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Q-PhotoMarket: A Design Space Exploration Framework for Photonic Hybrid Quantum Neural Networks in Financial Market Prediction

Alberto Marchisio, Hanzalah Mohamed Siraj, Muhammad Kashif, Nouhaila Innan, Muhammad Shafique

arXiv:2610.09641v1quant-phcs.LG

TL;DR

Photonic HQNN studies often examine a single architecture, leaving the effect of photonic design choices on financial prediction unclear. Q-PhotoMarket explores more than 5,000 configurations across multiple markets; results show that architectural choices influence predictive performance and recurring topologies appear among the strongest designs.

  • Problem

    Photonic QML studies typically evaluate a single manually designed architecture, limiting understanding of how photonic design choices influence financial prediction.

    Source: §I · p. 1

  • Method

    Q-PhotoMarket systematically explores photonic HQNN design dimensions across financial markets, combining exhaustive exploration with Bayesian optimization.

    Source: §I · pp. 1–2

  • Results

    Across more than 5,000 configurations, architectural choices consistently influence predictive performance, with Clements Mesh and sometimes Simple and Ring NN recurring among the highest-performing designs.

    Source: F. Discussion · p. 8

  • Takeaways & Limitations

    The framework provides a benchmark and methodology for studying how photonic architecture choices influence learning performance in financial prediction.

    Source: §V · p. 8

    Experiments use differentiable photonic simulation and daily prediction on three financial datasets, with exploration limited to the investigated architectures, measurements, and encodings.

    Source: F. Discussion · p. 8

Abstract

from arXiv · show

Photonic quantum computing has recently emerged as a promising platform for hybrid quantum machine learning due to its native realization of linear-optical circuits and the computational complexity of boson sampling. However, despite growing interest in quantum methods for finance, the influence of photonic circuit design choices on predictive performance remains largely unexplored. Existing studies typically evaluate a single architecture, leaving the broader photonic design space unexamined. In this work, we present Q-PhotoMarket, a systematic design space exploration (DSE) framework for photonic hybrid quantum neural networks (HQNNs) applied to financial market prediction. We explore over 5,000 valid photonic configurations spanning input photon states, circuit architectures, entangling models, and measurement strategies across their compatible computation spaces, for U.S., Indian, and cryptocurrency markets. To improve search efficiency, the exhaustive exploration is complemented with Bayesian optimization. We further incorporate threshold calibration and prediction-collapse diagnostics to enable reliable evaluation under increasingly imbalanced return thresholds. Experimental results show that systematic exploration of more than 5,000 photonic HQNN configurations reveals consistent architectural patterns across financial markets, identifies robust high-performing designs, and demonstrates competitive performance relative to classical machine learning baselines.

I. INTRODUCTION

Photonic HQNN studies often use a single manually designed architecture, leaving the effects of design choices on financial prediction unclear. Q-PhotoMarket explores this design space, where AUC varies broadly across configurations and markets.

I. INTRODUCTION

  • Prior photonic HQNN studies typically use single manually designed architectures, [9], leaving the effects of their richer design choices largely unexplored.This gap matters because gate-based HQNN performance has shown sensitivity to circuit design.Source: §I · p. 1
  • AUC distributions are broad across the three markets, with medians near random-ranking but notably higher values for the best configurations.The spread suggests predictive performance is sensitive to photonic design choices, so a manually selected architecture may give a misleading view of HQNN capability.Source: §I · p. 1, Figure 1 · p. 1
  • Financial prediction is a challenging setting with weak signals, non-stationarity, and severe class imbalance; finance QML studies also typically use fixed architectures,.Classical approaches generally achieve only modest improvements under rigorous walk-forward evaluation.Source: §I · p. 1
  • Q-PhotoMarket systematically explores photonic HQNN design dimensions across financial markets and return thresholds, combining exhaustive exploration with Bayesian optimization.The work also aims to provide empirical insights into design effects and a reproducible benchmark for photonic QML.Source: §I · pp. 1–2

II. BACKGROUND AND RELATED WORK

The paper situates photonic HQNNs within hybrid quantum learning and motivates systematic exploration of their rich design space. Q-PhotoMarket evaluates market prediction using a leakage-safe, multi-market framework.

