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arxiv: 2209.13164 · v3 · submitted 2022-09-27 · 🪐 quant-ph

Quantum state-preparation control in noisy environment via most-likely paths

Wirawat Kokaew , Thiparat Chotibut , Areeya Chantasri This is my paper

Pith reviewed 2026-05-24 11:19 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum controlopen quantum systemsstate preparationdephasing noisestochastic path integralmost-likely pathsqubitfidelity success rate
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The pith

Most-likely noise path controls prepare qubit states with higher success rates than mean-path methods under strong dephasing.

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

The paper develops a control method for preparing quantum states in noisy environments by focusing on the most probable noise trajectories rather than average behavior. It formulates a stochastic path integral whose extremum identifies control functions tied to the noise realization most likely to reach the target state. Applied to a qubit with dephasing, this yields analytical Rabi drive controls. Benchmarking shows these controls improve the probability of successful preparation compared to standard optimizations like GRAPE and CRAB, which maximize average fidelity.

Core claim

By extremizing a stochastic path integral over noise variables, the method derives control functions associated with the most-likely noise that achieves target states, leading to higher fidelity success rates than mean-path controls especially at strong dephasing for qubit state preparation.

What carries the argument

The stochastic path integral for noise variables, whose stationary point supplies the most-likely control functions.

If this is right

  • Most-likely controls achieve higher success rates than GRAPE and CRAB controls, particularly under strong dephasing.
  • Analytical expressions for controlled Rabi drives are obtained for arbitrary target qubit states.
  • A fidelity success rate metric is introduced to evaluate state preparation performance.
  • The approach unravels Lindblad master equation dynamics into hypothetical trajectories for control design.

Where Pith is reading between the lines

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

  • Applying the method to multi-qubit systems or other noise channels could improve gate fidelity probabilities in quantum processors.
  • Numerical optimization of the path integral might extend the technique beyond analytically solvable cases like single-qubit dephasing.
  • Success-rate optimization may be preferable in applications where completing the task reliably on first try matters more than average performance.

Load-bearing premise

The control functions obtained from the path integral extremum remain effective when the actual noise is sampled from the same distribution.

What would settle it

Simulations drawing many random noise realizations and checking whether the fraction of high-fidelity outcomes is larger for most-likely controls than for mean-path controls.

Figures

Figures reproduced from arXiv: 2209.13164 by Areeya Chantasri, Thiparat Chotibut, Wirawat Kokaew.

Figure 1
Figure 1. Figure 1: FIG. 1. The Bloch sphere plots describing our qubit model [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Examples of the MP and MLP Rabi controls, where the initial state is fixed at [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Comparison of the success rates between the MLP [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Numerical results of the multi-pulse controls, comparing the MLP single pulse (magenta) derived analytically in [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Schematic diagrams for deriving the MLP optimal [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Top row: distributions of mean values (total of 100 values) of qubit’s final states in the Bloch sphere components [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The difference of success rates from MLP and MP approaches, using the exact same trajectory data as in Figure [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Further investigation of the characteristics of each [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
read the original abstract

Finding controls for open quantum systems needs to take into account effects from unwanted environmental noise. Since actual realizations or states of the noise are typically unknown, the usual treatment for the quantum system's decoherence dynamics is via the so-called Lindblad master equation, which in essence describes an average evolution (mean path) of the system's state affected by the unknown noise. We here consider an alternative view of a noise-affected open quantum system, where the average dynamics can be unravelled into hypothetical noisy quantum trajectories, and propose a control strategy for the state-preparation problem based on the likelihood of noise occurrence. We formulate a stochastic path integral for noise variables whose extremum yields control functions associated with a most-likely noise to achieve target states. As a proof of concept, we apply our method to a qubit-state preparation under dephasing noise and analytically solve for controlled Rabi drives for arbitrary target states. Since the method is constructed based on the probability of noise, we also introduce a fidelity success rate as a measure of the state preparation. We benchmark against the mean-path approaches, e.g., GRAPE and CRAB controls, using both average fidelity and a success-rate metric. While standard mean-path controls maximize average fidelity, most-likely controls achieve higher success rates, especially at strong dephasing.

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 proposes an alternative to Lindblad-averaged control for open quantum systems by unravelling the dynamics into stochastic trajectories and extremizing a path integral over noise variables to obtain controls tied to the most-likely noise realization that reaches a target state. For a qubit under dephasing noise they derive closed-form Rabi-drive controls for arbitrary targets; they then benchmark these against GRAPE and CRAB using both mean fidelity and a success-rate metric (fraction of trajectories exceeding a fidelity threshold), claiming that most-likely controls outperform mean-path methods on the success-rate metric, especially at strong dephasing.

