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REVIEW 3 major objections 5 minor 21 references

Opportunities and challenges of quantum computing for climate modelling

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper argues quantum computing can improve and accelerate climate models on four fronts, most plausibly soon via quantum machine learning for subgrid-scale processes.

desk verdict A useful and honest roadmap for quantum–climate modeling, but the abstract's near-term NISQ promise is undercut by the paper's own runtime numbers. read the letter →

arxiv 2502.10488 v2 pith:5VYK4LYH submitted 2025-02-14 quant-ph physics.ao-ph

Mierk Schwabe , Lorenzo Pastori , Inés de Vega , Pierre Gentine , Luigi Iapichino , Valtteri Lahtinen , Martin Leib , Jeanette M. Lorenz
show 1 more author
Veronika Eyring
This is my paper · ORCID
classification quant-phphysics.ao-ph
keywords climatemodelingquantumcomputingmachinelearningdata-drivenparameterizationsmodeltuningsubgrid-scaleprocessesEarthsystemmodelsNISQdevices
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that quantum computing, including machine learning on today's noisy intermediate-scale quantum devices, could attack the two biggest weaknesses of current climate models: their limited horizontal resolution and the resulting uncertainty in regional projections. It maps four concrete roles for quantum hardware: solving the underlying fluid-dynamics equations faster with quantum linear algebra, replacing error-prone subgrid-scale parameterizations with quantum machine learning, automating the slow expert-driven tuning of model parameters, and generating and classifying climate data for model evaluation. The near-term weight falls on the second role, where the paper points to early demonstrations of quantum models emulating cloud and flux fields from the ClimSim dataset and a quantum-neural-network cloud-cover parameterization. The paper is explicit that all four research directions are still in their infancy and face numerous challenges, and that the whole program rests on whether high-dimensional climate states can be efficiently encoded into quantum states and the needed properties efficiently read out.

What carries the argument

The load-bearing mechanism is the exponential compression of high-dimensional data in quantum states: $N$ qubits span a $2^N$-dimensional state space, so a climate state vector of size $M$ can in principle be stored in $O(\log M)$ qubits, which is the source of the paper's polylogarithmic-versus-polynomial resource contrast for quantum linear algebra solvers. For the near-term pillar, the carrier is the parameterized quantum circuit (PQC), a shallow sequence of tunable quantum gates whose measurement outcomes define a cost function that a classical optimizer feeds back on, forming the hybrid quantum-classical loop that fits within NISQ coherence times. The same PQC design serves as a quantum neural network for subgrid parameterizations, a quantum kernel in Gaussian-process emulators for tuning, and a generative sampler of climate-variable distributions for analysis. The paper also identifies the two mechanisms that constrain the whole enterprise, state-preparation and readout efficiency, and the measurement-shot cost of every prediction, which it quantifies as roughly 1000 seconds per model time-step for a million-cell model running a QNN parameterization.

What would settle it

Run the ClimSim-based emulation benchmark the paper cites with a fixed total compute budget that counts circuit evaluations and measurement shots per grid cell per time step, including the roughly 100 shots per QNN call the authors report; if a classical neural network matches or beats the quantum models at equal wall-clock cost and error, especially on out-of-distribution forcings, the near-term QML pillar is falsified. For the PDE-expediting pillar, the decisive test is whether an efficient encoding exists for a high-resolution turbulent field: attempt to prepare a kilometre-scale convective state on a scalable circuit and measure a domain-averaged flux, and if the required measurement count grows exponentially in grid size, the shadow-tomography route the paper relies on does not rescue the exponential-speedup claim.

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Extended reading notes

Core claim

Building on hybrid physics-plus-machine-learning Earth system models, the paper's central claim is that quantum computation offers a structured four-part route to faster and more accurate climate models rather than a single universal speedup. Quantum linear algebra solvers could in principle solve the discretized Navier–Stokes and chemical-kinetics equations with resources scaling polylogarithmically in problem size, with quantum lattice–Boltzmann methods as an alternative that sidesteps linear-system solving; parameterized quantum circuits trained in a hybrid quantum-classical loop could represent subgrid-scale processes such as convection and cloud cover with fewer parameters and better generalization than classical neural networks, even on current NISQ hardware; quantum optimization and quantum Gaussian processes could automate the tuning of climate-model parameters; and quantum generative and classification models could emulate and label climate-data distributions for model evaluation. The paper grounds the near-term QML pillar in two recent demonstrations, quantum models that typically outperformed their classical counterparts on ClimSim-based emulation and a quantum-neural-network cloud-cover parameterization, while insisting that the exponential-speedup claims remain conditional on efficient encoding of climate states and efficient readout of the quantities of interest, both unproven. The stated conclusion is a call to start adapting simplified climate problems to quantum algorithms now, so that the field is ready when the hardware matures.

