Quantum circuit for a direct sum of two-dimensional unitary operators
Ville Bergholm, Juha J. Vartiainen, Mikko Möttönen, Martti M. Salomaa · arXiv (Cornell University) · 2004
In this article we study n-qubit quantum gates which may be represented as direct sums of two-dimensional unitary operators. We call this class of gates uniformly controlled one-qubit gates. We present a quantum circuit which implements any gate of this type using 2^{n-1} - 1 controlled-NOT gates, 2^{n-1} one-qubit gates and a single n-qubit diagonal gate. The construction is based on a modified version of the so-called quantum multiplexor circuit. We illustrate the versatility of the uniformly controlled gates by applying them to the decomposition of a general n-qubit gate and an n-qubit state-preparation procedure. Moreover, we study the implementation of these circuits using only nearest-neighbor gates and give the worst-case one-qubit and CNOT gate counts for all of the aforementioned applications. In all four cases, the proposed method either improves or achieves the previously reported upper bounds for the gate counts.