QRC SUSA: novel quantum-inspired models for financial volatility forecasts over strong classical baselines.

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Challenge submission

Team / organization	Monodromy
Members	Aliaksei Kaliutau
Project	QRC SUSA: Susceptible Architectures for Regime-Conditional Volatility Forecasting
Challenge	qBraid, MITRE & JonesTrading - Global Industry Challenge 2026
Track	Track A: Financial Volatility Prediction
Primary task	Forecast five-trading-day variance and identify transitions among calm, onset, recovery, and persistent-stress regimes

The contribution

We propose a novel class of architectures for QRC.

A conventional reservoir is usually selected for memory or nonlinear expressivity. SUSA instead learns from a controlled response contrast: the same input is propagated through two matched dynamical systems that differ by their inner structure. The difference in response or behaviour of signal propagating through those two reservoirs is a structural-susceptibility representation.

The project implements this idea twice:

• a quantum-inspired version with complex recurrent nodes, directional transport, open/ring counterfactuals, and a small classical QLIKE readout;
• a quantum realization with interacting qubits, repeated RY/RZ input encoding, coherent RXX/RYY interactions, optional CPTP transfer and damping, and Pauli-observable readout.

Both variants preserve the same forecasting contract: a reliable AR-Ridge anchor predicts the persistent component, while SUSA learns only a bounded residual correction. A phase-conditioned mixture of experts can interpret the same susceptibility features differently during calm, onset, recovery, and persistent-stress states.

Name conventions for further brevity:

• SC-RC (Structural-Contrast Reservoir Computing)
• SC-OSQRC (Structural-Contrast Open-System Quantum Reservoir Computing)
• PHASE-RC-MoE (Phase-Conditioned Reservoir Mixture of Experts)
• PHASE-OSQRC-MoE (Phase-Conditioned Open-System Quantum Reservoir Mixture of Experts)

Core hypothesis: weak transition information that is difficult to read directly may become easier to detect after a matched structural perturbation exposes how the encoded path responds to a boundary change.

The accompanying write-up contains the full motivation, literature, equations, and statistical analysis.

We published an extended supplementary paper https://arxiv.org/abs/2607.22491, with more details, theory and analysis.

This README focuses on technical architecture, execution, and reproducibility.

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Architecture at a glance

Rubric-level specification

Component	Implementation
Reservoir structure	Two fixed, matched reservoirs: an open nearest-neighbor chain and a periodic ring with the closing edge added.
Quantum unitary / dynamics	Repeated local RY/RZ encoding, fixed random input and phase masks, local RZ fields, and RXX/RYY interactions on reservoir edges. The open-system variant adds directional CPTP transfer and amplitude damping.
Input encoding	One causal log-variance observation is encoded at every time step on every node/qubit; the benchmark uses a 12-observation sequence.
Readout	Open/ring observables, signed contrast, normalized contrast, low-rank projection, and a bounded classical correction optimized directly under QLIKE.
Measured observables	Local Z populations; adjacent XX, YY, XY, and YX correlations; directed-current proxies; boundary imbalance; spatial concentration; entropy-like and temporal summaries.
Memory	The reservoir state evolves across the full input window. Dissipation supplies fading memory in the open-system model; no trainable recurrent weights are required.
Hybrid integration	forecast = AR-Ridge anchor + bounded SUSA correction. The MoE model combines four phase-specialized corrections with a classical gate.
Trainable part	Only the low-capacity classical readout, low-rank projection, and optional phase gate/experts. Reservoir parameters are fixed for each candidate.

Suitability for volatility forecasting

Volatility is persistent, heavy-tailed, regime-dependent, and low signal-to-noise. SUSA separates these difficulties rather than asking one nonlinear model to solve all of them:

1. the AR-Ridge anchor handles persistence;
2. open-versus-ring response differences expose path-dependent structural sensitivity;
3. the phase gate separates calm, onset, recovery, and persistent stress;
4. the bounded correction limits damage when residual signal is weak;
5. the quantum realization provides a richer family of coherence and correlation responses while preserving the same statistical head and evaluation protocol.

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Current results

The current benchmark covers 16 U.S. equity and ETF series, 3 disjoint chronological folds, a 12-day input window, and a 5-day variance horizon. Lower QLIKE is better.

Performance is heterogeneous across assets, and the cross-market average difference from GARCH is often statistically inconclusive. However, on some equities models demonstrated stable improvements over all baselines: IWM and XLP Another strong practical result is complementarity: SUSA can add a bounded, non-redundant signal to a strong classical forecast.

Pure quantum SUSA models demonstrated lower performance than quantum-inspired ones, still beating the AR baseline, but lagging behind GARCH.

Result	Held-out evidence	Interpretation
IWM	ΔQLIKE vs AR −0.070, 95% CI [−0.107, −0.033]	Significant improvement across the held-out folds.
XLP	ΔQLIKE vs AR −0.098, 95% CI [−0.146, −0.049]	Significant improvement across the held-out folds.
Quantum-inspired SUSA + HARQ	Mean gain over the better member 0.0116; win share 75.0%; DM p < 0.001	SUSA extracts information complementary to domain-specific volatility features.
Quantum SUSA-MoE + HARQ	Mean gain 0.0114; win share 79.2%; DM p < 0.001	The quantum feature branch also contributes complementary forecasts.

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Quick start

1. Launch on qBraid

Start a large instance at qBraid, ideally 8 CPU or more. Our benchmark code automatically splits the workload among cores. However, even on large machine it will take 20-30 min to reproduce the full 16-symbol benchmark.

