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International Journal of Theoretical Physics

Reduction of Theoretical Uncertainty in Quantum Computing

Hideaki Matsueda, David W. Cohen

Published Feb 1, 1999• 4 citations
Publisher
DOI
10.1023/a:1026663408959

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The rapid advancement of quantum computing provides unprecedented opportunities for the optimization of multiple-input, multiple-output (MIMO) systems. This paper investigates the efficacy of harnessing quantum algorithms, particularly the Quantum Approximate Optimization Algorithm (QAOA) and Grover's algorithm, for the optimization of MIMO systems. The paper establishes a theoretical framework that maps MIMO optimization problems onto quantum circuits, ensuring a reduction in computational complexity compared to classical algorithms. The proposed methodology is validated through a series of numerical simulations. Notable improvements are observed in both convergence speed and the quality of the optimized solutions. Furthermore, the synergy of quantum computing and MIMO presents new frontiers for reducing interference, enhancing throughput, and ensuring robustness against environmental uncertainties. These results affirm the potential of integrating quantum computing techniques in MIMO system optimization, heralding a transformative era for wireless communication paradigms.
One of the key obstacles in traditional deep learning is the reduction in model transparency caused by increasingly intricate model functions, which can lead to problems such as overfitting and excessive confidence in predictions. With the advent of quantum machine learning offering possible advances in computational power and latent space complexity, we notice the same opaque behavior. Despite significant research in classical contexts, there has been little advancement in addressing the black-box nature of quantum machine learning. Consequently, we approach this gap by building upon existing work in classical uncertainty quantification and initial explorations in quantum Bayesian modeling to theoretically develop and empirically evaluate techniques to map classical uncertainty quantification methods to the quantum machine learning domain. Our findings emphasize the necessity of leveraging classical insights into uncertainty quantification to include uncertainty awareness in the process of designing new quantum machine learning models.
General characterizations of physical measurements are discussed within the framework of the classical information theory. The uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for generalized dynamic systems governed by a Sturm--Liouville type of equation of motion. In the first step, the reduction of Kennard--Robertson type uncertainties due to boundary conditions with a mean-square error is discussed quantitatively with reference to the information entropy. Several concrete examples of generalized uncertainty relations are given. Then, by considering disturbance effects, a universally valid uncertainty relation is investigated for the generalized equation of motion with a certain boundary condition. Necessary conditions for violation (reduction) of the Heisenberg-type uncertainty relation are discussed in detail. The reduction of the generalized uncertainty relation due to the boundary condition is then tested experimentally by re-analyzing data for measured electron densities in a hydrogen molecule encapsulated in a fullerene C60 cage.