◦ Quantum Computing with Superconductors
2. Computing with Qubits
Very interestingly, it’s possible to much faster solve some problems which is practically troublesome with classical algorithms with using quantum computation.
For example, factorization of large numbers is the best instance to show effectiveness of a quantum algorithm proposed by P.Shor.
Shor showed that exponential steps are needed for factorization of large numbers through classical computers, meanwhile only polynomial steps are required for solving such a problem with quantum computers.
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We explain what it means with a modern workstation cluster. 10＾10 years are required to perform a factorization of a number N with L ＝ 400 digits. This time is larger than the age of the universe.
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But, it’s possible to reduce the time for the task to below 3 years through a single hypothetical (≒ virtual) quantum computer ！
Shor’s factorizing algorithm works with quantum computation to quickly determine the period of the function F ( x ) ＝ a＾x mod N .
※ In this case, a is a randomly chosen small number with no factors in common with N .
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Techniques developed in the number theory can be used to factorize N from this period with high probability.
Two main algorithmic methods, namely, modular exponentiation and the inverse quantum Fourier transform take only L＾3 operations.
