  Physical systems representing qubits typically have one or more accessible
quantum states in addition to the two states that encode the qubit. We
demonstrate that active involvement of such auxiliary states can be beneficial
in constructing entangling two-qubit operations. We investigate the general
case of two multi-state quantum systems coupled via a quantum resonator. The
approach is illustrated with the examples of three systems: self-assembled
InAs/GaAs quantum dots, NV-centers in diamond, and superconducting transmon
qubits. Fidelities of the gate operations are calculated based on numerical
simulations of each system.
