Contextual Quantum Neural Networks for Stock Price Prediction

TL;DR

This work tackles multi-asset stock price forecasting using contextual quantum neural networks designed for near-term quantum devices. It introduces the quantum batch gradient update (QBGU) to accelerate training by leveraging the linearity of quantum mechanics and a share-and-specify quantum multi-task learning (QMTL) architecture to jointly learn multiple assets with logarithmic qubit overhead. Empirical results on S&P 500 stocks (Apple, Google, Microsoft, Amazon) show that QMTL outperforms quantum single-task learning (QSTL), capturing inter-asset correlations and achieving faster convergence with fewer trainable parameters. The study demonstrates the viability of loading contextual distributions onto quantum states and using fidelity-based loss via SWAP tests, highlighting a path toward resource-efficient quantum algorithms for complex financial modeling and forecasting tasks.

Abstract

In this paper, we apply quantum machine learning (QML) to predict the stock prices of multiple assets using a contextual quantum neural network. Our approach captures recent trends to predict future stock price distributions, moving beyond traditional models that focus on entire historical data, enhancing adaptability and precision. Utilizing the principles of quantum superposition, we introduce a new training technique called the quantum batch gradient update (QBGU), which accelerates the standard stochastic gradient descent (SGD) in quantum applications and improves convergence. Consequently, we propose a quantum multi-task learning (QMTL) architecture, specifically, the share-and-specify ansatz, that integrates task-specific operators controlled by quantum labels, enabling the simultaneous and efficient training of multiple assets on the same quantum circuit as well as enabling efficient portfolio representation with logarithmic overhead in the number of qubits. This architecture represents the first of its kind in quantum finance, offering superior predictive power and computational efficiency for multi-asset stock price forecasting. Through extensive experimentation on S\&P 500 data for Apple, Google, Microsoft, and Amazon stocks, we demonstrate that our approach not only outperforms quantum single-task learning (QSTL) models but also effectively captures inter-asset correlations, leading to enhanced prediction accuracy. Our findings highlight the transformative potential of QML in financial applications, paving the way for more advanced, resource-efficient quantum algorithms in stock price prediction and other complex financial modeling tasks.

Figures (19)

• Figure 1: Quantum Neural Networks for Contextual Sequence Generation. Given historical data of context and continuations, a Quantum Neural Network is trained to produce quantum distributions over future prices, enabling downstream quantum advantage for tasks (labeled $M$ in the rightmost diagram at a particular future) over all sequences in superposition.
• Figure 2: Parameterized Quantum Circuit. Block diagram of the layered parametric quantum circuit showing various blocks in the $l^{th}$ layer such as fixed unitary and parametric rotation gates.
• Figure 3: SWAP Test. A diagram of the SWAP test, which measures the fidelity loss between two wavefunction states $\left|\boldsymbol{x}^{(T+\tau)}\right\rangle$ and $\left|\boldsymbol{y}^{(T+\tau)}\right\rangle$.
• Figure 4: Loading a distribution onto a hardware efficient ansatz. The circuit inside the blue box ($\hat{O}(\boldsymbol{\alpha},\boldsymbol{\beta})$) is applied sequentially for a sufficient number of iterations followed by an MSE loss with the SPSA update rule.
• Figure 5: Quantum Batch Learning. A diagram showing the learning procedure of our proposed quantum batch gradient update for a context of $T$. The top most qubit is an ancilla qubit. For a batch, a distribution over inputs is loaded succeeding qubits (the input qubits) and the following qubit(s) is for the output. The joint distribution of the inputs and outputs for the batch is loaded on the subsequent qubits. The circuit inside the Grey box ($\hat{U}(\boldsymbol{\theta})$) is applied sequentially for a required number of iterations, is a contextual quantum neural network to prepare an approximate of the loaded joint distribution. A SWAP test is then used to take the fidelity loss between the two distributions.