A. Photonic HQNNs

  • Photonic HQNNs encode information in bosonic modes and process it with trainable linear-optical circuits; differentiable simulators support their development and evaluation, [7].Beam splitters, phase shifters, and interferometers are common circuit components, and universal decompositions such as Reck and Clements realize arbitrary unitary transformations.Source: A. Photonic HQNNs · p. 2

B. Design Space Exploration in HQNNs

  • Photonic HQNN research typically evaluates one manually designed architecture, limiting understanding of how individual design choices affect performance.This contrasts with systematic DSE in gate-based HQNNs, which seeks architectures balancing expressivity, trainability, and hardware efficiency,,.Source: B. Design Space Exploration in HQNNs · p. 2

III. Q-PHOTOMARKET FRAMEWORK

  • Q-PhotoMarket explores four photonic design dimensions across U.S. equities, Indian equities, and cryptocurrencies, with computation space determined by measurement strategy.Its four stages are leakage-safe dataset construction, photonic HQNN exploration, unified evaluation, and Bayesian optimization to refine promising configurations.Source: §III · p. 2

A. Problem Formulation

  • The task is binary next-day return-direction classification at thresholds τ = 0, 0.5%, and 1.0%, with larger thresholds producing increasingly imbalanced classes.An expanding-window walk-forward protocol keeps each validation window after its training window to prevent look-ahead bias.Source: A. Problem Formulation · p. 2

1) Data Acquisition and Feature Engineering

  • Daily OHLCV data from 2018–2025 yield 23 engineered features, but photonic mode constraints limit experiments to 16 price-derived features and exclude external contextual signals.The feature set spans returns and momentum, volatility and risk, technical indicators, liquidity and microstructure, and price structure.Source: 1) Data Acquisition and Feature… · p. 2

2) Label Construction

Raising the return threshold reduces positive-class prevalence, while expanding-window walk-forward validation preserves temporal order and guards against look-ahead bias.

2) Label Construction

  • Positive-class prevalence falls from approximately 50% at τ = 0 to 20–34% at τ = 1%, as increasing thresholds induce greater label imbalance.Labels are generated independently for each threshold from the forward return.Source: 2) Label Construction · p. 2

3) Walk-Forward Cross-Validation

  • Training windows grow monotonically across five walk-forward folds, and each validation window follows its corresponding training window.The minimum training fraction is 0.5; the protocol is designed to respect temporal ordering and prevent look-ahead bias.Source: 3) Walk-Forward Cross-Validation · pp. 2–3

4) Dataset and Cross-Market Feature-Space Analysis

The study compares engineered market feature spaces and explores photonic architectures across compatible computation spaces. The feature spaces overlap but remain distinguishable, and the explored design spans multiple photon states and circuit topologies.

4) Dataset and Cross-Market Feature-Space Analysis

  • The three engineered market feature spaces overlap yet remain distinguishable, suggesting shared structure for cross-market comparisons alongside market-specific characteristics.The t-SNE visualization is a qualitative analysis of the engineered feature spaces.Source: 4) Dataset and Cross-Market… · p. 3

C. Photonic HQNN Architecture and Design Space

  • Q-PhotoMarket uses a differentiable photonic simulation with a trainable QuantumLayer and classical MLP head, exploring input state, circuit architecture, entangling model, and measurement strategy.The number of modes is fixed at nfeatures + 1, with nfeatures = 16; the measurement strategy determines the compatible computation space.Source: C. Photonic HQNN Architecture and… · p. 3, Table I · p. 3

1) Input Photon State

  • Four input photon-state configurations are considered: alternating, bunched, pair-bunched, and thermal-like occupations.These choices specify the initial photon occupation used to encode classical features into the photonic Hilbert space.Source: 1) Input Photon State · p. 3

2) Photonic Circuit Architecture

  • Five linear-optical topologies are explored: Simple, Ring NN, Clements Mesh, Phase-only, and Permuted Ring.The Clements Mesh is a universal rectangular interferometer providing maximal expressivity; the Phase-only network has no beamsplitter entanglement.Source: 2) Photonic Circuit Architecture · p. 3

3) Entangling Model

The design space includes two entangling primitives and five measurement strategies, with valid measurement combinations determining the computation space.

