LME model was freshly characterized. The paper's own stability data (Appendix I) shows fitted parameters drifting over one hour, so the 0.5% number is a favorable snapshot rather than a demonstrated reproducible property. The FTTPS PSD reconstruction loop in Fig. 5(a) is partly circular, but the subsequent CPMG prediction is out-of-sample, so this is minor. The model's completeness (no unmodeled context-dependent noise) is a load-bearing assumption, but that is the standard caveat for effective noise models.

Overall the central argument holds up: this is a useful engineering-oriented framework for predictive noise modeling. The VQE claim needs more data and a fairer baseline before it can be the paper's centerpiece.

This paper deserves a serious referee. The referee should focus on the VQE section, ask for repeated runs and error bars, and for a sensitivity analysis on the learned parameters. I would not desk-reject it.

Best,

[You]

Referee Report

3 major / 6 minor

Summary. The paper introduces a sparse, hybrid noise model for IBMQ transmon devices that combines Lindblad master equation terms (local GAD, phase damping, bit-flip control noise) with extended-Markovian degrees of freedom (TLSs, spectator crosstalk) and classical stochastic noise (dephasing and control PSDs). The model is parameterized by about ten parameters per qubit and three per qubit pair, learned from seven characterization experiments (SPAM, T1, T2, Ramsey, FTTPS, FPW, XT, CR). The authors validate the model on multiple IBMQ devices, showing agreement for Markovian qubits, TLS-induced Ramsey beats, crosstalk, correlated dephasing and control noise, and ECR gates. They then use the model to predict randomized benchmarking decay, multi-qubit dynamical decoupling curves, and a VQE dissociation curve for H2, claiming a 0.5% relative error in energy, a 7x improvement over the default IBM noise model.

Significance. If the results hold, the paper makes a useful contribution: it demonstrates that a physically motivated, low-parameter noise model can predict out-of-sample hardware dynamics across several experiment classes. The analytical Bloch-vector solutions in the appendices are checked against LME simulations (Fig. 10), the RB prediction in Fig. 2(e) is a genuine out-of-sample test, and the CPMG predictions in Figs. 5(c,d) use PSDs extracted from FTTPS, a different experiment class, which is a strong validation design. The multi-qubit DD and VQE demonstrations extend the model beyond single-qubit benchmarking. The reproducibility of the characterization protocol and the explicit parameter sparsity are also strengths. However, the headline quantitative claim (0.5% VQE error) is supported by a single unrepeated data point, and the paper's own stability data indicate parameter drift, so the central predictive claim is not yet robust as stated.

major comments (3)

[Sec. V B, Fig. 9] The headline claim of 0.5% relative error and 7x improvement over the default IBM model rests on a single experimental point at Ropt = 0.75 Å, with no repeated runs, no error bars, and no sensitivity analysis. In addition, the comparison is confounded by calibration age: the default IBM model uses backend properties collected roughly 9 hours before the experiment, while the proposed LME model was freshly characterized. Appendix I (Fig. 17) shows that fitted parameters drift within a one-hour window on a single qubit (e.g., TLS coupling xi varies by ~0.2 MHz; q, beta, and nu show visible trends). Thus, the assumption that characterization-time parameters transfer to the later VQE run is not established at the claimed 0.5% precision. I request either repeated VQE runs with statistics and error bars, a time-matched default model comparison, or a quantitative sensitivity analysis showing that parameter drift does not materially change the reported error.
[Sec. IV C, Fig. 5(a)] The PSD reconstruction for qubit 4 of ibm hanoi is obtained from FTTPS data and then used to 'predict' the same FTTPS data in the main panel of Fig. 5(a). This is an internal consistency check rather than an out-of-sample validation. The genuinely out-of-sample validation is the CPMG prediction in Figs. 5(c,d), which uses PSDs from FTTPS on different circuits. The text should clearly separate these two roles and avoid implying that Fig. 5(a) provides predictive evidence; currently the narrative could mislead a reader into thinking the FTTPS prediction is independent.
[Sec. II C, Eq. (8) and Appendix H] The model assumes every TLS is initialized in the |+> state at the start of each experiment and couples only via static ZZ interactions. This is a load-bearing and ad hoc assumption: any other initial TLS state would change the Ramsey and DD predictions. The paper provides no direct experimental test of this initial condition, and Appendix H shows that the distinction between TLS and crosstalk/detuning frequencies is resolved using a specific modeling assumption (beta = -J). I recommend either a direct test (e.g., varying TLS preparation or checking consistency across different experiments) or a sensitivity analysis showing that plausible deviations from |+> initialization do not affect the main predictions.

