Physics – Quantum Physics
Scientific paper
2003-12-30
Phys. Rev. Lett. 92 177902 (2004)
Physics
Quantum Physics
4 pages, 2 figures
Scientific paper
10.1103/PhysRevLett.92.177902
Optimal implementation of quantum gates is crucial for designing a quantum computer. We consider the matrix representation of an arbitrary multiqubit gate. By ordering the basis vectors using the Gray code, we construct the quantum circuit which is optimal in the sense of fully controlled single-qubit gates and yet is equivalent with the multiqubit gate. In the second step of the optimization, superfluous control bits are eliminated, which eventually results in a smaller total number of the elementary gates. In our scheme the number of controlled NOT gates is $O(4^n)$ which coincides with the theoretical lower bound.
Mottonen Mikko
Salomaa Martti M.
Vartiainen Juha J.
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