Abstract
In this paper, Proposed a algorithm based on quantum, to solve the 0-1-knapsack problem on a hypothetical quantum computer. Utilized the especial characteristics of the quantum environment, constantly split up into the state of vector space, reduced the probability of state vector which don’t meet the conditions of magnitude, increased the probability amplitude to meet the conditions, found a larger probability of obtaining the solution. Owing to the problem of solving the time complexity by traditional exponential is too complicated, turned it into the other problem which is relatively easy, then solving polynomial time with quantum computer, can reduce the difficulty of solving the problem. Analysis of the complexity of the algorithm and implementation results showed that the designed algorithm is effective and feasible. The designed algorithm can be extended to solve other NPC problems.
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Liu, H., Nie, S. (2012). Solving the 0-1 Knapsack Problem with Polynomial-Time Quantum Algorithm. In: Zhao, M., Sha, J. (eds) Communications and Information Processing. Communications in Computer and Information Science, vol 289. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31968-6_45
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DOI: https://doi.org/10.1007/978-3-642-31968-6_45
Publisher Name: Springer, Berlin, Heidelberg
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