minor comments (6)

[Appendix D] There is a typographical error: 'Krauss operators' should be 'Kraus operators'.
[Sec. IV C 1, Fig. 5(c,d)] The text says 'For qubit 0 [see Fig. 5(d)]', but Fig. 5(d) corresponds to qubit 2; the reference should likely be to Fig. 5(c) or to qubit 2.
[Sec. V B and Fig. 9] The relative error inset of Fig. 9 would benefit from error bars or shaded confidence intervals, especially since the experimental energies are estimated from 10,000 shots. The current single-point claim is difficult to assess without uncertainty quantification.
[Sec. IV D] The statement 'although more experimental data may be needed in order to refine the model' is a limitation that should be made more prominent in the main text, as it qualifies the ECR characterization results.
[Appendix A 4 e, Eq. (A21)] The notation in Eq. (A21) for the k=0 case ('cos(2 beta tau)') seems inconsistent with the earlier Ramsey expression in Eq. (15), where the argument is (beta tau) not (2 beta tau). Please clarify the prefactors.
[Sec. II D] The definition of the PSD as S_f(omega) = integral_0^tau C_f(t) e^{-i omega t} dt uses a finite-time window, while later uses infinite limits; the windowing conventions should be stated consistently, perhaps with a note about the large-tau limit.

Circularity Check

1 steps flagged · score 2.0 of 10

No load-bearing circularity: the headline RB, CPMG, DD, and VQE predictions are out-of-sample. The only circularity is a minor in-sample FTTPS reconstruction loop.

fitted input called prediction [Sec. IV C 1, Fig. 5(a), paragraph beginning "The inset of Fig. 5(a) presents the detected dephasing PSD..."]
"The inset of Fig. 5(a) presents the detected dephasing PSD obtained from QNS by fitting an auto-regressive moving average (ARMA) model, following the method introduced in Ref. [58]. To validate the noise reconstruction protocol, the spectrum is used to obtain predicted values of FTTPS via numerical integration of the overlap integral. This is shown in the main panel as solid lines, displaying good agreement between the experimental and predicted FTTPS."

The PSD S_beta(omega) is estimated from the same FTTPS experimental survival probabilities that are then 'predicted' using that PSD. Agreement therefore only confirms that the parametrized spectrum can reproduce the data it was fitted to; it is a consistency check of the reconstruction/inversion, not an out-of-sample model test. The paper calls the resulting curves 'predicted FTTPS,' but the inputs (FTTPS data) and outputs (FTTPS predictions) coincide by construction. This loop is limited to the reconstruction validation in Fig. 5(a) and does not affect the genuine out-of-sample applications (RB, CPMG, multi-qubit DD, VQE), which use experimental data not used in fitting those parameters. Self-citations such as Ref.

full rationale

The paper's central derivation chain is not circular. Single-qubit noise parameters are learned from the characterization circuits (T1, T2, Ramsey, FTTPS/FPW, SPAM) and then used to predict randomized benchmarking decay rates, CPMG curves, multi-qubit dynamical decoupling dynamics, and VQE energies without refitting to those experiments. These are genuine out-of-sample tests. The two-qubit ECR parameters are fitted to CR experiments and then used to simulate the same CR data, but the paper presents this as fitting/agreement rather than as a prediction, so it is not a circularity claim. The VQE comparison, while statistically thin (one point, no error bars, stale default IBM model), is not circular because the hardware energies are not used to adjust the model parameters. The only step that reduces by construction is the FTTPS PSD validation in Fig. 5(a): the PSD is extracted from FTTPS data and then used to 'predict' the same FTTPS data, which tests self-consistency only. This is a minor internal consistency loop and is not load-bearing for the paper's main predictive claims. Overall circularity score is therefore low: 2.