Click Launch on qBraid at the top of this page. In the cloned repository, open a terminal and run from the project folder:

pip install -e .
pip install -e '.[quantum]'

To validate that the installation is correct, run the command that lists supported models in our benchmark:

qrc-run list-models

Python 3.12 is the reference environment.

2. Reproduce the full 16-symbol benchmark

scripts/run_all_experiments.sh

This command runs four classical baselines, two quantum-inspired SUSA models, two Qiskit SUSA models, and then collects all results. It prints stage boundaries, an overall progress bar with ETA, and a final success or error message (if there are failures).

3. Visualise all results

Launch the analytical notebook notebooks/qrc_results_publication_analysis_merged.ipynb and run all cells to generate charts, tables and other analytics

Data modeling strategy

Item	Benchmark choice
Source	Public daily OHLCV from Yahoo; deterministic synthetic data is available for offline tests only.
Panel	SPY, QQQ, IWM, XLB, XLE, XLF, XLI, XLK, XLP, XLU, XLV, XLY, AAPL, MSFT, JPM, NVDA.
Date range	2006-01-01 through fixed cutoff 2026-07-01.
Input	Previous 12 causal log-variance observations.
Target	Mean variance over the next 5 observations.
Regime target	Calm, onset, recovery, or persistent stress, aligned to the forecast origin.
Features	Close-to-close returns, causal realized-variance proxies, HAR horizons, quarticity/stress proxies, drawdown, volatility-of-volatility, slope, and curvature.
Selection	Candidate fit on training; hyperparameter selection on validation; final refit on training + validation; test opened once.
Leakage controls	Trailing features only, origin-aligned predictors, training-only standardization/thresholds, purge gaps, disjoint outer folds, hash-verified inputs.
Primary metric	QLIKE.
Secondary metrics	RMSE/MAE in log variance, ROC-AUC, PR-AUC, F1, Brier score, calibration error, underprediction tails, moving-block bootstrap CI, and HAC/Diebold–Mariano tests.

Chronological folds

Dates are inclusive. Purge intervals separate training, validation, and test segments, and the outer folds do not overlap.

Fold	Training	Validation	Test
1	2006-01-26 - 2010-02-16	2010-02-23 - 2011-02-24	2011-03-03 - 2012-11-08
2	2012-11-15 - 2016-12-05	2016-12-12 - 2017-12-14	2017-12-21 - 2019-09-03
3	2019-09-10 - 2023-09-28	2023-10-05 - 2024-10-09	2024-10-16 - 2026-06-30

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Models

CLI name	Role	What it tests
ar_ridge	Common anchor	Linear persistence and the reference residual forecast.
har	Econometric baseline	Daily, weekly, and monthly volatility persistence.
harq	Econometric baseline	HAR plus quarticity and stress-related predictors.
garch	Econometric baseline	Gaussian-QMLE GARCH(1,1) conditional-variance recursion.
esn	Matched reservoir baseline	Fixed classical recurrent dynamics plus ridge readout.
sc_rc	Quantum-inspired SUSA	Open-versus-periodic complex-reservoir susceptibility.
phase_rc_moe	Quantum-inspired SUSA-MoE	Structural susceptibility with four phase-specialized experts.
sc_osqrc	Quantum SUSA	Qiskit density-matrix or qBraid open/ring reservoir.
phase_osqrc_moe	Quantum SUSA-MoE	Quantum susceptibility features with phase-conditioned experts.

ESN is the architecture-matched baseline. HARQ and GARCH are the most important domain baselines. Hyperparameters are selected on validation data only, and compact grids are used to keep tuning budgets light.

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Evaluation

Every model is evaluated on the same symbol, target, fold, anchor, and test observations:

train | purge-gap | validation | purge-gap | test

The test protocol is the same for each model:

1. fit each candidate on training data;
2. select one candidate using validation QLIKE plus stability penalties;
3. refit the selected candidate on training + validation;
4. evaluate once on the held-out test block;
5. compare pointwise QLIKE with the fold's AR-Ridge anchor;
6. write predictions, uncertainty statistics, runtime, resources, and resolved configuration.

How to interpret results:

delta_qlike_vs_ar_ridge < 0  =>  lower loss than the anchor

For cross-market conclusions, symbols are the top-level inference units. Dependence is handled with moving-block bootstrap intervals and HAC/Diebold–Mariano tests.

Repository map

.
├── src/qrc/
│   ├── cli.py                    # command-line interface
│   ├── config.py                 # typed run configuration
│   ├── data.py                   # schema validation and causal features
│   ├── splits.py                 # purged chronological folds
│   ├── metrics.py                # QLIKE, calibration, bootstrap, HAC/DM
│   ├── readouts.py               # ridge, low-rank QLIKE, and phase gate
│   ├── runner.py                 # one atomic experiment
│   ├── models/                   # baselines and SUSA implementations
│   └── quantum/                  # local Qiskit and qBraid engines
├── scripts/
│   ├── dataset-cli.py            # versioned public-data builder (this repo contains already downloaded data)
│   ├── run_matrix.py             # resumable parallel experiment launcher
│   ├── run_all_experiments.sh    # reproduce paper results
│   └── test_qbraid_healthcheck.py
├── configs/                      # benchmark and platform configurations
└── runs/                         # generated artifacts (ephemeral folder, generated by scripts)