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Large-Scale Benchmarking of Quantum Neural Network Configurations for Financial Time Series Forecasting

Jack Waller, Xing Liang, Dimitrios Makris, Rajagopal Nilavalan

arXiv:2610.12148v1cs.LGquant-ph

TL;DR

Systematic comparisons of QNN configurations have concentrated on classification, with less attention to financial time-series regression. This study benchmarks 1,368 configurations on GBP/USD forecasting and finds that the best individual QNN achieves R^2 = 0.98495, while real-device noise constrains standalone deployment.

  • Problem

    Systematic QNN configuration comparisons have focused on classification, leaving financial time-series regression comparatively underexamined.

    Source: §1 · p. 2

  • Method

    The study interchanges QNN components across 1,368 configurations for GBP/USD forecasting, compares them with constrained and unconstrained BiLSTM baselines, and evaluates hardware noise.

    Source: §1 · p. 2, §4.1 · p. 10, §4.3 · p. 12

  • Results

    R^2 = 0.98495 for the best GBP/USD QNN using angle encoding, ansatz (j), 4 qubits, 8 layers, and classical MSE; ten of twelve ansatz configurations outperform the constrained BiLSTM baseline.

    Source: §7 · p. 29

  • Takeaways & Limitations

    Hardware noise remains a significant barrier to standalone QNN deployment, and gate choice, layer count, and ansatz structure warrant hardware-aware selection.

    Source: Hardware Noise and Near-Term Deployment · p. 28

    On IQM Emerald, only a small subset of low-layer configurations retains meaningful predictive capability, and a modified ansatz exceeds compiler capacity beyond four layers.

    Source: §4.4 · p. 14, Hardware Noise and Near-Term Deployment · p. 28

Abstract

from arXiv · show

Quantum machine learning, and quantum neural networks (QNNs) in particular, are advancing fields with growing potential. Although systematic comparisons of QNN configurations have been explored primarily for classification tasks, comparatively little attention has been given to regression problems, particularly financial time series forecasting. This study presents a large-scale systematic comparative evaluation of QNN component configurations for financial time series forecasting, using the GBP/USD spot exchange rate as a case study. A grid search across encoding methods, ansatz designs, qubit counts, layer depths, and cost functions yields 1,368 distinct model configurations, each evaluated in terms of prediction accuracy, computational cost, and convergence behaviour. The results reveal unique insights into how the choice of methods influences performance, such as that gate selection and arrangement are more critical to model success than raw parameter count, and that entanglement is a system-level property of the full circuit rather than solely at the ansatz level. The best-performing QNN configuration achieves an $R^2$ score of 0.985, outperforming a classical BiLSTM baseline. Additionally, the impact of real quantum hardware noise is assessed through execution on the IQM Emerald device, revealing that gate errors and decoherence represent a significant barrier to practical deployment, with gate selection and circuit depth identified as key determinants of hardware noise resilience. Overall, the findings provide practical architectural guidance for QNN design and establish a baseline characterisation of QNN noise sensitivity on near-term quantum devices.

1 Introduction

The paper examines QNNs for GBP/USD forecasting against a gap in systematic comparisons of QNN configurations for regression, especially financial time series. It evaluates a broad set of component combinations, compares QNNs with a classical baseline, and tests the effect of real-device noise.

1 Introduction

  • GBP/USD spot exchange-rate forecasting is the case study used to assess QNN capabilities on challenging financial time series.The paper notes that financial series have complex distributions and characteristics that make them difficult to predict.Source: §1 · p. 2
  • Systematic QNN configuration comparisons had focused on classification, leaving regression—particularly financial time series—unaddressed by those studies.The paper positions its broader circuit configurations and performance measures as an application-focused comparison for this setting.Source: §1 · p. 2
  • The study evaluates 1,368 QNN configurations by interchanging component methods and establishes a classical BiLSTM baseline.The configurations are analysed for performance patterns and effective forecasting designs.Source: §1 · p. 2
  • Best-performing QNN configurations show competitive and, in several cases, superior predictive accuracy to the classical baseline.The introduction also notes that real quantum hardware noise is assessed by executing models on the IQM Emerald device.Source: §1 · pp. 2–3
  • The evaluation also investigates how real quantum hardware noise affects model performance on the IQM Emerald device.The paper frames this as an examination of practical constraints in current quantum systems.Source: §1 · p. 3

2 Literature Review

Prior QNN work spans forecasting, other time-series applications, and systematic architecture comparisons, but comparative benchmarks largely concern classification. This study extends that comparison to financial regression and adds computational cost, convergence, and real-hardware noise assessment.