Assumptions & free parameters 13 free parameters · 7 assumptions · 1 invented entities

The central claim rests on a fixed family of noise processes (local dissipation, static detuning, ZZ crosstalk, static-ZZ TLSs, Gaussian stationary stochastic dephasing and control noise) and on the transfer of parameters from characterization circuits to arbitrary circuits. The model includes 13+ fitted parameters per qubit pair, several of which are only demonstrated on selected qubits. The absence of released data and error bars increases the epistemic burden on the reader.

free parameters (13)

Single-qubit relaxation rate gamma_j = 0.0107 MHz (qubit 8, ibm_algiers)
Fit to T1 survival decay using Eq. (13).
Thermal excited-state population q_j = 0.86 (qubit 8, ibm_algiers)
Fit to T1 asymptotic population via Eq. (13).
Pure dephasing rate lambda_j = 0 MHz (qubit 8, ibm_algiers); nonzero on other qubits
Fit to Hahn echo decay via Eq. (14).
Static detuning beta_j = 0.208 MHz (qubit 8, ibm_algiers)
Fit to Ramsey and FTTPS k=0 oscillation frequency through Eqs. (15) and (A21).
Coherent control error epsilon_j = 0.121% (qubit 8, ibm_algiers)
Fit to FTTPS oscillation envelope cos(2*pi*k*epsilon) in Eq. (16).
Incoherent control error rate nu_j = 0.005 MHz (qubit 8, ibm_algiers)
Fit to finite-pulse-width decay in Eq. (17).
Measurement error probability s_j = 1.2% (qubit 8, ibm_algiers)
Fit to SPAM circuit, v(delta t) approx s.
TLS coupling strength xi_j = 0.01 to 0.32 MHz on ibm_algiers examples
Fit to Ramsey two-frequency beat using Eq. (15).
ZZ crosstalk coupling J_ij = Varies; up to 0.5 MHz in ECR example
Fit to joint Hahn echo via Eq. (18) and to CR data via Eq. (19).
ECR over-rotation epsilon_zx = 0.14 (qubits 0-1, ibm_lagos)
Fit to CR expectation-value oscillations via Eq. (19).
ECR offset zeta = 0.01 MHz (qubits 0-1, ibm_lagos)
Fit to asymmetry between control states in CR data via Eq. (19).
Dephasing PSD S_beta(omega), modeled as DC peak plus white floor or Lorentzian S0/[1+(omega/omega_max)^alpha] = e.g., alpha=2 (qubit 0, ibmq_belem), alpha=0 (qubit 2, ibmq_belem)
Fit to FTTPS decay rates via ARMA/QNS (Sec. IV C 1); used to predict CPMG curves.
Control noise PSD S_epsilon(omega), modeled as 1/f-like = Amplitude not stated numerically
Chosen to approximately reproduce FTTPS vs R-FTTPS contrast in Fig. 6; not independently characterized.

assumptions (7)

domain assumption Noise processes are Gaussian and wide-sense stationary, fully specified by mean and two-point correlation (Sec. II D).
Justifies PSD and filter-function description; non-Gaussian or non-stationary noise would break the model.
ad hoc to paper TLSs are initialized in |+> at the start of every experiment and couple to data qubits only through static ZZ interactions (Sec. II C, Eq. 8).
This choice reproduces Ramsey beats, but the paper provides no independent measurement of TLS state or coupling form.
domain assumption First-order Magnus expansion and weak-noise inequality ||g|| << ||G0|| are valid for all gates and pulses used in characterization circuits (Appendix A 3).
Analytic fit formulas rest on this perturbative truncation; the paper notes a case (J approx 0.5 MHz) where the ECR model breaks down.
domain assumption All SPAM error is modeled as a bit-flip measurement channel with rate s_j; state preparation is ideal (Sec. II B 2).
Standard simplification; if preparation error is significant, the fitted parameters are biased.
domain assumption No two-qubit dissipative terms, spectator-qubit noise, or TLS dissipation are required (Sec. II and Sec. IV D).
Authors infer this from fits, but it is an a priori completeness assumption; unmodeled correlated dissipative processes could violate predictions on new circuits.
standard math The Bloch-vector equations and LME solutions use standard open-quantum-system background (Lindblad form, GAD, phase damping) from Refs. [49-51].
Unproved background, standard in the field.
standard math Filter-function formalism and QNS inversion from Refs. [57, 84, 90-94] are valid for the circuits used.
Used for PSD reconstruction in FTTPS and CPMG; not re-derived in this paper.

