Hannes Leipold

Steven Kordonowy, Bibhas Adhikari, Hannes Leipold

We develop a perfectly distributable quantum-classical streaming algorithm that processes signed edges to efficiently estimate the counts of triangles of diverse signed configurations in the single pass edge stream. Our approach introduces a quantum sketch register for processing the signed edge stream, together with measurement operators for query-pair calls in the quantum estimator, while a complementary classical estimator accounts for triangles not captured by the quantum procedure. This hybrid design yields a polynomial space advantage over purely classical approaches, extending known results from unsigned edge stream data to the signed setting. We quantify the lack of balance on random signed graph instances, showcasing how the classical and hybrid algorithms estimate balance in practice.

David Quiroga, Hannes Leipold, Bibhas Adhikari

Loading high dimensional distributions is an important task for utilizing quantum computers on applications ranging from machine learning to finance. The high dimensionality leads to a curse of dimensionality, representing a d-dimensional distribution with k resolution requires dk qubits and an unstructured parameterized circuit would express a unitary in an exponential operator space in the number of qubits, leading to vanishing gradients and poor convergence guarantees even at high depth. Vine copula decompositions are widely used to represent high dimensional distributions classically, showing high quality approximation in many important applications, such as financial modeling. We present Qvine, a vine structured ansatz for quantum circuits, that mirrors the vine decomposition to construct scalable quantum circuits with efficient trainability while achieving similarly high quality approximation for amplitude encoding distributions. For regular vines (R-vines), we show that the circuit depth scales at most quadratic in the dimension of the distribution, while for D-vines, as well as many practical R-vines, the circuit depth scales linear in the dimension. For 3-dimensional and 4-dimensional Gaussians and empirical joint stock price return distributions for selected stocks, our experiments show Qvines achieve high quality loading.

Sharan Mourya, Hannes Leipold, Bibhas Adhikari

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.