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arxiv: 2605.16944 · v2 · pith:YF4GTRLDnew · submitted 2026-05-16 · 🪐 quant-ph

Efficient Hamiltonian Engineering for Adiabatic MIS Algorithms

Guy Karni , Noam Cohen , Adi Pick This is my paper

Pith reviewed 2026-05-22 09:58 UTC · model grok-4.3

classification 🪐 quant-ph
keywords Rydberg atom arraysadiabatic quantum computingmaximum independent setHamiltonian engineeringlocal controlsquantum optimizationgraph algorithms
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The pith

Local controls in Rydberg arrays accelerate convergence to the maximum independent set state in adiabatic algorithms.

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

The paper introduces a hybrid adiabatic algorithm for solving the maximum independent set problem using Rydberg atom arrays. It engineers local control pulses that preferentially target atoms with fewer neighbors, corresponding to low-degree nodes in the graph. These controls help speed up the evolution toward the solution while keeping the system away from trapping states. Numerical results indicate better performance than global driving methods, including a 25 percent slower loss of fidelity as the problem difficulty increases.

Core claim

We present a hybrid adiabatic algorithm for maximum independent set (MIS) using Rydberg atom arrays. We engineer local controls that preferentially excite atoms with few neighbors, which represent graph nodes with small degrees. Numerical simulations show that the designed pulses accelerate convergence to the MIS state and suppress population in trap states. We obtain higher success probabilities than traditional global controls and a 25% reduction in fidelity decay rate as problem hardness increases.

What carries the argument

Engineered local controls in the Rydberg Hamiltonian that preferentially excite low-degree atoms to guide the adiabatic evolution toward the MIS state.

If this is right

  • Higher success probabilities for finding the MIS solution compared to standard global control approaches.
  • Suppressed population in unwanted trap states during the algorithm run.
  • A 25% reduction in the rate of fidelity decay as the graph problem becomes harder.
  • The method combines adiabatic evolution with tailored local driving for improved quantum optimization.

Where Pith is reading between the lines

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

  • If the local controls prove robust, they could extend to other combinatorial problems solvable via Rydberg arrays.
  • Real-device experiments would reveal whether the simulated improvements hold when including additional noise sources.
  • This approach suggests that problem-specific Hamiltonian engineering can enhance adiabatic quantum computing beyond generic methods.

Load-bearing premise

The numerical model of the Rydberg Hamiltonian with the engineered local controls accurately captures the dominant dynamics and decoherence sources present in a real experimental array.

What would settle it

Performing the algorithm on actual Rydberg atom hardware and observing no increase in success probability or no reduction in fidelity decay rate compared to global controls would falsify the claims.

Figures

Figures reproduced from arXiv: 2605.16944 by Adi Pick, Guy Karni, Noam Cohen.

Figure 1
Figure 1. Figure 1: (a) King’s graph with vertices labeled by their degrees. Colored vertices highlight independent sets (IS) of size 3, 4, [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) A representative graph marking the MIS (red) and two independent sets (IS) of size |MIS| − 1: a connected IS, which is subset of the MIS (green), and a disconnected IS, which is not (yellow). The shaded nodes indicate vertices that are not common to all three sets. (b) Eigenvalue spec￾trum of H [Eq. (1)] at tf , sorted by the number of Rydberg excitations. The degenerate IS band in the traditional AQC … view at source ↗
Figure 4
Figure 4. Figure 4: (a) Average infidelity ⟨1 − PMIS⟩ versus total protocol time for specific hardest graphs subset (2.2 < HP ≤ 4.0). The traditional homogeneous AQC (purple) is compared against local detuning utilizing exponential (green) and inverse-power (red) functions. (b) Dependence of the local detuning function fi(a) on the control parameter a. The green curves correspond to the exponential profile fi(a) = exp(−dia), … view at source ↗
Figure 5
Figure 5. Figure 5: Statistical analysis of the data presented in Fig.3. [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
read the original abstract

We present a hybrid adiabatic algorithm for maximum independent set (MIS) using Rydberg atom arrays. We engineer local controls that preferentially excite atoms with few neighbors, which represent graph nodes with small degrees. Numerical simulations show that the designed pulses accelerate convergence to the MIS state and suppress population in trap states. We obtain higher success probabilities than traditional global controls and a $25\%$ reduction in fidelity decay rate as problem hardness 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 manuscript presents a hybrid adiabatic algorithm for the maximum independent set (MIS) problem using Rydberg atom arrays. Local controls are engineered to preferentially excite atoms with few neighbors (low-degree nodes). Numerical simulations demonstrate accelerated convergence to the MIS state, suppression of trap-state population, higher success probabilities than global controls, and a 25% reduction in fidelity decay rate as problem hardness increases.

