ABSTRACT
Two applications of virtual knot theory include quantum computation and textiles. Other applications of knot theory include chemistry and biology, with a specific emphasis on DNA recombination. Classical computers use a bit to encode information. A bit stores either a 0 or 1 and data is encoded in strings of 0's and 1's. Logical gates act on these strings of data—taking two bits as input and producing a single bit as output. Clearly, what we think of as a "computer computation" requires thousands of bits and operations. Two famous quantum algorithms are Shor's Algorithm and Grover's algorithm. Both of these quantum algorithms are "faster" than their classical counterparts. Another reason for knot theorists' interest in quantum computation is one of the models of quantum computation. Theoretical models of quantum computation involve three main steps: initialize the system, apply logical gates and measure the outcome.
