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arxiv: 2606.26162 · v1 · pith:NBEUUHWJnew · submitted 2026-06-24 · 🪐 quant-ph

Dissipative Quantum Multiplicative Weights with Sampling Feedback: A Classically Hard Primitive Realized via Engineered Open-System Dynamics

Agung Trisetyarso , Lenny Putri Yulianti , Kridanto Surendro This is my paper

Pith reviewed 2026-06-26 01:55 UTC · model grok-4.3

classification 🪐 quant-ph
keywords dissipative quantum dynamicsonline learningmultiplicative weightsGibbs samplingquantum advantageDavies dissipatorregret boundsopen quantum systems
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The pith

Engineered open quantum dynamics realize an online learning primitive with sublinear regret that efficient classical algorithms cannot match.

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

The paper presents DQMW-Sample, a method that uses measurements from an engineered open quantum system to generate loss feedback for online learning. This lifts the known hardness of sampling Gibbs states at constant temperature into a physically realizable algorithm that achieves sublinear regret. Sympathetic readers would care because it offers a complexity-theoretic separation between quantum and classical online learners. The work also shows that the dissipator's spectral gap can contract noise to keep regret sublinear.

Core claim

DQMW-Sample prepares a Gibbs state via a Davies-type dissipator whose computational-basis measurement supplies the loss feedback; this yields asymptotically sublinear regret while every efficient classical learner suffers constant average regret on a suitably constructed instance, and an efficient classical simulator of the full T-round adaptive process would collapse the polynomial hierarchy.

What carries the argument

The DQMW-Sample primitive that engineers a Davies-type dissipator to prepare a Gibbs state for sampling-based loss feedback in an online multiplicative-weights update.

If this is right

  • Sublinear regret holds asymptotically for the quantum learner.
  • Classical efficient learners suffer constant average regret on the constructed instance.
  • Sublinear noise-induced regret follows from the spectral gap contracting under balanced dissipation.
  • An efficient classical simulator of the adaptive T-round process collapses the polynomial hierarchy.

Where Pith is reading between the lines

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

  • This construction suggests that other open-system dynamics could be engineered for similar separations in different learning problems.
  • If the realizability holds on larger scales, it points to a path for quantum advantage in practical online optimization tasks.
  • Connections to other quantum sampling hardness results may allow broader classes of learning algorithms to inherit similar guarantees.

Load-bearing premise

A Davies-type dissipator can be engineered on quantum hardware such that the per-round feedback it supplies cannot be efficiently simulated by any classical algorithm.

What would settle it

Demonstration of an efficient classical algorithm that simulates the T-round feedback process of DQMW-Sample on the constructed instance without causing a collapse of the polynomial hierarchy.

Figures

Figures reproduced from arXiv: 2606.26162 by Agung Trisetyarso, Kridanto Surendro, Lenny Putri Yulianti.

