  The fundamental trade-off between robustness and tunability is a central
challenge in the pursuit of quantum simulation and fault-tolerant quantum
computation. In particular, many emerging quantum architectures are designed to
achieve high coherence at the expense of having fixed spectra and consequently
limited types of controllable interactions. Here, by adiabatically transforming
fixed-frequency superconducting circuits into modifiable Floquet qubits, we
demonstrate an XXZ Heisenberg interaction with fully adjustable anisotropy.
This interaction model is on one hand the basis for many-body quantum
simulation of spin systems, and on the other hand the primitive for an
expressive quantum gate set. To illustrate the robustness and versatility of
our Floquet protocol, we tailor the Heisenberg Hamiltonian and implement
two-qubit iSWAP, CZ, and SWAP gates with estimated fidelities of 99.32(3)%,
99.72(2)%, and 98.93(5)%, respectively. In addition, we implement a Heisenberg
interaction between higher energy levels and employ it to construct a
three-qubit CCZ gate with a fidelity of 96.18(5)%. Importantly, the protocol is
applicable to various fixed-frequency high-coherence platforms, thereby
unlocking a suite of essential interactions for high-performance quantum
information processing. From a broader perspective, our work provides
compelling avenues for future exploration of quantum electrodynamics and
optimal control using the Floquet framework.
