QLIF-CAST: Quantum Leaky-Integrate-and-Fire for Time-Series Weather Forecasting

Accurate and efficient time-series forecasting remains a challenging problem for both classical and quantum neural architectures, particularly in multivariate environmental settings. This work adapts the Quantum Leaky Integrate-and-Fire (QLIF) spiking neural network for time-series regression tasks, specifically short-term multivariate weather forecasting.

The gist: QLIFCAST achieves 15.4% lower MSE and 4.4% lower MAE compared to a parametermatched classical LIF baseline on a multivariate weather dataset, demonstrating that quantum neuronal dynamics reduce prediction error over classical equivalents while achieving up to 94% less training time than state-of-the-art quantum models like QLSTM and LSTM-QNN.

Model Architecture and Neuron Dynamics

The QLIF-CAST model is a hybrid recurrent architecture that encodes neuron excitation states as single-qubit quantum superpositions, driven by Rx rotation gates and T1 relaxation decay, embedded within a hybrid quantum-classical recurrent structure. The core innovation lies in the Quantum Leaky Integrate-and-Fire (QLIF) neuron model. Unlike standard variational quantum models, the QLIF circuit does not introduce separately trainable quantum gate parameters; instead, the rotation angles are computed directly from classical network outputs. This design choice preserves a simple quantum circuit structure that is easier to execute and analyze and avoids the additional optimization burden associated with trainable quantum parameters, making it closer in training complexity to a classical recurrent component.

The QLIF neuron model operates through several mechanisms:

1. State Encoding: The excitation probability α is encoded as a qubit rotation angle where α = sin2 (ϕ/2, ϕ = 2 arcsin√α).

2. Quantum Circuit Execution: At each timestep, every QLIF neuron executes a depth-2 single-qubit circuit (0⟩ → Rx(ϕ) → Rx(θinput) → Measure) yielding the updated excitation probability αnew = sin2 (ϕ + θinput/2).

3. Decay Mechanism: Without an input spike, the neuron undergoes quantum T1 relaxation, where the decay rate is defined by γ = -2 arcsinp(α · e−τ/T1)."

4. Input Integration and Spike Generation: The effective rotation angle θinput combines the learnable synaptic weight with the decay angle depending on whether a spike occurred in the previous step, governed by θinput = X · θ + (1 − X) · γ. A spike is emitted whenever the resulting excitation probability αnew exceeds the threshold of 0.75.

Hybrid Network Structure and Training Strategy

The QLIF-CAST model utilizes a seven-layer hybrid recurrent architecture that shares most layers with its classical counterpart, differing only in the neuronal update rule in Layer 2. The structure includes:

1. L1 - Feature Projection (TimeDistributed Dense layer).

2. L3 - Normalization (BatchNormalization followed by Dropout(0.2)).

3. L4 - Temporal Aggregation (an LSTM with 24 hidden units).

4. L5 & L6 - Regression Head Stages, consisting of a Dense layer (32 units) and another Dense layer (16 units), respectively.

5. L7 - Output Layer (a linear Dense layer producing the final forecast yˆ(t+1)).

The model is trained end-to-end via backpropagation with surrogate gradients for the non-differentiable spike operation in Layer 2. This surrogate gradient training resolves the issue where the Heaviside step function used to produce a binary spike has zero gradient almost everywhere and an undefined gradient at the threshold, by substituting a smooth, differentiable approximation, specifically using S˜(α) = 1/π arctan(πα) + 0.5, during backpropagation.

Evaluation Phases and Comparative Results

The study employs two distinct evaluation phases to characterize the model's performance trade-offs:

1. Phase 1 (Controlled Study): This phase compares QLIF-CAST against a parametermatched classical LIF baseline on the Weather History dataset (D1). The objective is to isolate the effect of quantum dynamics, showing that QLIF-CAST achieves MSE ↓ 15.4% MAE ↓ 4.4%, with lower error on variables with strong temporal structure like Temperature and Pressure.

2. Phase 2 (Comparative Analysis): This phase benchmarks QLIF-CAST against state-of-the-art quantum models, QLSTM and LSTM-QNN, on crossdomain benchmarks (D2 for Air Quality and D3 for Wind Speed).