invented entities (1)

Per-qubit two-level-system (TLS) effective degree of freedom independent evidence
purpose: Explains two-frequency Ramsey oscillations and DD dynamics by coupling to the data qubit via ZZ interaction with strength xi_j.
The TLS is not a new physical entity, but the paper relies on it as a model ingredient. The falsifiable handle is the beat frequency in Ramsey data (Fig. 3) and its suppression in DD experiments (Figs. 8 and 16), so there is independent evidence within the paper.

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Cite this review

Pith. "Pith review of Sparse Non-Markovian Noise Modeling of Transmon-Based Multi-Qubit Operations." pith.science (2026). https://pith.science/paper/3QMJNVIA

@misc{pith2026241216092,
  author       = {Pith},
  title        = {Pith review of: Sparse Non-Markovian Noise Modeling of Transmon-Based Multi-Qubit Operations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3QMJNVIA}},
  note         = {Machine review of arXiv:2412.16092}
}

abstract

The influence of noise on quantum dynamics is one of the main factors preventing current quantum processors from performing accurate quantum computations. Sufficient noise characterization and modeling can provide key insights into the effect of noise on quantum algorithms and inform the design of targeted error protection protocols. However, constructing effective noise models that are sparse in model parameters, yet predictive can be challenging. In this work, we present an approach for effective noise modeling of multi-qubit operations on transmon-based devices. Through a comprehensive characterization of seven devices offered by the IBM Quantum Platform, we show that the model can capture and predict a wide range of single- and two-qubit behaviors, including non-Markovian effects resulting from spatio-temporally correlated noise sources. The model's predictive power is further highlighted through multi-qubit dynamical decoupling demonstrations and an implementation of the variational quantum eigensolver. As a training proxy for the hardware, we show that the model can predict expectation values within a relative error of 0.5%; this is a 7$\times$ improvement over default hardware noise models. Through these demonstrations, we highlight key error sources in superconducting qubits and illustrate the utility of reduced noise models for predicting hardware dynamics.

Figures

Figures reproduced from arXiv: 2412.16092 by the authors.

**Figure 1.** Noise characterization protocol used to learn the model parameters. (A) The state is assumed to be perfectly initialized in the [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗

**Figure 2.** (a-d) Experimental implementation of the noise charac [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 4.** (a) Two-qubit crosstalk experiment (XT) results for all qubit [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

Figures from the paper (13 more)

**Figure 5.** Figure 5: (a) FTTPS experiment results (circles) and predictions [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

**Figure 6.** Figure 6: (a) FTTPS and R-FTTPS circuits, where the explicit dis [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]

**Figure 7.** Figure 7: Comparison between experiment and the LME model [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]

**Figure 8.** Figure 8: (a) Multi-qubit DD experiment schematics. The main (spec [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]

**Figure 9.** Figure 9: (a) Circuit implementing the VQE algorithm, from which [PITH_FULL_IMAGE:figures/full_fig_p016_9.png]

**Figure 10.** Figure 10: Comparison between FTTPS simulations (dots) and ana [PITH_FULL_IMAGE:figures/full_fig_p021_10.png]

**Figure 11.** Figure 11: FTTPS filter functions: (a) dephasing and (b) control. [PITH_FULL_IMAGE:figures/full_fig_p024_11.png]

**Figure 12.** Figure 12: Noisy simulation of FPW circuits for constant (blue) and [PITH_FULL_IMAGE:figures/full_fig_p025_12.png]

**Figure 13.** Figure 13: Experimental results (circles) obtained from running an [PITH_FULL_IMAGE:figures/full_fig_p026_13.png]

**Figure 16.** Figure 16: Ramsey experiments on qubits 0 and 3 of ibm cairo, where spectator qubits are left to evolve freely (dark-blue circles; FE) and decoupled via XY4 (light-blue triangles; DD). Note that XY4 is applied exclusively on spectator qubits. Solid lines correspond to multiqub…

