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SUMMARY:Quantum Algorithm for Finding Roots of $n^\\mathrm{th}$ Degree Pol
ynomials
DTSTART;VALUE=DATE-TIME:20150521T024500Z
DTEND;VALUE=DATE-TIME:20150521T030000Z
DTSTAMP;VALUE=DATE-TIME:20201127T092554Z
UID:indico-contribution-787708@indico.cern.ch
DESCRIPTION:Speakers: Theerapat Tansuwannont (Department of Physics\, Facu
lty of Science\, Chulalongkorn University\, Bangkok 10330\, Thailand)\nQua
ntum algorithm is an algorithm for solving mathematical problems using qua
ntum systems encoded as information\, which is found to outperform classic
al algorithms. The objective of this study is to develop a quantum algorit
hm for finding the roots of $n^{\\mathrm{th}}$ degree polynomials where $n
$ is any positive integer. In classical algorithm\, the resources required
for solving this problem increase drastically when $n$ increases and it w
ould be impossible to practically solve the problem when $n$ is large. It
was found that any polynomial can be rearranged into a corresponding compa
nion matrix\, whose eigenvalues are roots of the polynomial. This leads to
a possibility to perform a quantum algorithm where the number of computat
ional resources increases as a polynomial of $n$. In this study\, we const
ruct a quantum circuit representing the companion matrix and use eigenvalu
e estimation technique to find roots of polynomial. The complexity of this
quantum algorithm is also compared with a classical algorithm for solving
the same problem.\n\nhttps://indico.cern.ch/event/336199/contributions/78
7708/
LOCATION: Hemingways' Lounge
URL:https://indico.cern.ch/event/336199/contributions/787708/
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