Significance. If the central numerical claim holds, the work supplies a concrete, analytically solvable example in which optimizing for the mode of the noise distribution yields higher success probability than optimizing the mean trajectory. This distinction between mode-based and mean-based control is potentially useful in settings where the figure of merit is the probability of exceeding a performance threshold rather than the ensemble average. The provision of an exact Rabi solution and the explicit introduction of a success-rate metric are positive features.

major comments (2)
  1. [formulation of the path integral and numerical benchmarks] The transition from the saddle-point condition on the stochastic path integral to an improved ensemble success rate is not automatic. The most-likely noise is the mode of the conditional distribution, while success rate is the integrated measure of all noise realizations that produce fidelity above threshold. At strong dephasing the noise variance widens, so the paper must show explicitly (via the sampled-trajectory benchmarks) that the mode-derived control increases this integrated mass; the abstract asserts the advantage but the derivation of the path-integral extremum alone does not guarantee it.
  2. [numerical benchmarks section] The analytic Rabi-drive solution is presented as parameter-free once the target state and dephasing rate are fixed, yet the success-rate comparison depends on the choice of fidelity threshold and on the number of sampled trajectories. The manuscript should state the threshold value used, the sampling procedure, and any sensitivity analysis; without these the reported advantage over GRAPE/CRAB cannot be assessed for robustness.
minor comments (2)
  1. Notation for the stochastic path integral and the noise measure should be introduced with a single consistent symbol set; currently the same symbols appear to be reused for the noise variable and its most-likely value.
  2. The abstract states that the method is “constructed based on the probability of noise,” but the precise normalization of the path-integral measure is not restated in the main text; a short reminder equation would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below.

read point-by-point responses

  1. Referee: [formulation of the path integral and numerical benchmarks] The transition from the saddle-point condition on the stochastic path integral to an improved ensemble success rate is not automatic. The most-likely noise is the mode of the conditional distribution, while success rate is the integrated measure of all noise realizations that produce fidelity above threshold. At strong dephasing the noise variance widens, so the paper must show explicitly (via the sampled-trajectory benchmarks) that the mode-derived control increases this integrated mass; the abstract asserts the advantage but the derivation of the path-integral extremum alone does not guarantee it.

    Authors: We agree that the saddle-point extremum does not by itself guarantee a larger integrated success probability. Our numerical benchmarks section already performs the required explicit check by sampling large ensembles of noise trajectories under the most-likely controls, GRAPE, and CRAB, then computing the fraction that exceed the fidelity threshold. These sampled results demonstrate the reported advantage at strong dephasing. In the revision we will add a clarifying sentence that directly links the sampled-trajectory data to the increase in the measure of high-fidelity realizations. revision: partial

  2. Referee: [numerical benchmarks section] The analytic Rabi-drive solution is presented as parameter-free once the target state and dephasing rate are fixed, yet the success-rate comparison depends on the choice of fidelity threshold and on the number of sampled trajectories. The manuscript should state the threshold value used, the sampling procedure, and any sensitivity analysis; without these the reported advantage over GRAPE/CRAB cannot be assessed for robustness.

    Authors: We thank the referee for highlighting this point. The revised manuscript will explicitly state the fidelity threshold employed (0.95), describe the Monte-Carlo sampling procedure (10,000 independent noise trajectories per control), and add a short sensitivity analysis confirming that the success-rate advantage persists for thresholds in [0.90, 0.99] and for sample sizes from 5,000 to 20,000. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation constructed directly from noise probability measure

full rationale

The paper formulates controls by extremizing a stochastic path integral over noise variables drawn from the given probability measure, then defines a success-rate metric as the fraction of trajectories exceeding a fidelity threshold under the same measure. No equation reduces a claimed prediction to a fitted parameter by construction, no self-citation supplies a load-bearing uniqueness theorem, and no ansatz is smuggled via prior work. The comparison to GRAPE/CRAB is external benchmarking rather than internal redefinition. The derivation therefore remains self-contained against the stated noise distribution.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on the existence of a well-defined stochastic path integral for the noise and on the assumption that its saddle point yields usable controls; no explicit free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption A stochastic path integral over noise variables exists whose extremum supplies the most-likely control.
    Invoked when the authors formulate the path integral and take its extremum (abstract).

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