Quantum recurrent and convolutional architectures

  • QRNNs retain unmeasured qubits between circuit repetitions, while QLSTMs place quantum circuits within classical LSTM gates [37][38][39][40].A separate variant uses successive measurements to reduce state dimensionality for circuit-based convolutional processing [42].Source: §2 · p. 3

Financial time series

  • QNN-based financial forecasting has covered exchange rates, stock prices, and market indicators using hybrid, decomposition-ensemble, and recurrent approaches.The cited examples include USD/EUR exchange-rate prediction, Shenzhen Stock Exchange prices, hybrid financial regression [33], and QRNN stock-indicator forecasting [38].Source: §2 · p. 3

Other time-series applications

  • QNNs and QLSTMs have also been applied to renewable energy, environmental, physiological, and infrastructure time series.Examples include solar power [46][47], sea-drift trajectories, vital signs [50], and cloud workloads.Source: §2 · pp. 3–4

Configuration benchmarking

  • Prior configuration studies reported ansatz accuracy–cost trade-offs and ranked learning rate above entangling-gate choice in classification settings [34][35].A separate architecture comparison found architecture choice significantly influenced noise resilience.Source: §2 · p. 4

Literature gap

  • Prior systematic QNN configuration studies focused on classification, while this work extends comparison to financial forecasting and evaluates cost, convergence, and real-hardware noise.The earlier comparisons included ansatz configurations, circuit design choices, and noise robustness.Source: §2 · p. 4

3 Quantum Neural Network Architecture

The QNN architecture combines data encoding, variational circuit processing, measurement, and iterative parameter optimization. This section compares encoding schemes, ansatz designs, and cost functions, alongside qubit counts.

3.1 Structure of a QNN

  • QNNs encode classical inputs into quantum states, process them with a variational ansatz, then measure outputs and update circuit parameters until convergence.The cost compares measured outputs with targets, and gradients drive parameter updates.Source: §3.1 · pp. 4–5

3.2 Data Encoding

  • The study compares amplitude, angle, and circuit encoding, which trade off qubit efficiency, circuit complexity, and hardware practicality.Qubit count is also assessed as a factor affecting model behaviour.Source: §3.2 · p. 5, §3.1 · p. 5

Amplitude Encoding

  • Amplitude encoding maps a classical vector into quantum-state amplitudes, encoding 2^N values in N qubits with L2 normalization.Its data density advantage comes with circuit depth that grows as O(poly(N)), potentially limiting practicality at higher qubit counts.Source: Amplitude Encoding · pp. 5–6

Angle Encoding

  • Angle encoding uses one normalized data point to parameterize each qubit rotation, giving constant-depth encoding but requiring one qubit per input.Splitting inputs across circuit executions can reduce the qubit constraint at the cost of additional runs.Source: Angle Encoding · p. 6

Circuit Encoding

  • Circuit encoding uses a richer feature map, retaining single- and two-qubit interactions and repeating the encoder four times for forecasting.It encodes N points in N qubits, like angle encoding, but incurs greater depth and computational overhead.Source: Circuit Encoding · p. 6

3.3 Ansatz

  • The study evaluates twelve ansatz designs spanning expressibility, entangling capability, and computational complexity.The designs range from low-overhead nearest-neighbor connectivity to a fully connected, more resource-intensive topology; deeper and more connected circuits can increase noise sensitivity and execution time.Source: §3.3 · pp. 7, 9, Figure 2 · p. 8

3.4 Cost Function

  • Optimization minimizes a cost measuring prediction–target discrepancy, using either classical MSE after measurement or quantum-state fidelity.The forecasting setup measures the Pauli-Z expectation on the first qubit for the classical cost; the quantum cost compares the circuit’s terminal state with an encoded target state.Source: §3.4 · pp. 9–10

4 Methodology

The study evaluates QNN forecasting on daily GBP/USD data through a grid search of circuit configurations, compares the models with classical BiLSTM baselines, and tests selected circuits on noisy quantum hardware.

