6.6 Quantum Gate Decompositions
The most widely used NISQ computing technologies are trapped ions and superconducting qubits. In both cases, one-qubit gates are much faster than two-qubit gates (by an order of magnitude). Additionally, one-qubit gates have much higher fidelity [46, 178]. This means that we can treat one-qubit gates as computationally inexpensive and should not worry too much about their quantities. At the same time, we have to be economical with two-qubit gates: out of two equivalent circuits, the one with the smaller number of two-qubit gates would generally perform better. Therefore, we should be aware of the two-qubit gates that are native to any particular system – gates that can be implemented naturally using standard hardware control techniques. More complex gates can be decomposed into a subcircuit of the native gates but an even better solution would be to specify the algorithm that takes advantage of the native gates and bypasses the need of having...
