Quantum Time-Series Forecasting: Can a Hybrid Model Beat LSTM on a Real Dataset in Simulation?

Time-series forecasting is a core workload behind traffic management, energy grids, and financial systems, and any technique that promises even a small accuracy gain is worth testing because these systems run continuously and at scale. Accurate traffic forecasting plays a crucial role in modern Intelligent Transportation Systems (ITS) [1]. Quantum machine learning (QML) has been proposed as a new tool for this kind of sequential data, on the reasoning that quantum circuits can represent complex functions with few parameters. One paper explicitly frames its work as a heuristic exploration of QML potential applied to a specific transport problem, rather than a claim of general superiority [1]. That framing matters for how a builder should read every number that follows: these are early feasibility studies, not settled benchmarks, and the field has not yet produced the specific comparison this note's research question asks for.

The practical stakes are concrete. In the energy domain, a real comparison used ten years of hourly wind and solar energy data (2014-2023), comprising 87,648 data points, sourced from the NASA POWER database [4], and found that a classical LSTM decisively outperformed classical statistical baselines. In transport, the field's own experiments are being run on real high-resolution municipal data rather than synthetic series, which raises the bar for any quantum method to prove itself. A study investigating traffic forecasting used a case study for a major urban area in Athens (Greece), for which the authors possess high-resolution data [1]. If quantum-classical hybrids are ever to be useful for forecasting, they need to be tested against classical recurrent baselines on datasets exactly like this one, under matched training and evaluation protocols, and that comparison does not yet exist in the literature surveyed here.

At the same time, the tooling ecosystem for running such comparisons is still maturing. Photonic contributions currently account for approximately 6% of QML publications, with most being simulator-based [2]. This tells a builder that even the hardware side of quantum machine learning research is mostly conducted on classical simulators rather than physical devices, which is directly relevant to a question about simulated hybrid models. It also means that when a hybrid forecasting result appears in the literature, a reader should check whether it was obtained on a simulator or a real quantum processor before drawing conclusions about practical deployment.

Given this landscape, the right way to treat the question 'can a hybrid model beat LSTM on a real dataset in simulation' is as an open experimental question, not a settled one. The pieces needed to answer it, a real dataset, a classical LSTM baseline, and a trained hybrid model evaluated on the same split, exist separately in the literature but have not been assembled into one reported comparison. The rest of this note lays out what each component looks like on its own, what has been measured about each in isolation, and how a builder can combine them correctly to produce the missing result.

The QML forecasting work in this evidence set is built around Quantum Neural Networks (QNN) and a specific encoding trick called data re-uploading. The traffic-forecasting paper explores the application of Quantum Neural Networks (QNN) [1] and presents what it calls the first application of quantum data re-uploading in the context of transport forecasting [1]. Data re-uploading is a way of feeding classical data into a quantum circuit more than once during the computation, rather than encoding it a single time at the start, and the paper treats this as its central methodological contribution to the transport forecasting literature.

The stated motivation for re-uploading is expressive power: quantum data re-uploading allows quantum models to better capture complex patterns, such as traffic dynamics, by repeatedly encoding classical data into a quantum state [1]. This is a mechanism claim about why the technique might help, not a report that it did help on the Athens dataset; the two should not be conflated. A builder implementing a QNN for forecasting should treat re-uploading as one configurable design choice among several, alongside the number of layers, the encoding gate, and the ansatz structure, and should test whether the expressive-power argument actually translates into a measurable accuracy gain on their own data before assuming it will.

A separate, non-forecasting QML system in this evidence set gives a fully specified example of what a small variational circuit's architecture looks like in practice, and its component list is directly reusable for a forecasting circuit. That circuit design uses 8 qubits, 2 data re-uploading layers, Angle Encoding via RY gates, a Hardware-Efficient Ansatz with Ring Entanglement (CNOT gates), and a local cost function (per-qubit PauliZ) [7]. Even though this architecture was built for sentiment classification, its component choices, encoding scheme, ansatz style, entanglement pattern, and readout, are the same kind of choices a builder must make for a forecasting QNN, and the parameter count it achieves is instructive: the quantum circuit has only 419 trainable parameters [7]. This is a strikingly small parameter budget compared to typical classical recurrent networks.

