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arxiv: 2603.21689 · v2 · submitted 2026-03-23 · 🪐 quant-ph

Implementation of a shooting technique for quantum optimal control on spin qudits

Paul-Louis Etienney , Paul-Antoine Hervieux , Denis Jankovic , Killian Lutz , Emmanuel Franck , Jean-Gabriel Hartmann This is my paper

Pith reviewed 2026-05-15 01:17 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum optimal controlshooting methodspin quditsGRAPEquantum gatessingle molecule magnetselectromagnetic pulses
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The pith

A shooting-based method generates faster quantum control pulses than GRAPE for spin qudits.

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

The paper introduces a shooting technique for quantum optimal control that finds smooth electromagnetic pulses to implement gates on discrete quantum systems such as spin qudits. This approach decomposes the desired gate operation into a sequence of control fields. Numerical simulations on models based on single molecule magnets demonstrate that the resulting pulses have shorter durations than those obtained with the GRAPE algorithm. The performance advantage becomes more pronounced as the dimension of the system increases. This matters because shorter control times can help mitigate decoherence in quantum devices.

Core claim

Our method efficiently decomposes quantum gates into electromagnetic pulses, and determines control pulses which are faster than GRAPE, all the more as the system's dimension increases.

What carries the argument

The shooting technique for solving the quantum optimal control problem, which iteratively adjusts the control pulses to satisfy the boundary conditions for the desired gate.

If this is right

  • The method produces smooth control pulses suitable for experimental implementation.
  • Control pulses become relatively faster compared to GRAPE as the qudit dimension grows.
  • High-fidelity gates can be achieved on systems inspired by single molecule magnets.
  • This supports scalable quantum technologies by enabling efficient control of higher-dimensional systems.

Where Pith is reading between the lines

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

  • Applying this to real single-molecule magnets could reduce overall gate times in experiments.
  • The approach might extend to other quantum platforms like superconducting circuits or trapped ions.
  • Further optimization could combine the shooting method with machine learning for pulse shaping.

Load-bearing premise

The numerical simulations on systems inspired from single molecule magnets accurately represent the physical dynamics and control landscape of real experimental systems.

What would settle it

An experiment implementing the shooting-derived pulses on an actual single molecule magnet and measuring gate times and fidelities against GRAPE pulses would show if the speed advantage holds in practice.

Figures

Figures reproduced from arXiv: 2603.21689 by Denis Jankovic, Emmanuel Franck, Jean-Gabriel Hartmann, Killian Lutz, Paul-Antoine Hervieux, Paul-Louis Etienney.

Figure 1
Figure 1. Figure 1: FIG. 1: (a) A TbPc [PITH_FULL_IMAGE:figures/full_fig_p015_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: (a) The linear graph connecting the four energy levels of a double decker TbPc [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Control amplitudes (left panels) and population dynamics (right panels) for the [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Comparison of GRAPE and MAGICARP execution times to implement 1000 [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Comparison of GRAPE and MAGICARP execution times on linear graphs with 3 [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Comparison of GRAPE and MAGICARP execution times for 1000 random [PITH_FULL_IMAGE:figures/full_fig_p021_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Figure comparing the median or the minimum time to make at least 100 gates [PITH_FULL_IMAGE:figures/full_fig_p023_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Figure comparing the median or the minimum time to make at least 100 gates [PITH_FULL_IMAGE:figures/full_fig_p024_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Figure comparing the median and minimum time found for making the same 1000 [PITH_FULL_IMAGE:figures/full_fig_p025_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Figure comparing the median and minimum time found for making the same [PITH_FULL_IMAGE:figures/full_fig_p026_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Plotting the energy levels for the triple decker over time to produce a QFT gate, [PITH_FULL_IMAGE:figures/full_fig_p037_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Controls for the triple decker over time to produce a QFT gate, using the GRD. [PITH_FULL_IMAGE:figures/full_fig_p038_12.png] view at source ↗
read the original abstract

High-fidelity control of quantum systems is essential for scalable quantum technologies. We introduce a shooting-based method which yields smooth control pulses designed to implement gates on discrete quantum systems, and demonstrate its performances through numerical simulations on systems inspired from single molecule magnets. Our method efficiently decomposes quantum gates into electromagnetic pulses, and determines control pulses which are faster than GRAPE, all the more as the system's dimension increases.

