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Detailed contents are not shown here because of space limitation, in a word, two registers of n ＝ 2［ log 2 N ］and m ＝ ［ log 2 N ］qubits are used in Shor’s algorithm.
The algorithm is realized by five major computation steps, namely,
( 1 ) Initialization of both registers by preparing their initial states
( 2 ) Applications of a Hadamard transformation to the first n qubits
( 3 ) Multiplying the second register by a＾x mod N for some random a ＜ N without common factors with N
( 4 ) Performing the inverse quantum Fourier transformation ( based on two-qubit controlled phase rotation operator ) on the first register
( 5 ) Measurements of the qubits in the first register
