Physics, Mathematics & Computer Science

Event Title

Quantum Searches of Fitness Landscapes

Presenter Information

Samuel Smith, Butler University

Document Type

Oral Presentation

Location

Indianapolis, IN

Subject Area

Physics, Mathematics & Computer Science

Start Date

11-4-2014 1:00 PM

End Date

11-4-2014 3:00 PM

Description

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.

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Apr 11th, 1:00 PM Apr 11th, 3:00 PM

Quantum Searches of Fitness Landscapes

Indianapolis, IN

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.