Load-bearing premise

The whole roadmap stands or falls on the assumption that the high-dimensional state of a climate model can be loaded efficiently into quantum states and that the specific quantities scientists need, such as grid-cell fluxes, can be read out with few measurements; the paper itself states that this is still unclear.

Editorial extensions

If this is right

  • If the QML parameterization pillar is right, subgrid processes such as cloud cover can be learned offline from short high-resolution runs and then executed online by a quantum device, attacking exactly the convection and turbulence biases that dominate current model uncertainty.
  • If quantum linear algebra solvers mature, the dynamical core of climate models could run with resources scaling polylogarithmically in grid size, though the paper expects a workflow of many cheap quantum runs with sparse output rather than stored full-state data, because readout capacity stays limited.
  • If quantum-assisted tuning works, the slow expert-driven calibration of Earth-system-model parameters becomes an automatic loop of quantum-Gaussian-process emulation and quantum optimization, improving reproducibility and freeing computing time.
  • Because the paper proposes classical surrogates that emulate already-trained quantum models, a quantum device may only be needed during the training stage, which would make QML parameterizations deployable well before quantum hardware can run them online.
  • Concrete near-term milestones follow directly from the paper: 1D shallow-water equations on a few grid points, Lorenz-96 model tuning, and simplified cloud-classification tasks as first testbeds.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Counting the paper's own runtime numbers (about 1000 seconds per time-step for a million-cell model) implies the online-QML route is not viable on current hardware even if accuracy improves, so the practical near-term payoff is the training-stage surrogate route the paper lists but does not foreground.
  • Because the encoding-and-readout question is the crux for all four pillars, a portfolio rule that follows from the paper's own framing is to benchmark state-preparation and measurement-shot costs on real climate fields before committing resources to quantum PDE solvers.
  • A testable consequence the paper leaves implicit is that re-running the ClimSim comparison at matched total compute budget and parameter count, with out-of-distribution test sets, would settle whether the reported quantum advantage is real or an artefact of the experimental setup.
  • The four-pillar structure implies a sequencing the paper does not state: QML parameterization will be the first pillar to reach deployment because it tolerates noisy hardware, while the PDE-solver pillar waits on fault-tolerant error correction.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This position paper argues that quantum computing could improve and accelerate climate modeling in four areas: quantum linear algebra solvers for the underlying differential equations, QML-based subgrid-scale parameterizations, quantum-assisted model tuning, and QML for model analysis and evaluation. For each area, the paper reviews relevant quantum algorithms, discusses challenges such as data encoding, readout, noise, and HPC integration, and proposes concrete first steps such as solving 1D shallow-water equations and tuning the Lorenz-96 model.

Significance. If the roadmap is read as a research agenda rather than a set of established speedups, the paper is a useful and well-grounded contribution. Its strengths are the explicit discussion of limitations: Section 4.2 includes a back-of-envelope runtime estimate showing that online QNN parameterizations are prohibitive, Section 4.1 states that efficient encoding and readout of climate states is unsolved, and Section 3.3 concedes that practical QML advantage on real-world classical datasets is not yet demonstrated. The survey of quantum linear algebra, annealing, QML, and HPC-QC integration is competent and the references are current. However, the near-term NISQ claim in the abstract is in tension with the body's own runtime estimate, and the classical-surrogate fallback proposed in Section 5 relies on an unproven transfer-of-advantage assumption, so the central claim needs reframing.