Underneath any variational quantum model is the broader idea of variational quantum simulation, which explains why small circuits with few parameters can still be trained usefully. The variational method avoids the exponential space problem by considering trial states from a physically motivated small subset of the exponentially large Hilbert space [6]. This is the theoretical basis for why a QNN with only a few hundred parameters, running on a handful of qubits, is not simply undersized: it is deliberately restricted to a tractable subspace, at the cost of not being able to represent every possible state. A builder should understand that this restriction is a design feature, not a bug, but that it also means the model's capacity is bounded by the choice of ansatz, and a poorly chosen ansatz can leave real structure in the data unmodeled no matter how it is trained.

Variational quantum circuits, the class of model used in both the traffic QNN and the financial hybrid classifier, rest on variational quantum simulation (VQS), a two-level computational scheme. VQS methods divide the problem into two levels, using the quantum processor to solve the core and classically intractable problem and leaving the relatively easy task to a classical computer [6]. In a hybrid forecasting pipeline, this division typically means the quantum circuit produces some intermediate representation or output, and a classical optimizer updates the circuit's parameters based on a loss computed classically. This division of labor is the reason the term 'hybrid' is used at all: neither the quantum nor the classical part alone performs the full computation.

The theory underlying VQS has been extended well beyond simple state preparation. One foundational paper introduces variational quantum simulation of mixed states under general stochastic evolution [6], and for variational simulation of imaginary time evolution, the same work extends it to the mixed state scenario and discusses variational Gibbs state preparation [6]. It also elaborates on the design of ansatz that is compatible with post-selection measurement and the implementation of the generalised variational algorithms with quantum circuits [6], and it completes the theory of variational quantum simulation of general real and imaginary time evolution, stating that it is applicable to near-term quantum hardware [6]. None of this theory is specific to forecasting, but it is the mathematical foundation that every ansatz-based QNN, including the traffic and financial models discussed here, ultimately relies on.

For a builder, the practical takeaway is narrower than the full theory: the ansatz (ring-entanglement, angle-encoding, per-qubit readout) used in the financial hybrid model [7] is one specific, small, physically motivated instance of the general variational framework [6]. Choosing an ansatz means choosing which small subset of the full quantum state space the model is allowed to explore, and that choice interacts with how many qubits and layers are available in simulation, since deeper or wider circuits are more expensive to simulate classically.

The theory also flags a hard ceiling that constrains any hybrid model regardless of ansatz choice: implementing a universal quantum computer requires the coherent and accurate control of millions of qubits, while state-of-the-art quantum hardwares can only accurately control tens of qubits [6]. A related observation reinforces this from a different angle: practical applications from quantum computers are still not feasible due to heavy noise and limited qubit count [5]. Taken together, these two claims explain why the research question is framed around simulation rather than real quantum hardware.

The strongest, most complete quantitative result in this evidence set for time-series forecasting on a real dataset comes from the renewable-energy comparison, and it favors the classical LSTM. The LSTM model achieved superior performance (R^2 = 0.9860) using a fixed test set and demonstrated strong generalizability under time-series cross-validation (Avg R^2 = 0.9847) [4]. Against this, the classical statistical baselines fared much worse on the same data: ARIMA(2,1,2) and SARIMA(2,1,2)(1,1,1,24) models captured basic temporal patterns but struggled with non-linear dynamics, achieving R^2 scores of -0.0008 and -0.1104, respectively [4]. These numbers were obtained on 87,648 hourly data points spanning 2014-2023 from the NASA POWER database [4], so the LSTM's advantage is documented on a large, real, decade-long dataset. No quantum-classical hybrid model was evaluated on this same dataset, so this result establishes only that LSTM strongly beats ARIMA/SARIMA on real energy data; it says nothing about how a quantum hybrid would fare here.

In the transport domain, the only reported result comparing a hybrid quantum-classical model against a fully connected classical setting points toward underperformance. The source states: in fully connected network settings, hybrid quantum-classical models consistently underperform, with median scores approx [1]. That sentence is truncated at the source and the specific figure it was meant to give is missing; it cannot be repeated as a usable number and should not be treated as a precise statistic. What can be used is the directional finding: the hybrid underperforms in this fully connected setting relative to the classical alternative in the Athens traffic case study [1]. This is a real counterweight to any assumption that quantum methods automatically help; in the one transport setting reported here, they did not, even though the precise magnitude is not citable.