3) Entangling Model

  • MZI and Bell are the two evaluated entangling primitives; Bell is described as generating stronger inter-mode correlations.MZI is the canonical two-mode entangling unit.Source: 3) Entangling Model · p. 4

4) Measurement Strategy

  • Five strategies extract classical representations: Fock, unbunched, and dual-rail probabilities, plus mode expectations and mode correlations.Fock probabilities are restricted to at most four modes because of memory requirements.Source: 4) Measurement Strategy · p. 4
  • Invalid combinations are discarded, and the selected measurement strategy determines the associated computation space.Examples include pairing non-binary input states with unbunched or dual-rail probabilities.Source: 4) Measurement Strategy · p. 4

D. Experimental Protocol

The protocol trains HQNNs uniformly, handles threshold-driven imbalance through weighting and validation-based calibration, and monitors prediction collapse.

1) HQNN Model Training

  • All configurations use Adam and binary cross-entropy, with 8 Stage 1 epochs and 20 Stage 2 epochs.Training uses batch size 128 and 100 measurement shots per circuit execution; optional cosine annealing and validation-AUC early stopping are supported.Source: 1) HQNN Model Training · p. 4

2) Class Imbalance Handling and Threshold Calibration

  • For τ > 0, inverse-frequency weighting addresses imbalance; S&P 500 and NIFTY 50 favor balanced weighting, while cryptocurrency datasets favor none.Thresholds are calibrated on the validation fold by maximizing MCC, F1, or balanced accuracy.Source: 2) Class Imbalance Handling and… · p. 4

3) Prediction Collapse Diagnostics

  • Calibrated thresholds recover meaningful positive prediction rates across operating points, while collapse becomes more frequent as return thresholds become stricter.The diagnostic records the calibrated threshold, its objective, and PPR, and flags PPR outside [0.02, 0.98].Source: Figure 4 · p. 4, 3) Prediction Collapse Diagnostics · p. 4

E. Bayesian Optimization

Bayesian optimization searches the photonic design space with a TPE sampler, then refines promising configurations and incorporates prior sweep evidence.

E. Bayesian Optimization

1) Stage 1: TPE-Guided Search

  • Stage 1 ranks candidates by weighted AUC, F1, and GPS, subtracting a collapse penalty when PPR falls outside [0.05, 0.95].A resource guardrail skips configurations above a heuristic cost threshold, and a median pruner terminates unpromising trials early.Source: 1) Stage 1: TPE-Guided Search · p. 4

2) Stage 2: Local Refinement and Warm-Starting

  • Stage 2 seeds local dense refinement with top-k configurations and can warm-start from prior grid and confirm-run evidence.Warm-start rows are ranked by AUC and filtered to respect mode and shot constraints.Source: 2) Stage 2: Local Refinement and… · p. 4

3) Optimization Protocol

  • BO runs independent Optuna studies per market, with 150 trials per shard and 30 random startup trials before TPE activation.Studies are merged for parameter-importance and convergence analyses.Source: 3) Optimization Protocol · pp. 4–5

F. Performance Evaluation

Performance evaluation emphasizes metrics suited to imbalanced classification and supplements them with composite scores for unified ranking.

1) Primary Metrics

  • Evaluation reports accuracy, F1-score, MCC, AUC, and average precision; MCC accounts for all confusion-matrix elements, and balanced accuracy averages TPR and TNR.Increasing return thresholds produce progressively imbalanced tasks, making raw accuracy alone insufficient.Source: 1) Primary Metrics · p. 5

2) Composite Metrics

  • Four GPS variants use harmonic means of complementary metric subsets to provide unified rankings emphasizing different performance trade-offs.AccCV denotes mean walk-forward cross-validation accuracy.Source: 2) Composite Metrics · p. 5

3) Finance-Specific Metrics

The evaluation combines finance-specific measures and classical baselines with a broad photonic design-space screening. Results show that topology and measurement strategy have greater influence on performance than input photon states or entangling primitives.

