  Fixed-frequency superconducting qubits demonstrate remarkable success as
platforms for stable and scalable quantum computing. Cross-resonance gates have
been the workhorse of fixed-coupling, fixed-frequency superconducting
processors, leveraging the entanglement generated by driving one qubit
resonantly with a neighbor's frequency to achieve high-fidelity, universal
CNOTs. Here, we use on-resonant and off-resonant microwave drives to go beyond
cross-resonance, realizing natively interesting two-qubit gates that are not
equivalent to CNOTs. In particular, we implement and benchmark native ISWAP,
SWAP, $\sqrt{\text{ISWAP}}$, and BSWAP gates. Furthermore, we apply these
techniques for an efficient construction of the B-gate: a perfect entangler
from which any two-qubit gate can be reached in only two applications. We show
these native two-qubit gates are better than their counterparts compiled from
cross-resonance gates. We elucidate the resonance conditions required to drive
each two-qubit gate and provide a novel frame tracking technique to implement
them in Qiskit.