Outside forecasting, the only complete four-way comparison in this evidence set is on a financial sentiment classification task, and it is instructive precisely because it is so fully specified. The Hybrid VQC (FinBERT frozen, PCA(8), Variational Quantum Circuit) achieves a test accuracy of 78.96% on a common test set of 1,383 samples [7]. Against this, the BiLSTM baseline achieves a test accuracy of 71.22% on the same common test set [7], Logistic Regression achieves a test accuracy of 70.28% on the same common test set [7], and FinBERT (fine-tuned) achieves a test accuracy of 82.14% on the same common test set [7]. All four numbers come from the same 1,383-sample test set, which makes this the cleanest apples-to-apples comparison in the entire evidence base, even though it is a classification task rather than a forecasting task.

The parameter efficiency of the winning hybrid model in that comparison is also fully reported. The Hybrid VQC uses only 419 parameters [7], and the paper states directly that the Hybrid VQC, using 419 parameters, outperforms both Logistic Regression and the BiLSTM (with 390K parameters) [7]. The paper's own interpretation is that the Hybrid VQC demonstrates the potential of quantum representations for NLP tasks in resource-constrained settings [7]. This is a real, measured, peer-comparable result, but it is a classification result on text, not a regression result on a real-valued time series, so it cannot be read as direct evidence that a similarly-sized hybrid circuit would beat an LSTM on a forecasting task.

Laid out side by side, the evidence describes three different comparison settings, and none of them is the one the research question asks for. The first is a real forecasting dataset with only classical models compared: LSTM against ARIMA and SARIMA on renewable-energy data [4]. The second is a real forecasting dataset with a hybrid model mentioned, but only in a fully connected setting where it underperforms, without a matched LSTM baseline reported in the same comparison [1]. The third is a real classification dataset with a full four-way comparison including a hybrid model, an LSTM variant, a linear baseline, and a transformer, but the task is sentiment classification, not time-series forecasting [7]. A builder should keep these three settings strictly separate: strong evidence in one does not transfer to another.

Where the transport paper does directly address hybrid models, the finding is cautionary rather than encouraging. The paper's own framing describes the work as a heuristic exploration of QML potential [1], not a claim that the approach already beats classical alternatives, and the one comparison available in that paper indicates underperformance for the hybrid approach in a fully connected setting, even though the exact figure attached to it is not usable as quoted [1]. This matches a broader theme visible across the evidence: even where hybrid or quantum methods are tested on real data, the results reported here do not show a case of a hybrid model straightforwardly beating a strong classical recurrent baseline on a forecasting task.

By contrast, in the one domain where a complete comparison exists, classification of financial headlines, the hybrid model does win against a recurrent baseline. The Hybrid VQC beats the BiLSTM (78.96% versus 71.22%) [7] and beats Logistic Regression (78.96% versus 70.28%) [7], though it loses to fine-tuned FinBERT (78.96% versus 82.14%) [7]. This shows that a small variational quantum circuit, layered on top of frozen FinBERT embeddings reduced by PCA, can outperform a bigger classical recurrent network on a specific classification task, using far fewer trainable parameters [7]. It does not show that the same architecture would win on a forecasting task, since the mechanisms of text classification differ substantially from the mechanisms of time-series regression.

The tooling landscape adds a further comparison dimension: the software ecosystem for building hybrid models is mature enough that assembling the missing forecasting comparison is now a matter of engineering rather than waiting for new theory. Qiskit ML is a high-level Python library that combines elements of quantum computing with traditional machine learning [8], and it interfaces with classical machine learning frameworks such as scikit-learn and Python numerical-core libraries like NumPy, enabling integration of classical and quantum machine learning techniques [8]. It also has functionality for integrating neural networks with PyTorch to support design, training, and inference of hybrid quantum-classical models [8]. Other tools such as MerLin are designed around systematic benchmarking and reproducibility [2], which is exactly the property needed to produce a trustworthy answer to the research question.

