Quantum Finance
Forecasting withQCBM & QMCMC.
Point forecasts hide tail risk. This study learns the distribution of next-day AAPL returns — heavy tails included — and turns it into calibrated uncertainty, on circuits shallow enough to run on today's hardware.
Dat Chi (Ryan) Le · Abubakar (Sid) Iliyasu · Gyanateet Dutta
01 — The Problem
Classical baselines struggle with fat tails.
AAPL log-returns show fat tails and volatility clustering — confirmed by rejecting normality (Jarque–Bera) and finding ARCH effects in the autocorrelation of squared returns. Classical ARIMA and naive baselines assume away exactly this behaviour, so their prediction intervals end up too narrow to be useful for risk management (VaR/ES).
02 — Data & Setup
51 features, compressed to a handful of qubits.
Raw OHLCV data is expanded into 51–83 engineered features (return lags, realised volatility, technical indicators, spectral components), reduced via PCA, and encoded onto 4–5 qubits — small and shallow enough to stay NISQ-feasible.
2020–22
Daily AAPL OHLCV price history
51
Engineered features per day (lags, volatility, spectral)
4–5
Qubits, via PCA + angle/hybrid encoding
L ≤ 2
Circuit depth — shallow, NISQ-feasible
03 — Two Quantum Approaches
A generative model, and a sampler.
Generative
Quantum Circuit Born Machine (QCBM)
A parametrised quantum circuit whose measurement probabilities, via Born's rule, are trained to match the empirical return distribution. Both a hardware-efficient ansatz and a physics-inspired one (features mapped onto an Ising Hamiltonian) were tested; circular entanglement with a wider lag window performed best.
Sampler
Quantum Dynamical Hamiltonian Monte Carlo (QD-HMC)
Replaces the classical symplectic integration inside Hamiltonian Monte Carlo with quantum coherent evolution — kinetic and potential terms applied as unitaries, then measured and accepted or rejected via Metropolis–Hastings. Gate-based precision runs at roughly 2–3 qubits per parameter.
04 — Results
QD-HMC beat every classical baseline tested.
RMSE on next-day AAPL return prediction, against seven classical baselines on identical data. The scale below is logarithmic — QD-HMC's error is roughly 72× smaller than the best classical baseline, not just marginally better.
05 — Conclusions & Next Steps
Small-scale, but genuinely NISQ-feasible.
Both QCBM and QD-HMC ran at shallow depth and single-digit qubit counts while beating every classical baseline tested. Next: more precision per parameter, hardware runs, and benchmarking QD-HMC against classical HMC and other samplers like NUTS.