Title:  Accelerated Quantum State Tomography with Machine Learning Applications

Committee: 

Dr. Mukhopadhyay, Advisor   

Dr. Romberg, Chair

Dr. Datta

Abstract: The objective of the proposed research is to design an accelerator for quantum state tomography in classical hardware in order to (1) reduce classical computing power required for reconstruction of the exponential quantum state space, (2) reduce quantum circuit execution and measurement overhead, and (3) target improved accuracy in solving complex problems like machine learning. We first present a Quantum Hopfield Associative Memory which can be implemented on real quantum-computing hardware, but which is severely limited in its capacity by its susceptibility to hardware noise. Therefore, we approach the acceleration of the quantum state tomography problem for the rapid and accurate reconstruction of quantum states as a solution for reduced noise and improved calibration of quantum hardware, and potentially as a direct tool for more complex quantum machine learning paradigms. Traditional quantum state tomography is notoriously time consuming for classical hardware to compute, cited as taking weeks to compute for even an 8-qubit system. We propose to develop tomography accelerator hardware via (1) solving the direct complex least squares problem in FPGA for rapid reconstruction from tomographically complete measurement sets by utilizing the unique characteristics of the measurement matrix, and (2) accelerating the compressed sensing solution of quantum state tomography in FPGA using low-rank reconstruction techniques for high tomography accuracy with reduced quantum circuit overhead. This hardware-accelerated quantum state tomography has a wide variety of applications including accelerated quantum gate set calibration, error correction and error mitigation, and potentially paradigm-shifting algorithm creation via he improved readout and understanding of the states and processes created in NISQ-era quantum hardware.