  We demonstrate the use of optimal control to design two entropy-manipulating
quantum gates which are more complex than the corresponding, commonly used,
gates, such as CNOT and Toffoli (CCNOT): A 2-qubit gate called PE (polarization
exchange) and a 3-qubit gate called COMP (polarization compression) were
designed using GRAPE, an optimal control algorithm. Both gates were designed
for a three-spin system. Our design provided efficient and robust NMR radio
frequency (RF) pulses for 13C2-trichloroethylene (TCE), our chosen three-spin
system. We then experimentally applied these two quantum gates onto TCE at the
NMR lab. Such design of these gates and others could be relevant for
near-future applications of quantum computing devices.
