Novel Quantum Algorithms for Noisy Intermediate-Scale Quantum (NISQ) Devices

Quantum computers hold the immense potential to revolutionize the current computing technology. However, the available quantum hardware, known as noisy intermediate-scale quantum (NISQ) devices, poses a challenge as these devices have noise and imperfect qubits. Hence, there is a critical need to develop novel algorithms specifically designed to harness the capabilities of these devices. This work aims to develop and optimize such quantum algorithms for implementation on current quantum technologies by integrating principles from physics and machine learning. First, we developed the Quantum Imaginary Time Evolution (QITE) and Quantum Lanczos (QLanczos) algorithms on discrete-variable quantum computing settings to study the eigensystem of a many-body quantum system. We applied them to a system of collective oscillating neutrinos. The final results agreed with the exact results demonstrating that a neutrino system can be studied on quantum hardware. Subsequently, we constructed continuous-variable (CV) quantum neural networks, which can be experimentally realized as they are made up exclusively of Gaussian gates, with nonlinearity introduced via measurements. The network was tested across various scenarios in a supervised learning setting —curve fitting, fraud detection, image classification, and state preparation. The outcomes were consistently positive, achieving over 93\% accuracy across all studied cases. Furthermore, we constructed a quantum Boltzmann machine in the CV framework. This machine is designed to generate probability distributions for classical (synthetic aperture radar images) and quantum data (Gaussian and non-Gaussian (cat) states). In each instance, the Kullback-Leibler (KL) divergence between the target and generated distributions was calculated and found to be very close to zero, indicating an excellent match between the generated and actual distributions.

In this work, we have successfully advanced the field of quantum computing by developing and optimizing algorithms tailored for NISQ devices. Future research should expand the scope of systems studied using these algorithms, continually refining these algorithms through advanced error mitigation and machine learning techniques. The next goal in the CV setting is constructing quantum neural networks and Boltzmann machines in a lab using advanced photonic quantum computers. These algorithms hold promise for diverse applications, from medical imaging and gravitational wave detection to preparing complex quantum states.