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Benchmarking Quantum and Classical Sequential Models for Urban Telecommunication Forecasting

Chi-Sheng Chen, Samuel Yen-Chi Chen, Yun-Cheng Tsai

arXiv:2508.04488v2quant-phcs.AI

TL;DR

The paper addresses limited evidence on quantum-inspired sequence models for urban telecommunication forecasting, evaluating five models on univariate SMS-in prediction across input lengths. Performance varies by architecture and sequence length: the classical LSTM remains competitive or superior overall, while quantum-model advantages are conditional.

  • Problem

    Incomplete and sparse data constrain multivariate modeling, and systematic comparisons of quantum-inspired and classical models across sequence lengths are limited for urban telecommunication forecasting.

    Source: §I · pp. 1–2

  • Method

    The study benchmarks an LSTM and four quantum-inspired models on next-step SMS-in forecasting for each grid cell across six historical input lengths.

    Source: §I · p. 1

  • Results

    Across sequence lengths, LSTM is competitive or superior overall; QLSTM improves on its baseline by about 0.4% in MAE and 1.5% in MSE at T = 4 and 8, while QASA and QRWKV lack consistent gains and QFWP stays within 2% of LSTM.

    Source: §VI · p. 5, B. Results and Analysis · p. 5

  • Takeaways & Limitations

    Model selection can be guided by sequence length, complexity constraints, and quantum capacity; quantum enhancements are not universally advantageous.

    Source: §VI · pp. 5–6

    The evaluation is limited to univariate SMS-in signals because incomplete or sparse entries across modalities constrain multivariate modeling.

    Source: §I · p. 1

Abstract

from arXiv · show

In this study, we evaluate the performance of classical and quantum-inspired sequential models in forecasting univariate time series of incoming SMS activity (SMS-in) using the Milan Telecommunication Activity Dataset. Due to data completeness limitations, we focus exclusively on the SMS-in signal for each spatial grid cell. We compare five models, LSTM (baseline), Quantum LSTM (QLSTM), Quantum Adaptive Self-Attention (QASA), Quantum Receptance Weighted Key-Value (QRWKV), and Quantum Fast Weight Programmers (QFWP), under varying input sequence lengths (4, 8, 12, 16, 32 and 64). All models are trained to predict the next 10-minute SMS-in value based solely on historical values within a given sequence window. Our findings indicate that different models exhibit varying sensitivities to sequence length, suggesting that quantum enhancements are not universally advantageous. Rather, the effectiveness of quantum modules is highly dependent on the specific task and architectural design, reflecting inherent trade-offs among model size, parameterization strategies, and temporal modeling capabilities.

I. INTRODUCTION

The paper benchmarks classical and quantum-inspired sequence models for urban telecommunication forecasting, focusing on SMS-in because incomplete and sparse data constrain multivariate modeling. It examines how model performance varies with sequence length and reports distinct strengths across quantum architectures.

I. INTRODUCTION

  • Quantum-inspired variants adapt different mechanisms: QLSTM adds quantum gates, QASA quantum-enhanced attention, QRWKV quantum operations, and QFWP input-conditioned fast weights.The paper frames these architectures as hybrids that integrate quantum principles into classical frameworks.Source: §I · p. 1
  • Sparse and incomplete entries across modalities limit multivariate modeling, while non-stationarity and spatial variation complicate forecasting urban telecommunication signals.The optimal input sequence length is also uncertain because models may respond differently to short- and long-term dependencies.Source: §I · p. 1
  • The benchmark compares a classical LSTM baseline with QASA, QLSTM, QRWKV, and QFWP for univariate next-step SMS-in forecasting across six input lengths.The lengths are 4, 8, 12, 16, 32, and 64; each grid cell is modeled from its own historical SMS-in values.Source: §I · p. 1
  • The study constructs an SMS-in benchmark and compares classical and quantum sequential models to assess robustness and sequence-length sensitivity under real-world data sparsity.Its stated contributions also include investigating how QASA, QRWKV, QFWP, and QLSTM capture short- or long-range dependencies under limited-data conditions.Source: §I · p. 2

A. Time Series Forecasting Models

The paper reviews classical forecasting and quantum-inspired sequence models, motivates their relevance across sectors and urban telecommunication, and introduces a fixed-window, one-step forecasting setup.

