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Synthesis lectures on quantum computing

Quantum Search

Prateek Tandon, Stanley Lam, Ben Shih, Tanay Mehta, Alex Mitev, Zhiyang Ong

Published Jan 1, 2017• 0 citations
Publisher
DOI
10.1007/978-3-031-02520-4_3

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Quantum Searches of Fitness Landscapes

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Many natural and artificial processes in the universe can be modeled as searches for some unique value. The range of possibilities examined for the potential answer can all be assigned a numerical value ranking how well they match the criteria for the search. Such a range of values is called a fitness landscape. In the field of quantum computation, quantum searches have received a fair amount of study in the past 20 years. Typical quantum searches rely on the principle that the fitness value for any incorrect answer to the search is zero and the single correct answer is a one. The quantum search has been shown to be immensely faster than equivalent classical searches. There has not been much study yet on the quantum search of a fitness landscape consisting of a range of values. Our work is focused on understanding how quantum searches can be used on more advanced fitness landscapes and whether or not these searches are still faster than their classical counterparts. Thus far, there appears to be evidence that the quantum search is better at finding a particular point in a landscape than the classical, although not particularly faster than it. We've also observed that the quantum tends to have a faster mixing time than its classical counterpoint when in a constrained landscape. This leads us to believe that the quantum search would probably be better suited to finding optimum points in a landscape than the classical search. For the most part, our research has been carried out using the current applicable literature and run experimentally on the computer. If there is significant evidence a quantum search searches a fitness landscape better than a classical one, then we hope to show the application of our results to molecular evolution.

•Jan 1, 2014•0 citations
The Search Based Software Engineering (SBSE) is widely used in software engineering for identifying optimal solutions. However, there is no polynomial-time complexity solution used in the traditional algorithms for SBSE, and that causes the cost very high. In this paper, we analyze and compare several quantum search algorithms that could be applied for SBSE: quantum adiabatic evolution searching algorithm, fixed-point quantum search (FPQS), quantum walks, and a rapid modified Grover quantum searching method. The Grover’s algorithm is thought as the best choice for a large-scaled unstructured data searching and theoretically it can be applicable to any search-space structure and any type of searching problems.
Many natural and artificial processes in the universe can be modeled as searches for some unique value. The range of possibilities examined for the potential answer can all be assigned a numerical value ranking how well they match the criteria for the search. Such a range of values is called a fitness landscape. In the field of quantum computation, quantum searches have received a fair amount of study in the past 20 years. Typical quantum searches rely on the principle that the fitness value for any incorrect answer to the search is zero and the single correct answer is a one. The quantum search has been shown to be immensely faster than equivalent classical searches. There has not been much study yet on the quantum search of a fitness landscape consisting of a range of values. Our work is focused on understanding how quantum searches can be used on more advanced fitness landscapes and whether or not these searches are still faster than their classical counterparts. Thus far, there appears to be evidence that the quantum search is better at finding a particular point in a landscape than the classical, although not particularly faster than it. We've also observed that the quantum tends to have a faster mixing time than its classical counterpoint when in a constrained landscape. This leads us to believe that the quantum search would probably be better suited to finding optimum points in a landscape than the classical search. For the most part, our research has been carried out using the current applicable literature and run experimentally on the computer. If there is significant evidence a quantum search searches a fitness landscape better than a classical one, then we hope to show the application of our results to molecular evolution.