Significance. If the numerical results hold under realistic conditions, the work could improve the robustness of adiabatic quantum optimization on Rydberg platforms by incorporating graph-topology-aware local controls. This addresses a practical challenge in maintaining coherence during evolution for combinatorial problems and provides concrete simulation evidence of gains over standard global driving.

major comments (2)
  1. [Numerical Simulations section] The numerical simulations underlying the central claims (accelerated convergence, trap suppression, 25% fidelity-decay reduction) rely on a Rydberg master equation with engineered local controls, yet the precise decoherence terms (Rydberg lifetime, position-dependent laser inhomogeneity, motional heating) are not explicitly stated or justified in the simulation section. This omission is load-bearing because the reported improvements could be artifacts of an incomplete noise model.
  2. [Results section (e.g., Figure 3 or Table 2)] Success-probability and fidelity-decay results are presented without error bars, ensemble size, or data-exclusion criteria for the graph instances. This makes it impossible to assess whether the 25% reduction and outperformance over global controls are statistically robust across hardness levels.
minor comments (2)
  1. [Abstract] The abstract states a '25% reduction in fidelity decay rate' without defining the exact metric (e.g., per unit time or per hardness parameter) or the hardness range.
  2. [Hamiltonian Engineering section] Notation for the engineered local controls (e.g., how the degree-dependent detuning or Rabi frequency is constructed) should be introduced earlier and used consistently in the Hamiltonian equations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback, which has helped clarify several aspects of our presentation. We address each major comment below and have revised the manuscript to incorporate the requested details.

read point-by-point responses

  1. Referee: [Numerical Simulations section] The numerical simulations underlying the central claims (accelerated convergence, trap suppression, 25% fidelity-decay reduction) rely on a Rydberg master equation with engineered local controls, yet the precise decoherence terms (Rydberg lifetime, position-dependent laser inhomogeneity, motional heating) are not explicitly stated or justified in the simulation section. This omission is load-bearing because the reported improvements could be artifacts of an incomplete noise model.

    Authors: We agree that explicit specification of the decoherence model is necessary for reproducibility and to rule out artifacts. In the revised manuscript we have added a dedicated paragraph in the Numerical Simulations section that states the precise terms used in the Rydberg master equation, including the finite Rydberg lifetime, the modeled position-dependent laser inhomogeneity, and the motional-heating contribution. These parameters are justified by reference to standard experimental values reported for Rydberg-atom arrays. The updated text makes clear that the reported gains persist under this realistic noise model. revision: yes

  2. Referee: [Results section (e.g., Figure 3 or Table 2)] Success-probability and fidelity-decay results are presented without error bars, ensemble size, or data-exclusion criteria for the graph instances. This makes it impossible to assess whether the 25% reduction and outperformance over global controls are statistically robust across hardness levels.

    Authors: We acknowledge that the statistical characterization of the results was insufficient. In the revised Results section we now report error bars (standard error of the mean) on all success-probability and fidelity-decay curves, specify the ensemble size used for each hardness bin, and describe the data-exclusion criteria applied to the generated graph instances. These additions allow direct assessment of the statistical robustness of the 25 % reduction and the performance advantage over global controls. revision: yes

Circularity Check

0 steps flagged

No circularity: results from forward simulation of engineered Hamiltonian

full rationale

The paper's central claims rest on numerical simulations that propagate the Rydberg Hamiltonian under the designed local controls to obtain success probabilities, trap-state suppression, and fidelity decay rates. These quantities are generated as simulation outputs rather than fitted to the target metrics or reduced by construction to the inputs. No self-definitional steps, fitted-input predictions, or load-bearing self-citations appear in the derivation chain; the model and controls are specified independently of the reported performance numbers. The analysis is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work relies on standard quantum-mechanical time evolution and the Rydberg blockade Hamiltonian; no new free parameters, ad-hoc axioms, or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption The Rydberg atom array dynamics are accurately described by a time-dependent Hamiltonian with controllable local detunings and Rabi frequencies.
    Invoked implicitly when the authors state that numerical simulations of the engineered pulses produce the reported convergence and fidelity behavior.

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