Based on a meticulous review of the provided scientific paper, here are specific, actionable improvements for AI systems derived from the QLIF-CAST architecture:

The QLIF-CAST architecture offers three primary avenues for improvement in existing AI systems: enhancing predictive accuracy in continuous time-series regression, drastically reducing training latency/cost for real-time deployment, and enabling near-term quantum hardware utilization.

Here are the specific improvements and capabilities:

1. """Improve Continuous Multivariate Time-Series Regression Accuracy (Phase 1):

The system can achieve a measurable reduction in prediction error (MSE by 15.4%, MAE by 4.4%) over classical LIF baselines for complex, continuous multivariate forecasting tasks like weather prediction.

• Specific Capability: Superior modeling of variables with strong diurnal and long-range temporal structures (e.g., Temperature and Pressure) due to the quantum interference properties of the QLIF neuron compared to classical exponential decay models, leading to a more nuanced understanding of physical systems.

2. """Enable Ultra-Fast Training for Real-Time Systems (Phase 2):

The system can train recurrent models significantly faster than state-of-the-art quantum counterparts (QLSTM, LSTM-QNN).

• Specific Capability: Achieve training convergence in 26 epochs on air quality forecasting or 3.8 minutes on wind speed prediction, drastically reducing the computational cost and time required for retraining models on fresh sensor data compared to classical LSTMs (which require 100 epochs or 65 minutes). This makes the system viable for real-time, adaptive monitoring where frequent retraining is necessary.

3. """Bridge the Gap Between Quantum Advantage and Practical Deployment (Design Space Positioning):

The system can be strategically deployed in environments where training speed and hardware compatibility are more critical than achieving absolute peak predictive precision.

• Specific Capability: QLIF-CAST serves as a Pareto optimal choice for edge deployment, resource-constrained devices, or scenarios requiring near-term quantum hardware (NISQ). It offers a demonstrable quantum advantage over classical models without the prohibitive training complexity associated with deep variational quantum circuits.

4. """Validate and Deploy on Near-Term Quantum Hardware:

The system can be reliably executed on current Noisy Intermediate-Scale Quantum (NISQ) devices.

• Specific Capability: The depth-2, single-qubit circuit structure of QLIF-CAST is inherently resistant to the compounding gate errors found in deeper circuits (like QLSTM/LSTM-QNN). Hardware validation confirms a low average deviation (1.2%) on IBM Marrakesh, making it a proven architecture for immediate near-term quantum ML applications.

5. """Provide Robust, Generalized Cross-Domain Forecasting:

The system can be adapted to monitor and forecast across multiple distinct environmental domains without requiring core circuit modification.

• Specific Capability: The identical seven-layer architecture performs effectively across meteorological (weather), air quality (PM2.5), and wind energy benchmarks, proving the architectural generality of the QLIF-CAST design for diverse physical time-series data.

Accurate and efficient time-series forecasting remains a challenging problem for both classical and quantum neural architectures, particularly in multivariate environmental settings. This work adapts the Quantum Leaky Integrate-and-Fire (QLIF) spiking neural network for time-series regression tasks, specifically short-term multivariate weather forecasting. We extend QLIF beyond classification and demonstrate its applicability to continuous-valued prediction problems. The QLIF-CAST model encodes neuron excitation states as single-qubit quantum superpositions, driven by R x rotation gates and T1 relaxation decay, and is embedded within a hybrid quantum-classical recurrent architecture. We conduct two distinct evaluations. First, a controlled comparison against a parameter-matched classical LIF baseline on a multivariate weather dataset shows that QLIF-CAST achieves 15.4% lower MSE and 4.4% lower MAE, demonstrating that quantum neuronal dynamics reduce prediction error over classical equivalents. Second, a cross-domain comparative analysis with state-of-the-art quantum LSTM (QLSTM) and quantum neural network (QNN) models on air quality and wind speed benchmarks reveals that QLIF-CAST converges in up to 94% less training time, occupying a distinct position in the speed-error trade-off space. Hardware verification on IBM Marrakesh (156-qubit QPU) confirms reliable circuit execution with only 1.2% average deviation from simulation.