Figure 1
Figure 1. Figure 1: Initial hardware characterization of engineered dissipation on ibm kingston (Heron r2). Proba￾bility of measuring |1⟩ after applying different numbers of mid-circuit measurement and conditional-reset steps (used as a proxy for the engineered dissipation rate γ0). Data were collected across five physical qubits with 4096 shots per point; error bars are the standard deviation across the five qubits. The rela… view at source ↗
Figure 2
Figure 2. Figure 2: Hardware characterization of engineered dissipation on ibm kingston (Heron r2) under open￾plan constraints. Deconvolved mid-circuit measurement error as a function of engineered dissipation strength (number of mid-circuit measurement + conditional-reset steps). Data were acquired in a single batched job with 1024 shots per circuit across three physical qubits. The round-budget ratio is approximately 1.8 (b… view at source ↗
Figure 3
Figure 3. Figure 3: Phase-space representation of dissipative thermalization. Numerical simulation of a harmonic oscillator undergoing engineered dissipation (amplitude damping with thermal noise) toward a thermal Gibbs state. The system starts in the vacuum state and relaxes to a thermal state with mean photon number n¯ = 2. Both the Wigner function and the Husimi Q-function (Glauber–Sudarshan representation) remain positive… view at source ↗
Figure 4
Figure 4. Figure 4: Lindblad-model emulation of the noise–dissipation coupling δ(γ0). Steady-state deviation floor ∥ρss − ρGibbs∥1 versus engineered dissipation rate γ0, computed from the stationary state of the full Lindblad generator on a 2-qubit effective Hamiltonian. Noise scales are set by published ibm kingston calibration values. Three hypotheses for how noise couples to dissipation are shown: if (R2) holds (δ constant… view at source ↗
Figure 5
Figure 5. Figure 5: Lindblad-model emulation: cumulative tracking error of DQMW-Sample versus rounds, for two engineered-dissipation strengths, both in the strong-coupling regime of [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Lindblad-model emulation: engineered dissipation versus classical baseline on a simple tracking task. On this instance, where the loss vector can be evaluated exactly and efficiently by classical means, the classical multiplicative-weights baseline achieves the lowest cumulative error. Among the quantum variants, increasing the engineered dissipation strength still reduces the rate of error accumulation, c… view at source ↗
Figure 7
Figure 7. Figure 7: Power analysis: comparison of the round-budget ratio from the original low-statistics experiment versus [PITH_FULL_IMAGE:figures/full_fig_p024_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Bootstrap distribution of the round-budget ratio under the higher-statistics simulation ( [PITH_FULL_IMAGE:figures/full_fig_p025_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Simulated deconvolved mid-circuit measurement error [PITH_FULL_IMAGE:figures/full_fig_p026_9.png] view at source ↗
read the original abstract

We introduce \emph{Dissipative Quantum Multiplicative Weights with Sampling Feedback} (DQMW-Sample), an online-learning primitive in which engineered open quantum-system dynamics prepare a Gibbs state whose computational-basis measurement supplies the loss feedback. The central conceptual contribution is to lift the computational hardness of constant-temperature Gibbs sampling into a physically realizable online-learning primitive. By engineering a Davies-type dissipator whose per-round feedback cannot be efficiently simulated classically, we obtain a learning-theoretic separation in which DQMW-Sample achieves asymptotically sublinear regret while every efficient classical learner suffers constant average regret on a suitably constructed instance. We further prove that the spectral gap of the engineered dissipator contracts hardware noise, yielding sublinear noise-induced regret under a balanced dissipation schedule, and we strengthen the single-round hardness to the full adaptive interaction: an efficient classical simulator of the entire $T$-round feedback process would collapse the polynomial hierarchy. We state the required realizability assumption in explicit form and report an initial hardware characterization on the IBM Heron~r2 processor. These results position DQMW-Sample as a concrete route toward computational advantage in online learning that is grounded in complexity theory and compatible with near-term superconducting hardware.

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 manuscript introduces Dissipative Quantum Multiplicative Weights with Sampling Feedback (DQMW-Sample), an online-learning primitive that employs engineered Davies-type open-system dissipators to prepare a Gibbs state whose computational-basis samples supply loss feedback. It claims that, under an explicit realizability assumption, this yields asymptotically sublinear regret for the quantum protocol while every efficient classical learner incurs constant average regret on a suitably constructed instance; it further claims that an efficient classical simulator of the full adaptive T-round interaction collapses the polynomial hierarchy, that noise contraction under a balanced dissipation schedule yields sublinear noise-induced regret, and that an initial hardware characterization has been performed on the IBM Heron r2 processor.

