A Quantum Reservoir Computing Approach to Quantum Stock Price Forecasting in Quantum-Invested Markets

TL;DR

The paper addresses nonlinear forecasting of stock-volume time series in markets with quantum investments by introducing a minimal quantum reservoir computing (QRC) framework using up to six qubits. Inputs are encoded via Hamiltonian-parameter encoding, and learning occurs solely in a linear ridge-readout, enabling efficient training. Across a five-year horizon and intraday sessions, the QRC achieves high directional accuracy (DA > 86%) for many securities, with strong performance enhancements when using delay embeddings to inject memory; a comprehensive tail-risk analysis using standardized moments complements the forecasting, uncovering session-dependent tail behaviors. The approach is platform-agnostic and shows competitive or superior predictive power relative to classical baselines (MLP, ESN) and quantum-inspired variants, highlighting potential applicability to near-term quantum hardware for real-world financial forecasting.

Abstract

We present a quantum reservoir computing (QRC) framework based on a small-scale quantum system comprising at most six interacting qubits, designed for nonlinear financial time-series forecasting. We apply the model to predict future daily closing trading volumes of 20 quantum-sector publicly traded companies over the period from April 11, 2020, to April 11, 2025, as well as minute-by-minute trading volumes during out-of-market hours on July 7, 2025. Our analysis identifies optimal reservoir parameters that yield stock trend (up/down) classification accuracies exceeding $86 \%$. Importantly, the QRC model is platform-agnostic and can be realized across diverse physical implementations of qubits, including superconducting circuits and trapped ions. These results demonstrate the expressive power and robustness of small-scale quantum reservoirs for modeling complex temporal correlations in financial data, highlighting their potential applicability to real-world forecasting tasks on near-term quantum hardware.

Figures (10)

• Figure 1: The architecture of the QRC framework consists of an (a) input (b) encoding scheme (c) quantum reservoir (QR) (d) readout layer (e) linear regression and (f) output. A classical input time series is quantum encoded via Hamiltonian parameter encoding. The quantum reservoir consists of at most six qubits randomly connected and arranged in an all-to-all topology. The QR projects the quantum-encoded input to a higher dimensional feature space to capture temporal corelations. Readout layer generates a readout matrix containing the population inversion of each qubit populations. Linear Ridge regression determines the linear readout coefficients that relates the targeted input to the QR prediction. This framework models is motivated by the architecture of a D-Wave quantum system.
• Figure 2: Standardised Moment Ratios for (a) April 11, 2020 - 2025 in-market hours (b) July 7, 2025 pre-market hours and (c) July 7, 2025 after-market hours. During the 5 year period, nine companies exhibit heavy tails (see top row -- left plot) while eight companies experience lighter tails (see top row -- middle plot). Three companies QTUM, IBM and HON have mixed tails. For pre-market hours (BMH), most companies exhibit lighter tails (see second row -- middle plot) indicating stable volume and high liquidity. Numerous companies during after-market hours (AMH) experience heavy tails suggesting low liquidity and high volatility.
• Figure 3: 2D Colormap showcasing the dependency of MSE Test (top left), NMSE Test (top right), MAPE Test (bottom left) and RMSE Test (bottom right) on the number of qubits $N$ for the 20 quantum-invested companies. The MSE Test values range from $9.9301 \times 10^{-7}$ - $0.2879$. MSE Test, NMSE Test, RMSE Test and MAPE Test peak at $N = 1$ and slightly/drastically drop depending on the company at $N \geq 2$. At N = 5, eleven companies RGTI, QUBT, QMCO, IONQ, QNC.V, QTUM, QSI, LAES, IBM, NVDA, INTC) experience low MSE, NMSE and RMSE.
• Figure 4: The direction accuracy is a non-monotonic function of the number of qubits $N$. For nineteen companies, the accuracy is greater than $85\%$ when $N \geq 2$. ZPTA has the lowest accuracy at $N = 1$ and $N = 4$ with DA = 0.2813 and 0.7813 respectively.
• Figure 5: MAPE TEST (top) and NMSE Test (bottom) of MLP (blue), ESN (orange), QIESN (yellow) and HPE-QRC (purple) when HPE-QRC has five qubits. HPE-QRC outperforms MLP, ESN and QIESN in 12 companies for MAPE Test and 14 companies for NMSE Test.