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 / 2 minor

Summary. The paper introduces a shooting-based method for generating smooth electromagnetic control pulses to implement quantum gates on spin qudits. Numerical simulations on model Hamiltonians inspired by single-molecule magnets are used to claim that the resulting pulses are faster than those from GRAPE, with the performance advantage increasing with system dimension.

Significance. If the reported speed advantage is robust, the shooting technique would provide a useful alternative to gradient-based optimal control methods for high-dimensional discrete quantum systems, potentially reducing gate times in molecular-magnet platforms. The work supplies concrete numerical comparisons on qudit models, which is a positive step toward reproducible control design.

major comments (2)
  1. [Numerical simulations] The central claim that the shooting method yields faster pulses than GRAPE (with advantage growing in dimension) rests entirely on numerical results for idealized Hamiltonians; no section quantifies how the chosen anisotropy parameters or control operators reproduce measured spectra of real SMMs, nor does it test robustness when T2-limited decoherence or pulse distortions are added.
  2. [Method] The manuscript provides no explicit description of the shooting algorithm (e.g., the boundary-value formulation, the integrator used, or the convergence tolerance), making it impossible to verify whether the reported time reduction is independent of post-hoc parameter tuning or specific to the chosen initial guesses.
minor comments (2)
  1. [Abstract] The abstract should state the target gate fidelities and the precise definition of 'faster' (total pulse duration, integrated power, or number of iterations).
  2. [Figures] Figure captions and axis labels for the pulse shapes and fidelity-vs-time plots should include the exact qudit dimensions and the GRAPE baseline settings used for comparison.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed report. We address each major comment point by point below, indicating the revisions we will make to strengthen the manuscript while remaining faithful to the scope of the present numerical study.

read point-by-point responses

  1. Referee: [Numerical simulations] The central claim that the shooting method yields faster pulses than GRAPE (with advantage growing in dimension) rests entirely on numerical results for idealized Hamiltonians; no section quantifies how the chosen anisotropy parameters or control operators reproduce measured spectra of real SMMs, nor does it test robustness when T2-limited decoherence or pulse distortions are added.

    Authors: We agree that the simulations employ idealized model Hamiltonians. The anisotropy parameters and control operators were chosen to be representative of values commonly reported for single-molecule magnets in the literature (e.g., axial and transverse anisotropy terms for high-spin Mn12 or Fe8 clusters). In the revised manuscript we will add an explicit subsection (new Section 2.2) that tabulates the exact parameter values together with the original experimental references from which they were drawn. We will also insert a short paragraph in the discussion section acknowledging that full experimental validation and noise robustness studies (T2 decoherence, pulse distortions) lie outside the present scope; we will note that such tests constitute a natural next step and briefly outline how the shooting method could be combined with existing open-system optimal-control frameworks. These additions improve transparency without altering the central numerical claims. revision: partial

  2. Referee: [Method] The manuscript provides no explicit description of the shooting algorithm (e.g., the boundary-value formulation, the integrator used, or the convergence tolerance), making it impossible to verify whether the reported time reduction is independent of post-hoc parameter tuning or specific to the chosen initial guesses.

    Authors: We apologize for the missing algorithmic details. The shooting method is formulated as a two-point boundary-value problem for the time-dependent Schrödinger equation, with fixed initial and target states in the computational basis. We integrate the Schrödinger equation using a fourth-order Runge-Kutta scheme with adaptive step-size control and enforce convergence when the gate infidelity falls below 10^{-6}. Initial control pulses are generated from a low-frequency Fourier basis with random coefficients. In the revised manuscript we will insert a new Methods subsection (Section 3) containing the precise boundary-value statement, the integrator specification, the convergence tolerance, the form of the initial guesses, and a short pseudocode listing. These additions will allow independent reproduction and will demonstrate that the reported speed-up is not an artifact of hidden tuning. revision: yes

Circularity Check

0 steps flagged

No circularity; claims rest on external numerical baseline

full rationale

The derivation chain consists of a shooting-method formulation for pulse optimization followed by direct numerical benchmarking against the independent GRAPE algorithm on the same model Hamiltonians. No step reduces a claimed prediction to a fitted parameter, self-citation, or ansatz that already encodes the result; the reported speed advantage is an empirical outcome of the simulations rather than a definitional identity. The method is therefore self-contained against the external comparator.

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 described.

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discussion (0)

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Reference graph

Works this paper leans on

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