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arxiv: 2606.21762 · v1 · pith:KNV6EW2Rnew · submitted 2026-06-19 · 🪐 quant-ph

Dynamical Decoupling using Universal Optimal Tracking

Amit Devra , Emanuel Malvetti , Niklas J. Glaser , Abhishek Agarwal , Ivan Rungger , Santana Lujan , Max Werninghaus , Stefan Filipp
show 2 more authors
Leo Van Damme Steffen J. Glaser
This is my paper

Pith reviewed 2026-06-26 13:34 UTC · model grok-4.3

classification 🪐 quant-ph
keywords dynamical decouplingoptimal trackingquantum error suppressionsuperconducting qubitscontrol imperfectionspulse sequencesnoise resilience
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The pith

Universal optimal tracking designs dynamical decoupling sequences that prevent residual error accumulation from control imperfections.

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

The paper introduces a universal optimal tracking method to create dynamical decoupling sequences for error suppression. Standard DD repeats short pulse blocks but control flaws cause residuals to build up over extended idle times. The approach optimizes by checking qubit evolution at fixed waypoints, adjusting to cancel those residuals while keeping the refocusing action intact. It functions without depending on the initial qubit state. Experiments on superconducting qubits confirm reduced error growth for static imperfections, and simulations show retained performance against time-varying noise.

Core claim

By extending tracking to a fully state-independent optimization that monitors the qubit at predefined waypoints, dynamical decoupling sequences can be generated in which residual errors from imperfect pulses do not accumulate, as demonstrated by experiments on a superconducting-qubit platform under static control imperfections and by simulations under time-dependent noise.

What carries the argument

Universal optimal tracking, which monitors qubit evolution at predefined waypoints during optimization to compensate residual errors while preserving regular refocusing.

Load-bearing premise

The optimization process can monitor the qubit's evolution at predefined waypoints to dynamically compensate residual errors while preserving regular refocusing in a fully state-independent setting.

What would settle it

An experiment showing that optimal-tracking DD sequences accumulate errors at the same rate as conventional DD under static control imperfections would falsify the central claim.

Figures

Figures reproduced from arXiv: 2606.21762 by Abhishek Agarwal, Amit Devra, Emanuel Malvetti, Ivan Rungger, Leo Van Damme, Max Werninghaus, Niklas J. Glaser, Santana Lujan, Stefan Filipp, Steffen J. Glaser.

Figure 1
Figure 1. Figure 1: FIG. 1. Comparison of the design principles of two conven [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Effect of three dynamical decoupling sequences on qubit dynamics, shown on the Bloch sphere (top) and as pulse [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Process fidelities of different dynamical decoupling sequences as functions of pulse-amplitude error [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Top: Optimized U-TRACK4 pulse phases for 10 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Simulated fidelity of the three sequences at the end of [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Robustness profile of MLEV64 (top row), XY64 (middle row), and U-TRACK4 (bottom row), as functions of pulse [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Performance comparison of U-TRACK4 and XY4 [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Topology of the 20-qubit IQM Garnet device. The [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
read the original abstract

Dynamical decoupling (DD) is a widely used and resource-efficient technique for error suppression, but conventional DD relies on periodically repeating a short pulse block to refocus the qubit state during idle periods. Imperfections in this block cause residual errors to accumulate, ultimately degrading state recovery over long idle times. Here, we introduce a universal optimal tracking approach that extends the original tracking concept to a fully state-independent setting for designing DD sequences. By monitoring the qubit's evolution at predefined waypoints during optimization, the method dynamically compensates residual errors while preserving regular refocusing. Experimental demonstrations on a superconducting-qubit platform confirm the suppression of error accumulation under static control imperfections, in agreement with numerical predictions. Complementary simulations further show that optimal-tracking-based sequences maintain strong performance under time-dependent noise. These results establish optimal tracking as a practical and hardware-agnostic approach to designing short, robust DD sequences suitable for noisy quantum devices.

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

2 major / 1 minor

Summary. The paper introduces a universal optimal tracking method for designing dynamical decoupling (DD) sequences. It extends tracking concepts to a state-independent setting by monitoring qubit evolution at predefined waypoints during optimization to compensate residual errors from control imperfections while preserving refocusing. Experimental results on a superconducting-qubit platform demonstrate suppression of error accumulation under static imperfections, agreeing with simulations; additional simulations show robustness under time-dependent noise.

Significance. If the optimization produces sequences that are demonstrably universal (state-independent refocusing for arbitrary initial states), the approach offers a practical, hardware-agnostic route to short robust DD sequences. The reported experimental agreement on superconducting qubits and performance under time-dependent noise would strengthen the case for adoption in noisy intermediate-scale devices.

major comments (2)
  1. [Optimization procedure (method section describing cost function and waypoints)] The central claim of a 'fully state-independent setting' and 'universal' DD sequences requires that the optimization cost function enforce refocusing independent of the initial Bloch vector (i.e., total propagator close to identity). The manuscript description does not specify whether the cost explicitly averages fidelity over initial states or imposes a propagator-identity constraint; without this, waypoint monitoring alone may yield state-dependent performance, undermining the universality asserted in the abstract and experimental interpretation.
  2. [Experimental results section] Experimental confirmation is reported for suppression under static imperfections, but the manuscript provides no quantitative details on the prepared/tested states, number of initial states used in validation, or direct comparison of error accumulation across orthogonal initial states. This leaves open whether the observed agreement confirms the state-independent claim or only performance for the specific states employed.
minor comments (1)
  1. [Abstract] The abstract states 'in agreement with numerical predictions' but does not quantify the level of agreement (e.g., fidelity values or error rates); adding a brief numerical comparison would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback and positive assessment of the significance of our work. We address each major comment below, indicating revisions where appropriate to improve clarity and support for our claims.

