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Quantum Rep., Volume 6, Issue 4 (December 2024) – 2 articles

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11 pages, 385 KiB  
Article
A Solution to the Quantum Measurement Problem
by Zdzislaw E. Musielak
Quantum Rep. 2024, 6(4), 522-532; https://doi.org/10.3390/quantum6040035 (registering DOI) - 19 Oct 2024
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Abstract
A novel solution to the quantum measurement problem is presented by using a new asymmetric equation that is complementary to the Schrödinger equation. Solved for the hydrogen atom, the new equation describes the temporal and spatial evolution of the wavefunction, and the latter [...] Read more.
A novel solution to the quantum measurement problem is presented by using a new asymmetric equation that is complementary to the Schrödinger equation. Solved for the hydrogen atom, the new equation describes the temporal and spatial evolution of the wavefunction, and the latter is used to calculate the radial probability density for different measurements. The obtained results show that Born’s position measurement postulates naturally emerge from the theory and its first principles. Experimental verification of the theory and its predictions are also proposed. Full article
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13 pages, 304 KiB  
Article
Quantum-Enhanced Generalized Pattern Search Optimization
by Colton Mikes, David Huckleberry Gutman and Victoria E. Howle
Quantum Rep. 2024, 6(4), 509-521; https://doi.org/10.3390/quantum6040034 - 29 Sep 2024
Viewed by 329
Abstract
While the development of quantum computers promises a myriad of advantages over their classical counterparts, care must be taken when designing algorithms that substitute a classical technique with a potentially advantageous quantum method. The probabilistic nature of many quantum algorithms may result in [...] Read more.
While the development of quantum computers promises a myriad of advantages over their classical counterparts, care must be taken when designing algorithms that substitute a classical technique with a potentially advantageous quantum method. The probabilistic nature of many quantum algorithms may result in new behavior that could negatively impact the performance of the larger algorithm. The purpose of this work is to preserve the advantages of applying quantum search methods for generalized pattern search algorithms (GPSs) without violating the convergence criteria. It is well known that quantum search methods are able to reduce the expected number of oracle calls needed for finding the solution to a search problem from O(N) to O(N) However, the number of oracle calls needed to determine that no solution exists with certainty is exceedingly high and potentially infinite. In the case of GPS, this is a significant problem since overlooking a solution during an iteration will violate a needed assumption for convergence. Here, we overcome this problem by introducing the quantum improved point search (QIPS), a classical–quantum hybrid variant of the quantum search algorithm QSearch. QIPS retains the O(N) oracle query complexity of QSearch when a solution exists. However, it is able to determine when no solution exists, with certainty, using only O(N) oracle calls. Full article
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