The cost of quantum gate primitives

Abstract

The cost of the most frequently used gates in quantum computation is estimated by counting the sequence of basic physical operations required for implementation on a quantum computer. The sequence of physical operations comprising each gate is minimized using a software algorithm based on commutation rules. Because operation costs are machine dependent, an ideal practical quantum computer is presented and used for calculations. The presented gate costs are not necessarily minimal; however at least they provide reference to the upper bound.