Enhancing quantum state tomography: utilizing advanced statistical techniques for optimized quantum state reconstructions

Abstract

Quantum state tomography (QST) forms the foundational framework in quantum computing, enabling precise characterization of quantum states through specialized measurement arrays. This is crucial for assessing the fidelity and coherence of quantum states in various quantum systems. The complexity and high dimensionality of quantum states require advanced statistical methods to meet modern quantum paradigms’ precision and computational needs, as traditional methods often struggle with inefficiencies and inaccuracies. Conventional approaches in QST typically use linear inversion and maximum likelihood estimators, which often face computational redundancies and perform sub-optimally in high-dimensional quantum architectures. This exposition introduces pioneering statistical methodologies that combine Bayesian Inference, Variational Quantum Eigensolver, and Quantum Neural Networks to achieve enhanced fidelity approximation. The analytical discussion is supported by synthetic quantum states, demonstrating the efficacy and applicability of these statistical methods across various quantum matrices. Preliminary empirical results show a significant increase in fidelity and a notable reduction in error margins, highlighting the potential of these advanced statistical methodologies in optimizing quantum state reconstructions. Additionally, leveraging the inherent symmetry properties in quantum systems could further improve the efficiency and accuracy of state reconstructions, offering additional pathways for advancing the field.