A. Time Series Forecasting Models

  • LSTMs are presented as benchmarks for sequence prediction, while Transformer variants use attention to capture global interactions in long-horizon forecasting.The passage also contrasts these deep-learning approaches with statistical methods that may struggle with nonlinear dependencies and non-stationary data.Source: A. Time Series Forecasting Models · p. 2

B. Quantum-Inspired Sequence Models

  • The reviewed quantum-inspired models include QLSTM, QRWKV, QASA, and QFWP, which respectively use quantum circuits, quantum operations, unitary-inspired attention, and input-conditioned fast weights.QFWP generates context-sensitive quantum-network parameters from fast weights computed as outer products of neural-network outputs.Source: B. Quantum-Inspired Sequence Models · p. 2

C. QML Cross-Sector Application

  • Prior QML applications in finance, energy, and transportation motivate hybrid quantum–classical sequence models for telecommunication forecasting.Source: C. QML Cross-Sector Application · p. 2

D. Telecommunication Activity Prediction

  • The Milan dataset supports studies of urban activity, but sparse and incomplete modalities have constrained multivariate telecommunication forecasting.The paper identifies a gap in benchmarking these quantum-inspired models against classical baselines on this dataset while varying input sequence lengths.Source: D. Telecommunication Activity Prediction · p. 2

III. METHODOLOGY

  • The four hybrid models use fixed-length inputs to predict the subsequent time step, forming a T-to-1 rather than sequence-to-sequence forecasting task.The specified window lengths are 4, 8, 12, 16, 32, and 64; each model encodes classical inputs, processes them with a parameterized quantum circuit, then measures and decodes the output.Source: §III · p. 3

A. Quantum Adaptive Self-Attention (QASA)

QASA constructs quantum equivalents of self-attention by deriving query, key, and value embeddings from the input with dedicated parameterized quantum circuits.

A. Quantum Adaptive Self-Attention (QASA)

B. Quantum Fast Weight Programmer (QFWP)

QFWP dynamically adapts parameterized quantum-circuit parameters through fast weights conditioned on each input vector.

B. Quantum Fast Weight Programmer (QFWP)

C. Quantum Receptance Weighted Key-Value (QRWKV)

QRWKV uses PQC-derived query, key, and value states to calculate attention over time, while QLSTM uses quantum circuits to compute LSTM gates. Both architectures combine quantum processing with temporal sequence modeling.

C. Quantum Receptance Weighted Key-Value (QRWKV)

  • At each time step, QRWKV uses PQC-derived query, key, and value states to introduce temporal recurrence into attention.Inputs are encoded into quantum amplitudes and evolved through multi-layer PQCs to compute attention weights; predictions are weighted sums over past value vectors.Source: C. Quantum Receptance Weighted… · p. 3

D. Quantum Long Short-Term Memory (QLSTM)

  • QLSTM computes forget, input, output, and candidate gates from the current input and previous hidden state using quantum circuits.Inputs are encoded with RY rotations and passed through variational layers; each gate is computed from measured Pauli-Z expectation values.Source: D. Quantum Long Short-Term Memory… · p. 3
  • QLSTM updates its cell state from the forget-gated prior cell state and input-gated candidate, then computes the hidden state from the output gate and cell state.The updates are c_t = f_t ⊙ c_(t−1) + i_t ⊙ g_t and h_t = o_t ⊙ tanh(c_t).Source: D. Quantum Long Short-Term Memory… · p. 3

IV. EXPERIMENTS

The experiments forecast the next SMS-in value from historical values in Milan grid cells, using data restricted to the more complete SMS-in channel. They compare a classical LSTM baseline with four quantum-inspired models and describe model-complexity categories.

A. Dataset and Preprocessing

  • The benchmark uses 10-minute Milan telecommunication activity and restricts modeling to SMS-in because it has higher completeness across grid cells.Active cells with sufficient time coverage are selected, and SMS-in values are normalized to [0, 1].Source: A. Dataset and Preprocessing · p. 3
  • Each sample uses a fixed-length sequence of past SMS-in values to predict the next value, with input lengths of 4, 8, 16, 32, or 64.The data are split chronologically into 70% training, 15% validation, and 15% test sets.Source: A. Dataset and Preprocessing · p. 3

B. Models Compared

  • The comparison includes a standard LSTM baseline and QLSTM, which computes LSTM gates with parameterized quantum circuits.QASA performs attention with PQC-derived embeddings, while QRWKV uses time-dependent memory and attention.Source: B. Models Compared · pp. 3–4
  • QFWP dynamically updates quantum neural-network parameters, and all five models take past values as input and produce a scalar forecast.The complexity table identifies columns for qubit counts, circuit layers, parameter totals, trainable parameters, estimated quantum and classical parameters, and their ratio.Source: B. Models Compared · p. 4, Table I · p. 4

C. Training Setup and Experiment Details

The paper describes common optimization and loss settings alongside implementation details for the models. It also reports a separate experimental setup with a stated test split and sequence lengths.

C. Training Setup and Experiment Details

  • Models use AdamW with learning rate 0.001, batch size 16, MSE training loss, and up to 50 epochs with early stopping based on validation loss.The implementation uses PyTorch or PennyLane.Source: C. Training Setup and Experiment Details · p. 4

D. Experimental Setup

  • The reported experimental setup uses AdamW at 1 × 10^-3, batch size 16, 50 epochs, MSE, sequence lengths 4, 8, 12, 16, 32, and 64, and a 20% test split.Input and output dimensions are both 1; models are implemented in PyTorch with PennyLane for quantum simulation and trained on CPU and GPU.Source: D. Experimental Setup · p. 4
  • The LSTM baseline has two unidirectional layers with 64 hidden units, while QASA combines an 8-qubit, 4-layer circuit with a 128-dimensional transformer encoder and four attention heads.QRWKV uses a 4-qubit, 2-layer circuit; QFWP uses a 2-layer circuit with 8, 10, 12, or 14 qubits; QLSTM uses four independent 5-qubit, 5-layer variational circuits.Source: D. Experimental Setup · p. 4

E. Evaluation Metrics

The evaluation section specifies that metrics are computed on held-out test data and averaged over five independent runs.

