Optimizing State Preparation for Variational Quantum Regression on NISQ Hardware

Abstract: The execution of quantum algorithms on modern hardware is often constrained by noise and qubit decoherence, limiting the circuit depth and the number of gates that can be executed. Circuit optimization techniques help mitigate these limitations, enhancing algorithm feasibility. In this work, we implement, optimize, and execute a variational quantum regression algorithm using a novel state preparation method. By leveraging ZX-calculus-based optimization techniques, such as Pauli pushing, phase folding, and Hadamard pushing, we achieve a more efficient circuit design. Our results demonstrate that these optimizations enable the successful execution of the quantum regression algorithm on current hardware. Furthermore, the techniques presented are broadly applicable to other quantum circuits requiring arbitrary real-valued state preparation, advancing the practical implementation of quantum algorithms.