**Figure 15.** Figure 15: FTTPS experiment results (circles) and simulation (solid [PITH_FULL_IMAGE:figures/full_fig_p027_15.png]

**Figure 17.** Figure 17: Results (dots) obtained from characterization experiments [PITH_FULL_IMAGE:figures/full_fig_p028_17.png]

**Figure 18.** Figure 18: Device connectivity and coherence times properties. We [PITH_FULL_IMAGE:figures/full_fig_p029_18.png]

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Reference graph

Works this paper leans on

141 extracted references · 52 canonical work pages · cited by 2 Pith papers

[1]

For simplicity, we suppress the qubit index j

Single-Qubits In the Markovian limit, the dynamical evolution under the above mentioned processes can be studied directly using the LME. For simplicity, we suppress the qubit index j. We as- sume constant x-control with duration δt that executes a ro- tation θ, i.e., Ω(t) = θ/δt. Thus, the control Hamiltonian [Eq. (3)] during the implementation of a gate ...
[2]

Following the steps outlined in the previous section, we set θ = ν = 0 since no control noise is present in the absence of qubit drive

Identity Gates In the case of identity operations, the LME can be solved exactly. Following the steps outlined in the previous section, we set θ = ν = 0 since no control noise is present in the absence of qubit drive. Defining for notational convenienceα= γ/2+λ, we write the LME solution in Bloch vector form ⃗v(t0+ τ)= ⎛ ⎜ ⎝ e−ατ cos(βτ) −e−ατ sin(βτ) 0 e...
[3]

We follow the perturbative approach of the FFF [91]

Perturbative Solution for X control In this section, we provide a solution to the LME in the pres- ence of X control in the weak noise regime. We follow the perturbative approach of the FFF [91]. For a non-zero rotation, such as those corresponding to X, √ X gates, the generator G can be written as a perturbation from the noiseless generator G0. Writing t...
[4]

Here, we show how it can be used to compute the results shown in Eqs

Prediction of Characterization Circuits The results from the above sections can be used to com- pute predictions for the characterization experiments. Here, we show how it can be used to compute the results shown in Eqs. (13−17). Denoting by ⃗v(τ) the Bloch vector state at the end of a given circuit, the effect of SPAM errors on the Bloch vector is to tak...
[5]

Here, we provide an overview for the FFF focusing on a single qubit governed by the noise Hamiltonian HN,1(t) [Eq

Filter Function Formalism The FFF takes a frequency domain perspective on the ef- fect of spatio-correlated noise on a quantum system. Here, we provide an overview for the FFF focusing on a single qubit governed by the noise Hamiltonian HN,1(t) [Eq. (10)] and control Hamiltonian HC(t) given by Eq. (3), where Θ(t) = ∫ t 0 Ω(s) ds. In the toggling frame, th...
[6]

The advantage of using FTTPS for QNS lies in the large spectral concentration of their FFs [58]

Dephasing QNS with FTTPS In order to extract information about a device’s dephasing noise PSD, we leverage the FTTPS. The advantage of using FTTPS for QNS lies in the large spectral concentration of their FFs [58]. This feature results in a favorable condition number in the FF matrix and thus, reduces the chance of encountering an ill-posed inversion prob...
[7]

Imperfect control can manifest via fluctuating fields in the control lines, and can be stochastic or coherent

FTTPS in the Presence of Stochastic Control Noise Another type of correlated noise was observed via FTTPS: correlated control noise. Imperfect control can manifest via fluctuating fields in the control lines, and can be stochastic or coherent. In the case of stochastic noise, a common approach is to treat the noise fluctuations as white, uncorrelated nois...
[8]

We start with the time-dependent dephasing Hamiltonian given in Eq

Dephasing Noise and Phase Damping Here, we establish a Hamiltonian description of the phase damping quantum channel. We start with the time-dependent dephasing Hamiltonian given in Eq. (10) with ϵ(t) ≡ 0. The noise-averaged state of the system after time τ is E(ρ) = ⟨U(τ)ρU †(T)⟩β = ⟨(1 0 0 e−i ∫ τ 0 β(t)dt)( ρ00 ρ01 ρ10 ρ11 )( 1 0 0 ei ∫ τ 0 β(t)dt)⟩ β =...