E. Evaluation Metrics

  • All metrics are computed on the held-out test set and averaged over five independent runs to account for training variance.The passage identifies y_i as the ground truth, ŷ_i as the prediction, and N as the number of test samples.Source: E. Evaluation Metrics · p. 4

A. Model Complexity Analysis

The section estimates quantum-versus-classical parameter allocation to compare model complexity, and reports architectures ranging from quantum-centric to classical-dominant.

A. Model Complexity Analysis

  • The complexity accounting separates core and auxiliary qubits and distinguishes total from trainable parameter counts.Source: A. Model Complexity Analysis · p. 4
  • Quantum-specific parameters are estimated from qubit count, quantum layers, and R = 3 gates per qubit per layer, then compared with classical parameters using γ_i.ε = 1 avoids division by zero.Source: A. Model Complexity Analysis · pp. 4–5
  • QFWP variants use 14 qubits and 2 quantum layers and are described as having relatively compact total parameter counts.The supplied passage does not give the total-count values.Source: A. Model Complexity Analysis · p. 5
  • QLSTM reaches γ_i = 20, while QASA (approximately 6×10^-5) and QRWKV (approximately 9×10^-6) are classical-dominant; QLSTM and QFWP are quantum-centric.QLSTM uses 5 qubits and 5 quantum layers; QASA has over 595K classical parameters.Source: A. Model Complexity Analysis · p. 5

B. Results and Analysis

The LSTM baseline is consistently competitive, while the quantum-inspired models show different performance patterns as input sequence length changes.

B. Results and Analysis

  • MAE = 1.034 and MSE = 4.561 are the LSTM averages, and it is best or second-best across lengths, with MSE falling from 4.69 to 4.41 as T grows.Source: B. Results and Analysis · p. 5
  • At T = 4 and 8, QLSTM beats the baseline by approximately 0.4% in MAE and 1.5% in MSE, but its error increases when T ≥ 12.Source: B. Results and Analysis · p. 5
  • QRWKV and QFWP underperform the baseline at every length, with average MAE exceeding it by 3.5% and 2.0%, respectively; both reach their lowest error at T = 8.Their errors increase as sequence length grows.Source: B. Results and Analysis · p. 5
  • QASA has the highest error and greatest sequence-length sensitivity, averaging approximately 13% higher MAE than the baseline.Its MAE rises from 1.1613 at T = 4 to 1.2004 at T = 16.Source: B. Results and Analysis · p. 5

VI. DISCUSSION AND CONCLUSION

Quantum enhancements are not uniformly beneficial: performance depends on architecture and sequence length, with trade-offs among model size, parameter composition, and temporal modeling capacity. Compact QLSTM and QFWP show promise, while the classical LSTM remains a strong baseline.

VI. DISCUSSION AND CONCLUSION

  • The classical LSTM remains competitive or superior across sequence lengths with minimal parameter overhead, and its MSE decreases as input length increases.TABLE III reports average MSE across models and sequence lengths.Source: §VI · p. 5, Table III · p. 6
  • QLSTM slightly outperforms LSTM at T = 4 and T = 8, but its advantage diminishes at longer sequence lengths.The authors attribute this likely to qubit-capacity and quantum-circuit-expressiveness limitations; its γ = 20 and minimal parameter footprint suggest potential for low-resource settings.Source: §VI · p. 5
  • QASA and QRWKV lack consistent advantages over LSTM on this univariate dataset, and their performance degrades with longer sequences.Both are dominated by classical components, with γ < 10^-4; the authors suggest careful architectural co-design or quantum-specific regularization may be needed.Source: §VI · p. 5
  • QFWP performs within 2% of LSTM while retaining high quantum contribution and relatively small parameter size.Fast weight programming dynamically updates quantum parameters and may suit non-stationary or rapidly changing environments.Source: §VI · p. 5
  • Quantum enhancements are not uniformly beneficial; their utility depends on task and architecture, with trade-offs among model size, parameter composition, and temporal modeling capacity.Compact QLSTM and QFWP show promise for capturing local sequence dynamics with fewer resources.Source: §VI · pp. 5–6
  • The study establishes performance baselines and model-selection guidance by sequence length, complexity constraints, and quantum capacity; future work includes multivariate forecasting and real quantum hardware evaluation.The authors also propose exploring quantum-aware learning objectives for improved stability and generalization.Source: §VI · p. 6
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