4.1 Data

  • The dataset contains 5,000 daily GBP/USD spot rates from 8 June 2005 to 19 March 2025, split chronologically into training, validation, and test sets.The 60/10/30 split uses 3,000 training, 500 validation, and 1,500 test samples.Source: §4.1 · p. 10

4.2 Experimental Design

  • The grid search varies five design dimensions across 1,368 QNN configurations, assessing prediction accuracy, training time, and convergence.The dimensions include qubit count, encoding, ansatz, layer count, and cost function; 12-qubit models use up to four layers due to computational constraints.Source: §4.2 · pp. 11–12

4.3 Classical Baseline

  • The classical BiLSTM comparison uses constrained and unconstrained architectures, whose best test R2 scores are 0.9529 and 0.9805, respectively.The constrained model uses 8-point non-overlapping windows; the unconstrained model uses a 50-point lookback with fully overlapping windows.Source: §4.3 · p. 12

4.4 Quantum Hardware Implementation

  • Hardware evaluation tests modified ansatz variants on a readout-noise simulator and IQM Emerald, with the latter adding gate errors and decoherence.Inference uses 1,024 shots per circuit; an additional modified ansatz (d) exceeded the compiler's capacity beyond four layers after non-native gates were decomposed.Source: §4.4 · pp. 13–14

5 Results

Across the evaluated QNN configurations, accuracy, training cost, and convergence varied with model design, while real-device execution revealed substantial hardware-noise effects. The strongest individual QNN forecast exceeded both BiLSTM baselines, but performance depended on encoding, ansatz, depth, qubit count, and cost function.

Model Complexity

  • Amplitude encoding had the best mean performance across encodings, while ansatz (h) had the best mean accuracy and (k) the worst.The five ansatz with the highest best-individual accuracy were (d), (e), (f), (h), and (j), with very similar high R2 scores.Source: Model Complexity · pp. 14–15, Table 4 · p. 15
  • R2 = 0.98495 was the best individual QNN result, exceeding the constrained BiLSTM (R2 = 0.9529) and unconstrained BiLSTM (R2 = 0.9805) baselines.It used angle encoding, ansatz (j), 4 qubits, 8 layers, and classical MSE; the best quantum model's MSE was 5.6693 × 10−5.Source: Figure 6 · p. 15, Model Complexity · p. 16
  • Increasing depth generally improved accuracy, but single-layer ansatz rarely converged under angle or circuit encoding, and qubit-count effects varied by encoding.Amplitude encoding performed best at four qubits; circuit encoding's convergence and accuracy declined as qubit count increased, while angle encoding showed no strong correlation.Source: Model Complexity · p. 16
  • 6 of the 9 models with R2 > 0.983 used classical cost, although quantum cost had better mean MSE (0.02956±0.00212 vs 0.05441±0.00649) and R2 (−6.810±0.559 vs −13.216±1.693).Cost-function effects also depended on encoding and qubit count: angle encoding favored quantum cost, while circuit encoding's preference reversed between four and ten qubits.Source: Model Complexity · pp. 16, 20

Computational Cost

  • Training time increased exponentially with qubit count and linearly with layer count; amplitude encoding was fastest, and quantum cost generally took longer than classical cost.Mean times were 50.48 ± 5.09 seconds for amplitude, 126.27 ± 13.45 for angle, and 132.21 ± 13.68 for circuit encoding.Source: Computational Cost · pp. 20–21

Time to convergence

  • The apparent decrease in mean convergence epoch with more qubits was confounded by poor models plateauing earlier than successful models.R2 < 0 models averaged 54.24 ± 1.72 epochs, compared with 85.22 ± 1.10 for models with R2 ∈[0.8, 1].Source: Time to convergence · pp. 21, 23

