Quantum-enhanced signal processing via VQE for improved biomechanical feedback control

The Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical algorithm that has demonstrated significant potential for solving quantum chemistry problems, particularly in determining the ground state energy of small molecules like H₂. In this paper, we extend the application of VQE beyond quantum chemistry by utilizing it to analyze sensor data from engineered socks equipped with an accelerometer, and gyroscope sensors. Our goal is to explore the sensitivity of accelerometer and gyroscope signals to specific motion frequencies by encoding their data into the quantum states of the H₂ molecule's qubits. We introduce an automatic control mechanism based on a classical feedback loop, where the output of the VQE is compared to the desired input, and corrective actions are applied using a constant K to ensure the output follows the input closely. This feedback loop is designed to assist the algorithm in managing local minima, noise, and computational challenges. Using this feedback-controlled VQE system, we optimize sensor signal analysis and determine which sensor exhibits higher sensitivity to specific biomechanical frequencies. Our experimental results indicate the potential flexibility of VQE in analyzing specific biomechanical data, providing preliminary insights into the broader applications of quantum algorithms in wearable technology. As quantum hardware advances, VQE may offer applications in complex systems and diverse fields, including personalized healthcare and motion capture.