read point-by-point responses

  1. Referee: [Optimization procedure (method section describing cost function and waypoints)] The central claim of a 'fully state-independent setting' and 'universal' DD sequences requires that the optimization cost function enforce refocusing independent of the initial Bloch vector (i.e., total propagator close to identity). The manuscript description does not specify whether the cost explicitly averages fidelity over initial states or imposes a propagator-identity constraint; without this, waypoint monitoring alone may yield state-dependent performance, undermining the universality asserted in the abstract and experimental interpretation.

    Authors: We appreciate the referee's careful reading and agree that the methods section would benefit from greater precision on this point. The optimization procedure is formulated to minimize the deviation of the composite propagator from the identity operator by evaluating the evolution at the chosen waypoints; this propagator-level constraint is what enforces state independence rather than any averaging over specific initial states. We will revise the manuscript to include an explicit statement and mathematical description of the cost function that makes this constraint clear. revision: yes

  2. Referee: [Experimental results section] Experimental confirmation is reported for suppression under static imperfections, but the manuscript provides no quantitative details on the prepared/tested states, number of initial states used in validation, or direct comparison of error accumulation across orthogonal initial states. This leaves open whether the observed agreement confirms the state-independent claim or only performance for the specific states employed.

    Authors: We agree that additional quantitative information is needed to fully substantiate the state-independent performance. The experiments were performed on multiple initial states spanning different directions on the Bloch sphere, with results compared to simulations for each. In the revised manuscript we will add explicit details on the prepared states, the number of states tested, and direct comparisons of error accumulation across orthogonal initial states. revision: yes

Circularity Check

0 steps flagged

Optimization-based DD design with external experimental validation; derivation self-contained against benchmarks

full rationale

The abstract frames the contribution as an optimization procedure that monitors qubit evolution at waypoints to compensate errors while preserving refocusing, followed by experimental confirmation on superconducting qubits and separate simulations under time-dependent noise. No equations, cost-function definitions, or derivation steps are supplied that reduce the claimed state-independent universality or performance metrics to fitted parameters, self-citations, or input data by construction. The method is presented as extending a prior tracking idea via numerical search with independent hardware validation, satisfying the criteria for a self-contained, non-circular result.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on abstract only; limited visibility into specific implementation details. The method relies on numerical optimization whose convergence and waypoint selection are not detailed.

axioms (1)
  • domain assumption Optimization at waypoints can compensate residual errors without disrupting the refocusing property of DD sequences.
    Invoked in the description of the universal optimal tracking approach.

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Reference graph

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    Optimization of U-TRACK sequences a. Overview The sequence is optimized using a composite pulse made of a concatenation of severalπ-rotations with nu- merically optimized phasesϕ n without inter-pulse delays. Oneπ-rotation of phaseϕ n is assumed to be of the form: P ϵδ n =e −iϕn σz 2 e−i(Ω(1+ϵ) σx 2 +δ σz 2 )Tπ eiϕn σz 2 ,(A1) whereσ x,y,z are the Pauli m...

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    Local optimization via gradient descent Propagation. As explained earlier, the optimization is performed assuming an ensemble of two-level systems of different amplitude errorsϵand detuningδ. For a given pair (ϵ, δ), the evolution operator afterMDD blocks is given by: P ϵδ M NP ϵδ M N−1 · · ·P ϵδ 2N+1 P ϵδ 2N · · ·P ϵδ N+1 P ϵδ N · · ·P ϵδ 1| {z } U ϵδ 1 ...

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    Global optimization via genetic algorithm While the GRAPE algorithm explained in the previous section can efficiently compute the gradient of the total fidelityFwith respect to the pulse phasesϕ n, and hence allows for implementing a gradient-based local optimiza- tion, it turns out that the cost function contains many lo- cal minima that are far from bei...

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    The GRAPE’s gradient computation is performed in two steps

    Highly parallel implementation The optimization algorithm described in the previous two sections lends itself to parallelization. The GRAPE’s gradient computation is performed in two steps. A for- ward and a backward propagation. The same operation must be performed for each value of the amplitude error and detuning (ϵ k, δℓ). Using a GPU, all of these ca...

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    Evolution operator In the methods described in the appendix. A, Eq. (A1) represents the evolution of a two-level system driven by a constantπ-pulse subject to detuning and amplitude errors. In practice, however, all DD sequences in this work are implemented on transmon-based quantum pro- cessors, where native gates use DRAG pulses calibrated to suppress e...

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    Computation of DRAG pulses To compute the coefficientsAandBof the DRAG pulse defined in Eq. (C3), we use thefminuncoptimiza- tion routine inMatlabto minimize the following cost function: JDRAG = 1− 1 4 ⟨0|X † πU(T π)|0⟩+⟨1|X † πU(T π)|1⟩ 2 , (C7) where: •X π =|0⟩ ⟨1|+|1⟩ ⟨0|corresponds to aπrotation about thexaxis in the computational subspace spanned by|...