5.2 Impact of Quantum Hardware Noise on Accuracy

  • On IQM Emerald, shallow ansatz (j) configurations retained meaningful forecasting performance, reaching a best R2 of 0.77, while deeper circuits degraded in accuracy.The depth-related decline was also observed for ansatz (b) and (j); six-qubit configurations for these ansatz performed notably worse than corresponding configurations at other qubit counts.Source: §5.2 · pp. 24–25
  • Readout noise lowered R2 by about 0.06 on average, while IQM Emerald execution lowered it by about 1.25 on average relative to noiseless simulation.The real-device decline reflects gate errors and decoherence beyond readout noise alone.Source: §5.2 · p. 24, Figure 18 · p. 24, Figure 19 · p. 25

6 Discussion

The discussion finds that well-chosen QNN configurations can outperform constrained and unconstrained BiLSTM comparisons, while gate composition and circuit-wide entanglement shape model behaviour. On IQM Emerald, gate errors and decoherence constrain standalone deployment.

Ansatz Design and Circuit Composition

  • 10 of 12 ansatz configurations exceeded constrained BiLSTM (R2 = 0.9529), and the eight best also exceeded unconstrained BiLSTM (R2 = 0.9805).The unconstrained BiLSTM used a substantially longer lookback window and fully overlapping windows.Source: Ansatz Design and Circuit Composition · pp. 25–26
  • Gate choice and arrangement mattered more than raw parameter count; all top four ansatz by mean accuracy included single-qubit parameterised rotations.The comparison of ansatz (a) and (i) links the rotations to better performance on both reported metrics.Source: Ansatz Design and Circuit Composition · p. 26
  • Entanglement is a system-level property: encoding can compensate for limited ansatz entanglement in some settings, but not for its complete absence.Amplitude and circuit encoding could support convergence with minimally entangling ansatz under classical MSE; the pattern did not arise under a quantum cost function.Source: Ansatz Design and Circuit Composition · pp. 26–27

Optimisation Landscape and Cost Function Trade-offs

  • Barren plateaus may partly explain qubit-scaling declines and cost-function trade-offs, but this interpretation remains speculative.Their possible stronger effect with circuit encoding and the proposed loss-landscape explanation require further investigation.Source: Optimisation Landscape and Cost… · p. 27

Computational Considerations

  • Training time rose linearly with circuit depth and exponentially with qubit count, while low apparent convergence epochs often reflected failed runs, not faster learning.The cost-function epoch comparison was limited to largely converged 8-layer models.Source: Computational Considerations · p. 27

Hardware Noise and Near-Term Deployment

  • On IQM Emerald, gate errors and decoherence outweighed readout noise; deeper layers compounded two-qubit errors, limiting meaningful prediction to a small subset of low-layer standalone configurations.Ansatz (k) was less noise-sensitive but predicted poorly, while CRX decomposition made ansatz (b) deeper despite its apparently lower circuit depth.Source: Hardware Noise and Near-Term Deployment · pp. 27–28

7 Conclusions and Future Work

The study benchmarks QNN component choices for GBP/USD forecasting and reports a best individual model that exceeds BiLSTM comparisons. It concludes that circuit design offers practical guidance, while data scale, barren plateaus, and current hardware constraints remain areas for further research.

Conclusions

  • R2 = 0.98495 was achieved by the best individual GBP/USD model, using angle encoding, ansatz (j), 4 qubits, 8 layers, and classical MSE.Source: §7 · p. 29
  • Ten of twelve ansatz configurations exceeded the constrained BiLSTM baseline, and the eight best-performing configurations also exceeded an unconstrained BiLSTM.Source: §7 · p. 29
  • Gate choice and arrangement mattered more than raw parameter count, additional layers tended to improve performance, and entanglement depended on the full circuit.Source: §7 · p. 29
  • On IQM Emerald, gate errors and decoherence substantially degraded accuracy, establishing a baseline for hardware noise sensitivity and hardware-aware QNN design.Source: §7 · p. 29

Future Work

  • Large-scale datasets remain challenging under current NISQ constraints, and substantial further research is needed before QNNs reach practical utility comparable to classical models.Source: §7 · p. 29
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