The periodfindingsub-problem for this task is possible using a superposition of states.
One algorithm for doing this uses exponent vectors and bitwise adds the values of those vectors mod2; that algorithm, for some input n, multiplies squares and their remainders mod n together to find acongruence of squares mod n in a manner that improves upon Dixon's method for doing this. The periodfindingsub-problem for this task is possible using a superposition of states. The most efficient classicalalgorithm for this is the (*) general number field sieve. However, a big-Oh of log n cubed quantum algorithm fordoing this named for Shor is fast enough for very large products of primes, which would break RSA encryption. For10 points, name this procedure which, for a number of the form a squared minus b squared results in a plus b and aminus b.
One algorithm for doing this uses exponent vectors and bitwise adds the values of those vectors mod2; that algorithm, for some input n, multiplies squares and their remainders mod n together to find acongruence of squares mod n in a manner that improves upon Dixon's method for doing this.
integer factorization [accept prime factorization]