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arxiv: 2604.24467 · v1 · submitted 2026-04-27 · 🪐 quant-ph · physics.comp-ph

Adaptive Tensor Network Sampling for Quantum Optimal Control

Zeki Zeybek , Rick Mukherjee , Peter Schmelcher This is my paper

Pith reviewed 2026-05-08 04:18 UTC · model grok-4.3

classification 🪐 quant-ph physics.comp-ph
keywords quantum optimal controltensor networksmatrix product statesgradient-free optimizationdiscrete controlsampling heuristicquantum gatesstate preparation
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The pith

A matrix product state defines an adaptive sampling distribution to optimize discrete quantum control sequences without gradients.

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

The paper develops a search strategy for finding effective sequences of discrete control parameters in quantum systems by representing their quality through a compact tensor network structure. This structure generates candidate sequences according to an evolving probability distribution, which is refined at each step by keeping the better-performing sequences and adjusting the network locally to favor similar high-quality options going forward. The technique is demonstrated on standard problems such as moving a qubit from one state to another, creating entangled pairs, implementing gates on qutrits, and transferring population in open systems. A reader would care because many quantum technologies depend on precise control sequences, yet the underlying search space is high-dimensional and filled with local traps that defeat simple random or gradient-based methods.

Core claim

We introduce a gradient-free matrix product state/tensor train sampling heuristic for discrete quantum optimal control. The MPS defines a score function over the space of discrete control parameters, which in turn induces a sampling distribution over candidate control sequences. This distribution is iteratively refined through selection of better performing sequences and local tensor updates to bias the search toward high-performing sequences. We evaluate the method on a range of benchmark problems, including single-qubit state transfer, Bell-pair preparation, qutrit gate implementation, and open-system population transfer. Across these tasks, the method exhibits stable convergence behavior.

What carries the argument

An adaptive matrix product state that functions as an updatable score function, generating and progressively biasing a sampling distribution over discrete control sequences through selection and local tensor adjustments.

Load-bearing premise

That an MPS can be maintained and locally updated so that its induced sampling distribution consistently directs future samples toward higher-performing control sequences in a non-convex landscape.

What would settle it

Applying the method to the listed benchmark tasks and finding that it fails to reach fidelities comparable to established gradient-free algorithms or exhibits erratic rather than stable convergence across repeated runs.

Figures

Figures reproduced from arXiv: 2604.24467 by Peter Schmelcher, Rick Mukherjee, Zeki Zeybek.

Figure 1
Figure 1. Figure 1: FIG. 1: The schematic illustration of the optimization view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Illustration of MPS sampling and updating pro view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Single-qubit optimal control for population view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Optimal Bell-pair view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Qutrit NOT-gate optimization using piecewise view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Optimal population transfer in a three-level open view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Convergence behavior of TT-EDA and PROTES across benchmark functions and problem dimensions. view at source ↗
read the original abstract

Quantum optimal control (QOC) provides a systematic framework for achieving high-fidelity operations in quantum systems and plays a central role in tasks such as gate synthesis, state transfer, and pulse design. Existing QOC methods broadly fall into two categories: gradient-based and gradient-free algorithms. The associated optimization landscape is often high-dimensional, non-convex, and populated by numerous local minima, making efficient gradient-free search strategies essential. To address this, we introduce a gradient-free matrix product state/tensor train (MPS/TT) sampling heuristic for discrete quantum optimal control. In our approach, the MPS defines a score function over the space of discrete control parameters, which in turn induces a sampling distribution over candidate control sequences. This distribution is iteratively refined through selection of better performing sequences and local tensor updates to bias the search toward high-performing sequences. We evaluate the method on a range of benchmark problems, including single-qubit state transfer, Bell-pair preparation, qutrit gate implementation, and open-system population transfer. Across these tasks, the method exhibits stable convergence behavior and competitive empirical performance relative to established gradient-free baselines. These results suggest that tensor network sampling offers a viable heuristic framework for discrete quantum control.

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

1 major / 0 minor

Summary. The manuscript introduces a gradient-free heuristic for discrete quantum optimal control that represents a score function over control sequences via a matrix product state (MPS) or tensor train. Candidate sequences are sampled from the induced distribution, high-performing sequences are selected, and the MPS tensors are updated locally to bias subsequent sampling toward better solutions. The method is evaluated on four standard benchmark tasks—single-qubit state transfer, Bell-pair preparation, qutrit gate implementation, and open-system population transfer—where it is reported to exhibit stable convergence and competitive performance relative to established gradient-free baselines.

Significance. If the empirical claims are substantiated with quantitative data, the work would supply a novel adaptive sampling heuristic that leverages tensor-network representations to navigate high-dimensional, non-convex discrete control landscapes. This could be useful in regimes where gradient information is unavailable or unreliable, and the cross-application of MPS techniques from many-body physics to control optimization is conceptually interesting.

major comments (1)
  1. [Abstract] Abstract: the central claim that the method 'exhibits stable convergence behavior and competitive empirical performance' is unsupported by any numerical results, tables, figures, error bars, or implementation details in the provided text. Without these, the empirical contribution cannot be assessed or reproduced.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting this important point about the abstract. We address the comment below and are prepared to make revisions to improve the clarity and substantiation of our empirical claims.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the method 'exhibits stable convergence behavior and competitive empirical performance' is unsupported by any numerical results, tables, figures, error bars, or implementation details in the provided text. Without these, the empirical contribution cannot be assessed or reproduced.

    Authors: We agree that the abstract, as currently worded, summarizes the empirical findings at a high level without embedding specific quantitative details or direct references to supporting data. The full manuscript contains the requested elements: convergence plots and performance comparisons across the four benchmarks (single-qubit state transfer, Bell-pair preparation, qutrit gate implementation, and open-system population transfer) are presented in the results section with accompanying figures, tables of fidelity and runtime metrics, error bars derived from repeated trials, and implementation details (including MPS bond dimension, sampling parameters, and baseline configurations) provided in the methods and appendix. To address the referee's concern directly, we will revise the abstract to include a brief, high-level reference to these results (e.g., noting stable convergence on the listed benchmarks and competitive performance relative to the baselines) while adding explicit cross-references to the relevant figures and sections. This will make the empirical contribution more readily assessable from the abstract alone. revision: yes

Circularity Check

0 steps flagged

No significant circularity; heuristic is self-contained and empirically evaluated

full rationale

The paper introduces an MPS/TT-based iterative sampling heuristic for discrete QOC as a novel algorithmic framework. The description consists of defining a score function via MPS, inducing a sampling distribution, performing selection of high-performing sequences, and applying local tensor updates. These steps are presented as a constructive procedure without any mathematical derivation that reduces claimed performance to a fitted parameter, self-referential definition, or self-citation chain. Evaluation is purely empirical on standard benchmarks (state transfer, Bell-pair preparation, etc.), with comparisons to external baselines. No load-bearing step equates outputs to inputs by construction, satisfying the criteria for a non-circular finding.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that an MPS can compactly represent a useful score function over discrete control sequences and that iterative selection plus local updates will improve sampling; several typical heuristic hyperparameters (bond dimension, sample count per round, update schedule) are left unspecified.

free parameters (2)
  • MPS bond dimension
    Hyperparameter controlling expressivity of the score-function tensor network; value not stated in abstract.
  • Selection and update schedule parameters
    Controls how many top sequences are kept and how local tensor updates are performed; not quantified.
axioms (1)
  • domain assumption The score function over the space of discrete control parameters can be effectively approximated by a matrix product state.
    This approximation is required to induce the sampling distribution and enable local tensor updates.

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