major comments (3)
  1. [Abstract; Sections 4.2 and 5] The abstract states that QML could improve subgrid-scale representation in ESMs "even with currently available noisy intermediate-scale quantum devices," but Section 4.2's own estimate (10 microseconds per QNN evaluation, about 100 measurement shots, 1 million grid cells) yields 1000 seconds per model time-step and is described as "clearly prohibitive." The fallback proposed in Section 5, namely classical surrogates or shadows of QML models, shifts the burden to the assumption that a classical surrogate trained on QML outputs outperforms a classical neural network trained directly on the same data. That assumption is not established; Section 3.3 says "it is not yet clear whether a practical advantage of QML on real-world classical datasets can be demonstrated." The near-term payoff claimed in the abstract therefore depends on an unproven transfer step, not merely on future hardware improvements. Please either soften the NISQ-era claim or provide a substantive argument for the transfer-of-advantage.
  2. [Sections 4.1 and 4.2] The exponential speedups for quantum PDE solvers and the benefits claimed for QML parameterizations both presuppose that high-dimensional climate state vectors can be efficiently encoded into quantum states and that the quantities of interest can be measured with few shots. The paper itself states in Section 4.1 that "it is still unclear what type of climate states can be efficiently encoded in quantum states, and which properties of the climate can be efficiently measured." Because this is a load-bearing input for both the long-term and near-term parts of the roadmap, the paper should state explicitly that failure of efficient encoding and readout would invalidate both applications, and should discuss what partial encodings or compressed representations (for example, the tensor-network compression mentioned in Section 4.2) could salvage.
  3. [Sections 4.2 and 3.3] The case for QML parameterizations relies on the higher expressivity of QNNs, citing Du et al. 2020 and 2021 and Yu et al. 2023b, and on their generalization benefits. However, Section 3.3 itself cites recent results on classical simulability of certain variational quantum models (Cerezo et al. 2023), and Section 4.4 notes that QCNNs may be classically simulable. The paper does not address how these simulability results affect the advantage claim for QML parameterizations on classical climate data. Please add a discussion of the boundary between QML models that retain an advantage and those that are classically simulable, and explain why the proposed QNN parameterizations are expected to fall on the advantageous side.
minor comments (5)
  1. [Figure 1] The labels in Figure 1 are garbled (for example, "Universi/g415es" and "pla/g414orms"), and the abbreviations NISQ, NILSQ, and FTQC are not expanded in the caption; please fix the labels and define all abbreviations.
  2. [Box 1] Equations (2) and (4) contain rendering artifacts such as "/C0" and "/C16/C17" that make the mathematics hard to read; please correct the typesetting.
  3. [Section 4.2] The phrase "For nowadays' implementations" should read "For current implementations."
  4. [Section 3.1] Notation such as "O polylog MðÞ" is difficult to parse; please typeset as O(polylog M) and similarly for "O polyMð)".
  5. [Figure 5 caption] The caption says "summarized by variables x" but panel (b) lists variables x and parameterizations P2-P4; please clarify the notation so the caption matches the figure.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: this is an openly hedged position paper with no derivation chain that reduces to its own inputs.

full rationale

This is a position paper with no claimed derivation chain, so the classic circularity failure modes (self-definitional definitions, fitted parameters renamed as predictions, imported uniqueness theorems, ansatz-by-citation, renaming known results) are absent. The central claims are explicitly hedged: §3.3 states "it is not yet clear whether a practical advantage of QML on real-world classical datasets can be demonstrated"; §4.1 states "it is still unclear what type of climate states can be efficiently encoded in quantum states, and which properties of the climate can be efficiently measured"; and §4.2's own runtime estimate (1000 s per model time-step for a QNN parameterization on 10^6 grid cells) directly undermines the online-NISQ scenario rather than hiding it. Section 5 likewise concedes "All these research efforts are still in their infancy and face numerous challenges." The two author-overlapping citations (Pastori et al. 2025 for the QML cloud-cover parameterization and Bonnet et al. 2024 in the tuning discussion) are disclosed demonstrations, not premises that force the conclusions; even if they were removed, the paper would remain a research-agenda statement. The classical-surrogate fallback in §5 raises an open question about transfer-of-advantage, but that is a correctness and evidence risk, not circularity. No equation or claim reduces by construction to its own input, so the circularity score is 0.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The paper's thesis rests on several imported assumptions from climate science and quantum computing that it does not verify: the importance of subgrid parameterizations, the expressive-power advantage of QML, the promise of quantum PDE solvers, and the Tennie-Palmer encoding estimate. The two runtime parameters in Section 4.2 are assumed values, not fitted. No new entities are invented.

