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The goal of the quantum subroutine of Shor's algorithm is, given coprime integers and < <, to find the order of modulo , which is the smallest positive integer such that (). To achieve this, Shor's algorithm uses a quantum circuit involving two registers.
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In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression. These rules are formalized with a ranking of the operations.
The order of a group G is denoted by ord(G) or | G |, and the order of an element a is denoted by ord(a) or | a |, instead of ( ), where the brackets denote the generated group. Lagrange's theorem states that for any subgroup H of a finite group G , the order of the subgroup divides the order of the group; that is, | H | is a divisor of | G | .
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Google Search (also known simply as Google or Google.com) is a search engine operated by Google. It allows users to search for information on the Internet by entering keywords or phrases. Google Search uses algorithms to analyze and rank websites based on their relevance to the search query. It is the most popular search engine worldwide.
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In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean -valued outcome: success (with probability p) or failure (with probability ).
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.