A builder assembling the missing comparison needs concrete building blocks, and Qiskit ML supplies most of them, though only the parts actually used below are worth listing. For a forecasting task with continuous-valued targets, neural-network-style models such as EstimatorQNN or SamplerQNN [8] are the natural fit, since they can be wired into a regression loss. These are trained via Qiskit ML's PyTorch integration, which supports design, training, and inference of hybrid quantum-classical models [8], alongside its scikit-learn and NumPy interfaces for classical preprocessing and evaluation [8].

On the classical side, the two reference architectures a builder needs are already fully specified in the evidence. The LSTM used in the renewable-energy study was trained and evaluated on 87,648 hourly data points across 2014-2023 [4], giving a concrete sense of the data volume needed for a fair classical baseline in an energy or similarly periodic domain. The BiLSTM used in the financial sentiment study has approximately 390K parameters [7], against the Hybrid VQC's 419 parameters [7], illustrating the scale of parameter-count difference a builder should expect between a small variational circuit and even a modest classical recurrent network.

For the quantum side, the fully specified circuit from the financial study is the most concrete implementation template available: 8 qubits, 2 data re-uploading layers, Angle Encoding via RY gates, a Hardware-Efficient Ansatz with Ring Entanglement using CNOT gates, and a local cost function using per-qubit PauliZ [7], with 419 trainable parameters in total [7] and 78.96% accuracy achieved on the stated test set [7]. Adapting it to forecasting would mean replacing the PCA(8)-reduced FinBERT embeddings [7] with a suitable fixed-length encoding of a time-series window, and replacing the classification readout with a regression readout, while keeping the qubit count, layer count, and ansatz structure as a documented starting configuration.

Data preparation is a real cost that should not be underestimated. Building the financial dataset alone required merging and deduplicating five sources to yield approximately 34.3k unique headlines [7], which shows that even a relatively contained NLP dataset needs substantial preprocessing work before model training begins. The renewable-energy study's 87,648 data points come from ten years of hourly records pulled from a single source, NASA POWER [4], which is a smaller preprocessing burden because the source is unified, but still requires careful handling of missing hours, timezones, and train/test splits across a decade. A builder should budget real time for data assembly and cleaning before any model, classical or quantum, is trained, since none of the reported accuracy or R^2 numbers include this cost.

The central limit of this evidence base is direct: no claim reports a controlled comparison of a trained quantum-classical hybrid forecasting model against a classical LSTM on the same real-world time-series dataset. The renewable-energy LSTM result [4] and the transport hybrid result [1] come from different papers, different datasets, and different model architectures, so they cannot be combined into a single finding. Any claim that a hybrid model 'beats' or 'loses to' LSTM specifically on a shared forecasting benchmark would be an inference beyond what the sources state, and this note has deliberately avoided making that inference.

A second limit concerns the transport paper's own reported hybrid result. The source sentence describing this result is truncated ('in fully connected network settings, hybrid quantum-classical models consistently underperform, with median scores approx') and the specific figure is missing, so it is flagged here as unusable as a quoted number, not restated as fact. The usable content is only the qualitative direction: at least one hybrid configuration underperformed in at least one fully connected classical-network setting on real Athens traffic data [1], and nothing stronger should be drawn from it.

A third limit concerns generalizing from the financial classification result to forecasting. The Hybrid VQC's win over BiLSTM and Logistic Regression [7] is a real, well-documented result, but it is a classification task built on frozen FinBERT embeddings reduced by PCA, not a raw time-series regression task. The mechanisms that let a small quantum circuit succeed here, a low-dimensional, pre-processed, semantically rich input space from a pretrained language model, may not exist in the same form for a raw numerical time series such as traffic counts or wind speed. This is a reason for caution, not a reason to dismiss the result; it simply cannot be transferred to forecasting without a fresh experiment.

Finally, the broader hardware context should temper any conclusion a builder draws from a single simulated experiment. Practical applications from quantum computers are still not feasible due to heavy noise and limited qubit count [5], and state-of-the-art quantum hardware can only accurately control tens of qubits against the millions needed for a universal quantum computer [6]. Photonic contributions currently account for approximately 6% of QML publications, with most being simulator-based [2], underscoring that most of the field, including any new forecasting experiment a builder runs, will necessarily be a simulation result. Any conclusion from a simulated hybrid-versus-LSTM forecasting experiment should be reported as exactly that: a simulation result, not evidence of a practical quantum computing advantage.