Show all 141 references

[9]

weak” by default, while varying one parameter set as “strong

Isotropic Uncorrelated Noise and Depolarization The control noise case discussed in the main text is en- tirely analogous to the dephasing case. Rather, to show- case the versatility of the stochastic Hamiltonian description, we turn to depolarizing noise. In the superoperator...

2024
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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

For simplicity, we suppress the qubit index j

Single-Qubits In the Markovian limit, the dynamical evolution under the above mentioned processes can be studied directly using the LME. For simplicity, we suppress the qubit index j. We as- sume constant x-control with duration δt that executes a ro- tation θ, i.e., Ω(t) = θ/δt. Thus, the control Hamiltonian [Eq. (3)] during the implementation of a gate ...

[2] [2]

Following the steps outlined in the previous section, we set θ = ν = 0 since no control noise is present in the absence of qubit drive

Identity Gates In the case of identity operations, the LME can be solved exactly. Following the steps outlined in the previous section, we set θ = ν = 0 since no control noise is present in the absence of qubit drive. Defining for notational convenienceα= γ/2+λ, we write the LME solution in Bloch vector form ⃗v(t0+ τ)= ⎛ ⎜ ⎝ e−ατ cos(βτ) −e−ατ sin(βτ) 0 e...

[3] [3]

We follow the perturbative approach of the FFF [91]

Perturbative Solution for X control In this section, we provide a solution to the LME in the pres- ence of X control in the weak noise regime. We follow the perturbative approach of the FFF [91]. For a non-zero rotation, such as those corresponding to X, √ X gates, the generator G can be written as a perturbation from the noiseless generator G0. Writing t...

[4] [4]

Here, we show how it can be used to compute the results shown in Eqs

Prediction of Characterization Circuits The results from the above sections can be used to com- pute predictions for the characterization experiments. Here, we show how it can be used to compute the results shown in Eqs. (13−17). Denoting by ⃗v(τ) the Bloch vector state at the end of a given circuit, the effect of SPAM errors on the Bloch vector is to tak...

[5] [5]

Here, we provide an overview for the FFF focusing on a single qubit governed by the noise Hamiltonian HN,1(t) [Eq

Filter Function Formalism The FFF takes a frequency domain perspective on the ef- fect of spatio-correlated noise on a quantum system. Here, we provide an overview for the FFF focusing on a single qubit governed by the noise Hamiltonian HN,1(t) [Eq. (10)] and control Hamiltonian HC(t) given by Eq. (3), where Θ(t) = ∫ t 0 Ω(s) ds. In the toggling frame, th...

[6] [6]

The advantage of using FTTPS for QNS lies in the large spectral concentration of their FFs [58]

Dephasing QNS with FTTPS In order to extract information about a device’s dephasing noise PSD, we leverage the FTTPS. The advantage of using FTTPS for QNS lies in the large spectral concentration of their FFs [58]. This feature results in a favorable condition number in the FF matrix and thus, reduces the chance of encountering an ill-posed inversion prob...

[7] [7]

Imperfect control can manifest via fluctuating fields in the control lines, and can be stochastic or coherent

FTTPS in the Presence of Stochastic Control Noise Another type of correlated noise was observed via FTTPS: correlated control noise. Imperfect control can manifest via fluctuating fields in the control lines, and can be stochastic or coherent. In the case of stochastic noise, a common approach is to treat the noise fluctuations as white, uncorrelated nois...

[8] [8]

We start with the time-dependent dephasing Hamiltonian given in Eq

Dephasing Noise and Phase Damping Here, we establish a Hamiltonian description of the phase damping quantum channel. We start with the time-dependent dephasing Hamiltonian given in Eq. (10) with ϵ(t) ≡ 0. The noise-averaged state of the system after time τ is E(ρ) = ⟨U(τ)ρU †(T)⟩β = ⟨(1 0 0 e−i ∫ τ 0 β(t)dt)( ρ00 ρ01 ρ10 ρ11 )( 1 0 0 ei ∫ τ 0 β(t)dt)⟩ β =...