free parameters (2)
  • QNN execution time per circuit evaluation = 10 microseconds
    Assumed in Section 4.2 from Pastori et al. 2025 to compute a runtime estimate for online QML parameterization; not fitted in this paper, but the conclusion of prohibitive runtime depends on this order of magnitude.
  • Number of measurement shots per QNN evaluation = 100
    Assumed in Section 4.2 alongside the 10 us per run; used in the 1000 s per time step estimate.
assumptions (5)
  • domain assumption The fundamental equations of ESMs (Navier-Stokes, continuity, first law) are an adequate basis for climate modeling.
    Box 1 states these equations without derivation; standard in the field.
  • domain assumption Subgrid-scale parameterizations and model tuning are dominant sources of ESM uncertainty.
    Section 2 motivates the whole paper on this basis, citing IPCC and model bias literature.
  • domain assumption QML models have higher expressive power and better generalization from limited training data than classical models.
    Section 4.2 and 4.4 rely on these properties, citing Yu et al. 2023b, Abbas et al. 2021, Caro et al. 2022, Huang et al. 2021. The paper does not verify them for climate data.
  • domain assumption Quantum linear algebra and QLBM can solve fluid dynamics PDEs with exponential speedup, contingent on efficient encoding and readout.
    Section 4.1 follows Gaitan 2020, Budinski 2022, Li et al. 2023; the paper itself concedes encoding/readout and stability are open.
  • domain assumption 30 logical qubits can store and time-evolve one billion climate variables with polynomial-depth circuits.
    Section 4.1 cites Tennie and Palmer 2023; the paper calls it 'still unclear' which climate states can be efficiently encoded.

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Cite this review

Pith. "Pith review of Opportunities and challenges of quantum computing for climate modelling." pith.science (2026). https://pith.science/paper/5VYK4LYH

@misc{pith2026250210488,
  author       = {Pith},
  title        = {Pith review of: Opportunities and challenges of quantum computing for climate modelling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5VYK4LYH}},
  note         = {Machine review of arXiv:2502.10488}
}
read the original abstract

Adaptation to climate change requires robust climate projections, yet the uncertainty in these projections performed by ensembles of Earth system models (ESMs) remains large. This is mainly due to uncertainties in the representation of subgrid-scale processes such as turbulence or convection that are partly alleviated at higher resolution. New developments in machine learning-based hybrid ESMs demonstrate great potential for systematically reduced errors compared to traditional ESMs. Building on the work of hybrid (physics + AI) ESMs, we here discuss the additional potential of further improving and accelerating climate models with quantum computing. We discuss how quantum computers could accelerate climate models by solving the underlying differential equations faster, how quantum machine learning could better represent subgrid-scale phenomena in ESMs even with currently available noisy intermediate-scale quantum devices, how quantum algorithms aimed at solving optimization problems could assist in tuning the many parameters in ESMs, a currently time-consuming and challenging process, and how quantum computers could aid in the analysis of climate models. We also discuss hurdles and obstacles facing current quantum computing paradigms. Strong interdisciplinary collaboration between climate scientists and quantum computing experts could help overcome these hurdles and harness the potential of quantum computing for this urgent topic.

Figures

Figures reproduced from arXiv: 2502.10488 by the authors.

Figure 1
Figure 1. Evolution of the number of physical qubits of quantum computing and quantum simulation platforms by several companies and university research groups. The underlying data was collected from online sources and journal publications(D:Wave, 2023; IBM, 2023; PASQAL, 2023; rigetti, 2023; Google QAI, 2023; AQT, 2023; Quantinuum, 2023; Zhong et al., 2020; Scholl et al., 2021; Wu et al., 2021; Semeghini et al., 2021; Joshi e… view at source ↗
Figure 2
Figure 2. Schematic of an Earth system model (ESM). The ESM represents the state of the atmosphere, ocean and sea ice, and land using a grid covering the globe. For each component, physical properties such as water content in the atmosphere and soil or salinity of the ocean, the kinetic energy contained in the wind and currents, and the thermal energy contained in the temperature are represented. Following Gettelman and Rood … view at source ↗
Figure 3
Figure 3. Representation of a qubit state as a vector on the Bloch sphere. The poles correspond to the basis states ∣0〉 and ∣1〉. Environmental Data Science e35-5 https://doi.org/10.1017/eds.2025.10010 Published online by Cambridge University Press [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Overview of the climate modeling tasks and the category of matching quantum computing algorithms. (Image of the Earth by NASA/Apollo 17). e35-8 Mierk Schwabe et al. https://doi.org/10.1017/eds.2025.10010 Published online by Cambridge University Press [PITH_FULL_IMAGE:…
Figure 5
Figure 5. Figure 5: Hybrid quantum-classical approach for QML-based parameterizations. (a) Offline training: variables from cloud-resolving models are coarse-grained to the scale of the target climate model. The subgrid part of the variables of interest (e.g., fluxes) is calculated and us…
Figure 6
Figure 6. Figure 6: General steps of an automatic tuning protocol for climate models. In Step (i), the tuning goals and parameters are chosen. Then, in Step (ii) and (iii), emulators are constructed to approximate the model output and to speed up the calibration process. Potentially optim…

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