3) Finance-Specific Metrics

  • Pseudo-Sharpe summarizes predicted-positive returns relative to their variability, while magnitude-weighted accuracy gives greater weight to correct predictions on larger market movements.The baselines are majority-class classification, logistic regression, and a shallow multilayer perceptron; experiments also record calibrated thresholds, prediction rates, probabilities, and collapse diagnostics.Source: 3) Finance-Specific Metrics · p. 5, 4) Baselines and Diagnostic Outputs · p. 5

A. Overall Design Space Exploration

  • Across markets, Clements Mesh/Simple architectures and Fock-probability measurements generally yield higher mean AUC at τ = 1%; screening covers approximately 1,080 configurations per market.Figure 5 reports mean AUC at the most challenging threshold, τ = 1%.Source: Figure 5 · p. 5, A. Overall Design Space Exploration · p. 5

B. Influence of Photonic Design Choices

  • Topology and measurement matter most: Clements Mesh leads architecture results, input states have modest influence, entangling models overlap, and measurement winners vary by market.Fock-basis probability measurements perform strongly on S&P 500 and NIFTY 50, while correlation-based measurements become more competitive for crypto.Source: B. Influence of Photonic Design Choices · pp. 5–6

C. Cross-Market and Threshold Sensitivity

Increasing return thresholds improves mean and best AUC across the three markets, despite greater class imbalance. Multi-fold evaluation and recurring high-ranking architectures provide additional checks on shortlisted designs.

D. Configuration Selection and Bayesian Refinement

  • Phase 2 training consistently improves shortlisted configurations’ median AUC while fold variance remains comparable to Phase 1.Figure 10 compares fold-wise AUC distributions across the two phases.Source: D. Configuration Selection and… · p. 6
  • The best reported Phase 2 designs use Simple/Bell/Fock-probability for S&P 500 (mean AUC 0.528 ± 0.019) and Clements Mesh/MZI/Fock for NIFTY 50 (0.514 ± 0.028).Clements Mesh, Ring NN, and Simple architectures also recur among the highest-ranked configurations across metrics and markets.Source: D. Configuration Selection and… · p. 6

C. Cross-Market and Threshold Sensitivity

  • Mean AUC rises from 0.500 to 0.528 for S&P 500, 0.499 to 0.517 for NIFTY 50, and 0.500 to 0.510 for cryptocurrencies as τ increases from 0 to 1%.The passage attributes the pattern to more discriminative tasks focused on economically significant price movements, despite increasing class imbalance.Source: C. Cross-Market and Threshold… · p. 6, Figure 9 · p. 7

E. Comparison with Classical Baselines

The best photonic HQNN consistently beats the majority baseline and performs competitively against conventional machine-learning models. The discussion emphasizes systematic design-space characterization and notes limits in simulation, prediction setting, datasets, and explored designs.

E. Comparison with Classical Baselines

  • Across evaluated markets and thresholds, the photonic HQNN consistently outperforms the majority baseline and remains competitive with conventional machine-learning models.Improvements over classical neural networks are described as modest, with the performance gap more apparent at higher return thresholds.Source: E. Comparison with Classical Baselines · p. 7, Figure 11 · p. 8

F. Discussion

  • Across more than 5,000 configurations, topology and measurement strategy contribute larger performance variations than input photon states or entangling primitives.Clements Mesh, and in several cases Simple and Ring NN, recur among high-performing configurations across markets and metrics.Source: F. Discussion · p. 8
  • Higher return thresholds generally improve AUC despite stronger class imbalance, while increasing the risk of prediction collapse.The discussion emphasizes calibration-aware evaluation and imbalance-sensitive metrics for this setting.Source: F. Discussion · p. 8
  • Experiments use differentiable photonic simulation for daily prediction on three financial datasets, and cover only the investigated topologies, measurements, and encoding schemes.Future work is proposed on larger architectures, hardware-aware optimization, real-device execution, and additional applications.Source: F. Discussion · p. 8

V. CONCLUSION

  • Q-PhotoMarket is presented as a benchmark and foundation for automated photonic architecture optimization and application-driven design-space exploration across QML domains.The framework jointly explores photonic design dimensions under a unified evaluation protocol.Source: §V · p. 8
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