Efficient Quantum State Preparation of Multivariate Functions Using Tensor Networks

Explore a 20-minute conference talk presenting novel classical algorithms based on tensor network methods for efficient quantum state preparation of high-dimensional multivariate functions. Learn about the research conducted by Marco Ballarin, Juan José García-Ripoll, David Hayes, and Michael Lubasch that addresses the critical challenge of preparing quantum states for complex functions while maintaining quantum advantage. Discover how the researchers tackle the barren plateau problem through a smooth transformation procedure that evolves quantum circuits from easily preparable initial functions to target multivariate functions. Examine the numerical optimization results for multivariate Gaussians up to 17 dimensions using 102 qubits, and understand how the approach incorporates hardware-native quantum gates while accounting for realistic experimental noise. Review the experimental validation on Quantinuum's H2 quantum computer, where a 9-dimensional Gaussian with polynomially decaying correlations was successfully prepared using 54 qubits, demonstrating the practical feasibility of this tensor network-based approach for quantum state preparation in machine learning applications.