The following procedure lets a competent engineer assemble the missing comparison: a trained quantum-classical hybrid forecasting model against a classical LSTM baseline, on one real dataset, in simulation. Steps 1 to 3, 7 to 9, and 11 to 12 follow methods and numbers directly reported in the cited sources; steps 4 to 6 and 10 are the authors' own proposed design choices for adapting those methods to a forecasting task not covered by any single source.

1. Pick one real forecasting dataset with a documented classical baseline. The renewable-energy dataset used in the LSTM study is a strong default choice: ten years of hourly wind and solar data (2014-2023), 87,648 data points, from the NASA POWER database [4]. Using this dataset lets you compare directly against a documented LSTM result (R^2 = 0.9860 on a fixed test set, Avg R^2 = 0.9847 under time-series cross-validation) [4].
2. Reproduce the classical LSTM baseline first. Train an LSTM on the same data split and evaluate it with both a fixed test set and time-series cross-validation, matching the two evaluation protocols reported in the source [4]. If your reproduction is far from R^2 = 0.9860, fix that before touching the quantum side.
3. Also reproduce the ARIMA/SARIMA baselines as a sanity floor. ARIMA(2,1,2) and SARIMA(2,1,2)(1,1,1,24) achieved R^2 scores of -0.0008 and -0.1104 respectively on this dataset [4]. Any serious forecasting model should clear this floor easily.
4. Choose a quantum circuit architecture from the fully specified financial example, adapted for regression. Start from 8 qubits, 2 data re-uploading layers, Angle Encoding via RY gates, a Hardware-Efficient Ansatz with Ring Entanglement (CNOT gates), and a local cost function (per-qubit PauliZ) [7], which trained successfully with only 419 parameters [7] in a different task. Replace the classification readout with a regression readout suited to continuous R^2-style evaluation.
5. Select the software stack. Use Qiskit ML, choosing EstimatorQNN or SamplerQNN as the neural-network-style quantum model class [8], its PyTorch integration to build and train the hybrid model end to end [8], and its scikit-learn/NumPy interfaces for classical preprocessing and evaluation [8].
6. Design the classical-to-quantum encoding. Because the financial example reduced FinBERT embeddings to 8 dimensions via PCA before quantum encoding [7], design an analogous fixed-length numeric encoding of your time-series input window, matched to the 8-qubit angle-encoding scheme.
7. Train the hybrid model with a classical optimizer in the outer loop. This follows the general two-level VQS structure: the quantum processor (or simulator) handles the circuit evaluation, and a classical optimizer updates the trainable parameters based on a classically computed loss [6].
8. Evaluate on the same fixed test set and the same cross-validation protocol used for the LSTM. Report R^2 on the fixed test set and average R^2 under time-series cross-validation, exactly as done for the LSTM baseline [4].
9. Report parameter counts alongside accuracy, as the financial study does. State the hybrid model's parameter count next to the LSTM's, mirroring how the financial study reported 419 parameters for the Hybrid VQC against 390K for the BiLSTM [7].
10. Record simulation cost. Track wall-clock time and memory for simulating the quantum circuit at your chosen qubit count and depth, a direct consequence of the exponential Hilbert space the variational method is designed to avoid exploring in full [6].
11. Check the result against the transport finding. Compare your outcome to the reported underperformance direction of hybrid quantum-classical models in a fully connected setting on real traffic data [1], keeping in mind that the exact magnitude of that transport result is not citable.
12. Publish the full comparison table. Report LSTM, ARIMA, SARIMA, and hybrid QNN results together, with dataset size, split protocol, parameter counts, and simulation cost, following the level of completeness set by the financial study's four-way comparison on a common 1,383-sample test set [7].

for epoch in range(n_epochs):
    x_batch, y_batch = next(data_loader)
    x_encoded = classical_preprocess(x_batch)   # e.g. PCA to 8 dims
    q_out = quantum_circuit(x_encoded, theta)    # simulated on classical hardware
    y_pred = classical_readout(q_out)
    loss = mse(y_pred, y_batch)
    theta = classical_optimizer.step(loss, theta)
evaluate(model, fixed_test_set)
evaluate(model, time_series_cv_splits)