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SPIE Quantum Information Science, Sensing, and Computation

Quantum tomographic reconstruction: a Bayesian approach using the extended Kalman filter

Khaled Obaideen, Mohammad A. Al-Shabi, S. Andrew Gadsden, Talal Bonny

Published Apr 19, 2024• 0 citations
Publisher

Abstract

This study presents a comprehensive bibliometric analysis of the fusion between quantum tomography and the Extended Kalman Filter (EKF), emphasizing its superiority in refining quantum tomographic reconstructions compared to conventional methodologies. By intersecting quantum mechanical principles with sophisticated filtering technologies, our analysis uncovers emergent research trajectories within the domain of quantum information science. It underscores the significant potential that this integration holds for the evolution of quantum technology applications. Furthermore, this paper delineates the expansive impact of improved quantum state information across a spectrum of scientific fields, thereby enriching the discourse on quantum state estimation and its applications. Through this investigation, we contribute to a deeper understanding of the pivotal role that advanced filtering techniques, specifically the EKF, play in advancing quantum tomography, paving the way for future innovations in quantum computing and beyond.

DOI
10.1117/12.3015939

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This study presents a comprehensive bibliometric analysis of the fusion between quantum tomography and the Extended Kalman Filter (EKF), emphasizing its superiority in refining quantum tomographic reconstructions compared to conventional methodologies. By intersecting quantum mechanical principles with sophisticated filtering technologies, our analysis uncovers emergent research trajectories within the domain of quantum information science. It underscores the significant potential that this integration holds for the evolution of quantum technology applications. Furthermore, this paper delineates the expansive impact of improved quantum state information across a spectrum of scientific fields, thereby enriching the discourse on quantum state estimation and its applications. Through this investigation, we contribute to a deeper understanding of the pivotal role that advanced filtering techniques, specifically the EKF, play in advancing quantum tomography, paving the way for future innovations in quantum computing and beyond.
Quantum state vector reconstruction is a fundamental problem in quantum information theory, crucial for tasks like quantum state tomography and quantum error correction. Traditional methods often struggle with noisy measurements and lack a principled framework for uncertainty quantification. This paper introduces a novel algorithm, Quantum State Vector Reconstruction via Bayesian Inference, that leverages Bayesian inference to reconstruct a quantum state vector from a set of measurements, enhancing accuracy and offering a more robust approach compared to existing methods. We detail the core mechanism, emphasizing the integration of Bayesian estimation for uncertainty quantification and refinement of the reconstruction process. The algorithm incorporates a probabilistic approach to estimate the state vector distribution, improving reconstruction by incorporating uncertainty estimates directly into the reconstruction process. This results in a more reliable and accurate state vector reconstruction, particularly when dealing with noisy measurements. This work addresses the limitations of conventional methods by providing a principled Bayesian framework for state vector reconstruction, offering a significant advancement in this field.
Quantum computing has emerged as a transformative paradigm, capable of tackling complex computational problems that are infeasible for classical methods within a practical timeframe. At the core of this advancement lies the concept of quantum supremacy, which signifies the ability of quantum processors to surpass classical systems in specific tasks. In the context of tomographic image reconstruction, quantum optimization algorithms enable faster processing and clearer imaging than conventional methods. This study further substantiates quantum supremacy by reducing the required projection angles for tomographic reconstruction while enhancing robustness against image artifacts. Notably, our experiments demonstrated that the proposed algorithm accurately reconstructed tomographic images without artifacts, even when up to 50% error was introduced into the sinogram to induce ring artifacts. Furthermore, it achieved precise reconstructions using only 50% of the projection angles from the original sinogram spanning 0° to 180°. These findings highlight the potential of quantum algorithms to revolutionize tomographic imaging by enabling efficient and accurate reconstructions under challenging conditions, paving the way for broader applications in medical imaging, material science, and advanced tomography systems as quantum computing technologies continue to advance.
Abstract In quantum physics, a stochastic master equation (SME) estimates the state (density operator) of a quantum system in the Schrödinger picture based on a record of measurements made on the system. In the Heisenberg picture, the SME is a quantum filter. For a linear quantum system subject to linear measurements and Gaussian noise, the dynamics may be described by quantum stochastic differential equations (QSDEs), also known as quantum Langevin equations, and the quantum filter reduces to a so-called quantum Kalman filter. In this article, we introduce a quantum extended Kalman filter (quantum EKF), which applies a commutative approximation and a time-varying linearization to systems of nonlinear QSDEs. We will show that there are conditions under which a filter similar to a classical EKF can be implemented for quantum systems. The boundedness of estimation errors and the filtering problem with ‘state-dependent’ covariances for process and measurement noises are also discussed. We demonstrate the effectiveness of the quantum EKF by applying it to systems that involve multiple modes, nonlinear Hamiltonians, and simultaneous jump-diffusive measurements.
Quantum Computing (QC) is a rapidly evolving research field that has garnered significant attention due to its potential to revolutionize various domains such as cryptography, optimization, and machine learning. In this article, we conduct an extensive analysis of the evolution of QC research within the realm of High Performance Computing (HPC) over a span of ten years, up to 2023. Through bibliometric analysis and advanced science mapping techniques, we uncover key thematic areas that have emerged in the field, including quantum algorithms, simulation, parallel-computing, deep learning, machine learning, and encryption. This analysis highlights the interdisciplinary nature of QC, which intersects with disciplines such as physics, mathematics, computer science, and materials science. Furthermore, our study elucidates the close relationship between HPC and QC, showcasing how advancements in one field can significantly impact the other. The findings of this study not only provide valuable insights into the past trends and research landscape but also serve as a guide for future research directions, enabling the advancement of knowledge and fostering innovation in computer science. Additionally, our analysis sheds light on the global distribution of research contributions, identifying countries and regions that have made significant strides in QC research, thus presenting potential collaboration opportunities. Overall, this comprehensive study contributes to a deeper understanding of the development of QC within the realm of HPC, offering valuable insights and paving the way for future advancements in this exciting field.
The Quantum Kalman Filter (QKF) emerges as an innovative approach to address the challenges of state estimation in quantum systems, adapting classical Kalman filtering to the complexities of quantum mechanics. This paper examines the theoretical framework, practical implementation hurdles, and potential applications of QKF in quantum information processing and sensing. By incorporating quantum measurement principles and stochastic dynamics, QKF offers a solution for optimal state estimation in noisy quantum environments. The study presents simulation results and comparative analyses with classical Kalman filtering for tracking single targets, underscoring the advantages and limitations of QKF in advancing quantum technology applications.