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Control theory to harness quanta : a beacon for the realization of quantum computers : forging new fields which merge mathematical engineering with quantum mechanics

ユウコ ヒラツカ, Yuko Hiratsuka, 裕子 平塚

Published Jan 1, 2019• 0 citations
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Abstract

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Control theory to harness quanta : a beacon for the realization of quantum computers : forging new fields which merge mathematical engineering with quantum mechanics

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In the escalating race between cryptographic security and quantum computing capabilities, the need for robust encryption methodologies that can withstand the prowess of quantum algorithms is more pressing than ever. This paper introduces a novel cryptographic framework, grounded in the principles of quantum mechanics and the entropic uncertainty principle, to forge a path towards quantum-resilient encryption. At the heart of this approach lies the integration of the entropic uncertainty inherent in quantum states, a fundamental aspect often overlooked in traditional cryptographic strategies. By harnessing this intrinsic uncertainty of quantum mechanics, we propose a mathematical framework that not only challenges the conventional paradigms of encryption but also sets a new benchmark for security in the quantum computing era. The paper delves into the theoretical underpinnings of quantum mechanics relevant to cryptography, with a particular focus on the entropic uncertainty principle. This principle, which posits a natural limit on the precision with which certain pairs of physical properties can be known, serves as the cornerstone of our proposed encryption method. We meticulously develop and outline a mathematical model that leverages this principle, ensuring that the encrypted information remains secure against the formidable computational capabilities of quantum algorithms. We contrast our approach with existing cryptographic methods, highlighting the enhanced security features offered by the entropic uncertainty-based model. The findings underscore the potential of this framework to serve as a resilient encryption mechanism in a landscape increasingly dominated by quantum computing technologies. This research paves the way for a new era of encryption, one that embraces the uncertainty of quantum mechanics as its shield against the threats posed by quantum computing.

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Quantum computing comes with the potential to push computational boundaries in various domains including, e.g., cryptography, simulation, optimization, and machine learning. Exploiting the principles of quantum mechanics, new algorithms can be developed with capabilities that are unprecedented by classical computers. However, the experimental realization of quantum devices is an active field of research with enormous open challenges, including robustness against noise and scalabilty. While systems and control theory plays a crucial role in tackling these challenges, the principles of quantum physics lead to a (perceived) high entry barrier for entering the field of quantum computing. This tutorial paper aims at lowering the barrier by introducing basic concepts required to understand and solve research problems in quantum systems. First, we introduce fundamentals of quantum algorithms, ranging from basic ingredients such as qubits and quantum logic gates to prominent examples and more advanced concepts, e.g., variational quantum algorithms. Next, we formalize some engineering questions for building quantum devices in the real world, which requires the careful manipulation of microscopic quantities obeying quantum effects. To this end for N-level systems, we introduce basic concepts of (bilinear) quantum systems and control theory including controllability, observability, and optimal control in a unified frame. Finally, we address the problem of noise in real-world quantum systems via robust quantum control, which relies on a set-membership uncertainty description frequently employed in control. A key goal of this tutorial paper is to demystify engineering aspects of quantum computing by emphasizing that its mathematical description mainly involves linear algebra (for quantum algorithms) and the handling of bilinear control systems (for quantum systems and control theory) but does not require too much detailed knowledge of quantum physics.
In the escalating race between cryptographic security and quantum computing capabilities, the need for robust encryption methodologies that can withstand the prowess of quantum algorithms is more pressing than ever. This paper introduces a novel cryptographic framework, grounded in the principles of quantum mechanics and the entropic uncertainty principle, to forge a path towards quantum-resilient encryption. At the heart of this approach lies the integration of the entropic uncertainty inherent in quantum states, a fundamental aspect often overlooked in traditional cryptographic strategies. By harnessing this intrinsic uncertainty of quantum mechanics, we propose a mathematical framework that not only challenges the conventional paradigms of encryption but also sets a new benchmark for security in the quantum computing era. The paper delves into the theoretical underpinnings of quantum mechanics relevant to cryptography, with a particular focus on the entropic uncertainty principle. This principle, which posits a natural limit on the precision with which certain pairs of physical properties can be known, serves as the cornerstone of our proposed encryption method. We meticulously develop and outline a mathematical model that leverages this principle, ensuring that the encrypted information remains secure against the formidable computational capabilities of quantum algorithms. We contrast our approach with existing cryptographic methods, highlighting the enhanced security features offered by the entropic uncertainty-based model. The findings underscore the potential of this framework to serve as a resilient encryption mechanism in a landscape increasingly dominated by quantum computing technologies. This research paves the way for a new era of encryption, one that embraces the uncertainty of quantum mechanics as its shield against the threats posed by quantum computing.