Advanced Knowledge of the Solution in Quantum Algorithms Addressing Structured Problems
Year: 2011
Type: preprint
Abstract: In previous work, we showed that quantum correlation, between selection of the problem on the part of Bob and read out of the solution on the part of Alice, can explain the quantum speed up. All is like Alice’s read out contributed to selecting the problem, which becomes Alice knowing in advance 50% of the bits of the solution. This explanation, developed for unstructured data-base search, was coarsely extended to the quantum algorithms that address structured problems. Now, thanks to a more general representation of Alice’s advanced knowledge of the solution, we provide a detailed explanation of the mechanism of the speed up also for the latter algorithms. This should significantly increase the plausibility of our argument. 1 Foreword In Ref. [1], we showed that quantum correlation, between selection of the problem on the part of Bob (the problem setter) and read out of the solution on the part of Alice (the problem solver), can explain the mechanism of the quantum speed up. Because of it, all is like the final read out of the solution on the part of Alice contributed to selecting the problem. Back evolved to before running the algorithm, by the inverse of the time-forward unitary transformation, this contribution becomes Alice knowing in advance 50% of the bits of the solution. The quantum algorithm is the quantum superposition of all the possible ways of taking 50% of the bits of the solution and, given the advanced knowledge of these bits, classically computing the missing bits. According to this explanation, the quantum speed up comes from comparing two classical algorithms, with and without advanced knowledge of 50% of the solution. This would be a useful result, it would allow us to characterize the problems solvable with a quantum speed up in an entirely classical framework. The subject explanation benefits of the special problem-solution symmetry existing in Grover’s algorithm, which depends on the unstructured character of
Source: arXiv (Cornell University)
Author: Giuseppe Castagnoli
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1488676752