The Singular Quantum

S. B. Treiman

Wusheng Zhu, Martina Smit, HERSCHEL A. RABITZ

Singularities can arise in the external field obtained by tracking control of quantum mechanical systems. Whether or not the trajectory is disturbed by the presence of a singular point is shown to mainly depend on the average momentum along the trajectory at the moment of passing the singular point. If the singularity occurs on a turning point, the tracking will be quite unstable since the direction taken by the trajectory is very sensitive to field errors. The theoretical analysis of these situations yields detailed conclusions about the impact of field singularities in quantum tracking control. A rank index is defined to characterize nontrivial singularities, and the rank is shown to play an important role in determining the tracking quality while passing over a singular turning point where the field has a unique solution. A special class of nontrivial singularities is identified by the ability to remove the singularity under a proper limiting process. These insights into the nature and influence of singularities in tracking control of quantum systems are beneficial for developing numerical schemes and for designing controls.

Luis de la Peña, Ana Marı́a Cetto, Andrea Valdés-Hernández

P. S. Aithal, Shubhrajyotsna Aithal

Purpose: There is a need to establish a comprehensive conceptual framework that focuses on the synergies between quantum computing and technological singularities. The quest is to unfold an investigation on how quantum computers play a pivotal role in supporting the realization of both AI-based Digital Singularity and Nanotech-based Molecular Singularity, offering insights into their transformative potential at the intersection of artificial intelligence and nanotechnology. Method: The study method is exploratory in nature and predicts, analyses, and interprets various possibilities of further developments of AI-based Digital Singularity and Nanotech-based Molecular Singularity, which comes under technological singularities- a stage where technology overtakes human abilities to solve existing problems related to need, wants, and dreamy desire. Analysis and Outcome: The research addresses the innovative concept of the intersection between AI-based Digital Singularity and Nanotech-based Molecular Singularity, supported by quantum computing, and explores how this convergence drives further advancements in solving complex technological and societal challenges. The paper includes a detailed ABCD analysis for both AI and nanotech singularities, evaluating the Advantages, Benefits, Constraints, and Disadvantages of quantum computing integration in each context. Lastly, the research aims to provide valuable suggestions in the form of postulates, offering potential avenues for further exploration and experimentation in the rapidly evolving fields of quantum computing and technological singularities. Originality/Value: The paper provides a structured approach to exploring the intersection of quantum computers with AI-driven Digital Singularity and Nanotech-driven Molecular Singularity. Type of Paper: Exploratory Analysis.

Jan C. A. Boeyens

Xin Wang, Zhixin Song, Youle Wang

Singular value decomposition is central to many problems in engineering and scientific fields. Several quantum algorithms have been proposed to determine the singular values and their associated singular vectors of a given matrix. Although these algorithms are promising, the required quantum subroutines and resources are too costly on near-term quantum devices. In this work, we propose a variational quantum algorithm for singular value decomposition (VQSVD). By exploiting the variational principles for singular values and the Ky Fan Theorem, we design a novel loss function such that two quantum neural networks (or parameterized quantum circuits) could be trained to learn the singular vectors and output the corresponding singular values. Furthermore, we conduct numerical simulations of VQSVD for random matrices as well as its applications in image compression of handwritten digits. Finally, we discuss the applications of our algorithm in recommendation systems and polar decomposition. Our work explores new avenues for quantum information processing beyond the conventional protocols that only works for Hermitian data, and reveals the capability of matrix decomposition on near-term quantum devices.