Significance. If the realizability assumption can be met and the regret and complexity arguments hold, the work supplies a concrete, complexity-theoretic route to computational advantage in online learning that is compatible with near-term superconducting hardware. The explicit statement of the assumption and the attempt to lift constant-temperature Gibbs-sampling hardness into an adaptive online-learning setting are notable strengths.

major comments (2)
  1. [hardware characterization section] § on realizability assumption and hardware characterization: the manuscript states the assumption explicitly but provides only an 'initial hardware characterization' on IBM Heron r2; no quantitative bounds are given showing that realistic control errors and decoherence preserve both the #P-hardness of the per-round samples and the adaptive PH-collapse property of the T-round process.
  2. [noise contraction section] § on noise-induced regret: the claim that the spectral gap contracts hardware noise to yield sublinear noise-induced regret under a balanced dissipation schedule is central to the separation; the manuscript must supply the explicit contraction mapping or error-propagation bound that relates the engineered dissipator's gap to the realized hardware noise strength.
minor comments (1)
  1. [regret analysis] Notation for the balanced dissipation schedule should be introduced with a clear equation reference before it is invoked in the regret analysis.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below, indicating revisions where appropriate and noting limitations where the requested analysis exceeds the current scope.

read point-by-point responses

  1. Referee: [hardware characterization section] § on realizability assumption and hardware characterization: the manuscript states the assumption explicitly but provides only an 'initial hardware characterization' on IBM Heron r2; no quantitative bounds are given showing that realistic control errors and decoherence preserve both the #P-hardness of the per-round samples and the adaptive PH-collapse property of the T-round process.

    Authors: The manuscript explicitly states the realizability assumption and labels the IBM Heron r2 data as an 'initial hardware characterization.' We agree that quantitative bounds relating control errors and decoherence to preservation of #P-hardness and the adaptive PH-collapse are not supplied. Such bounds would require a separate, detailed error-propagation analysis that is outside the scope of the present work; we will revise the text to clarify this limitation and the conditions under which the hardness claims are expected to hold. revision: partial

  2. Referee: [noise contraction section] § on noise-induced regret: the claim that the spectral gap contracts hardware noise to yield sublinear noise-induced regret under a balanced dissipation schedule is central to the separation; the manuscript must supply the explicit contraction mapping or error-propagation bound that relates the engineered dissipator's gap to the realized hardware noise strength.

    Authors: The noise contraction section contains the proof that the spectral gap of the engineered dissipator contracts hardware noise, yielding sublinear noise-induced regret under the balanced schedule. We will revise the manuscript to present the contraction mapping and the associated error-propagation bound in fully explicit form, including the relevant inequalities relating the dissipator gap to the noise strength. revision: yes

standing simulated objections not resolved
  • Providing quantitative bounds that demonstrate preservation of #P-hardness and the adaptive PH-collapse property under realistic control errors and decoherence.

Circularity Check

0 steps flagged

No significant circularity; central separation is explicitly conditional on a stated realizability assumption rather than derived by construction.

full rationale

The paper states the required realizability assumption in explicit form (abstract) and does not derive the classical hardness of the per-round feedback from the DQMW-Sample construction itself. The learning-theoretic separation (sublinear quantum regret vs. constant classical regret) and the PH-collapse claim for the T-round process are presented as consequences of this assumption plus standard complexity arguments. No self-citations, fitted parameters renamed as predictions, self-definitional equations, or ansatzes smuggled via prior work appear in the provided text. The derivation chain for regret bounds and noise contraction is therefore self-contained against external benchmarks once the assumption is granted.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Based on abstract, relies on standard quantum open systems assumptions and a new realizability assumption for the dissipator; no free parameters or invented entities explicitly listed.

axioms (1)
  • domain assumption Davies-type dissipator can be engineered with per-round feedback that is classically hard to simulate
    Central to the learning separation and stated as the required realizability assumption.
invented entities (1)
  • DQMW-Sample no independent evidence
    purpose: Online learning primitive using dissipative quantum dynamics for Gibbs state feedback
    Newly defined primitive in the paper.

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discussion (0)

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Reference graph

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    Under the standard hardness assumption that no such efficient classical sampler forµ ⋆exists (on pain of collapsing the polynomial hierarchy), no such classical algorithmA class can exist. Consequently, there is no efficient classical algorithm that can simulate the sampling step that supplies the loss feedback to the multiplicative-weights update of DQMW...