Programmable Heisenberg interactions between Floquet qubits

The fundamental trade-off between robustness and tunability in quantum devices is a central challenge in the pursuit of practical quantum advantage and fault-tolerant quantum computing. In particular, certain emerging solid-state quantum architectures are designed to achieve high coherence at the expense of having invariable spectral configurations, thus limiting the range of native interactions between the qubits. Here, by encoding computational information onto frequency-modifiable Floquet states, we demonstrate an XXZ Heisenberg interaction model with fully adjustable anisotropy between statically coupled fixed-frequency transmon circuits. Such an archetypal model allows quantum simulation of exotic many-body physics such as quantum phase transitions of spin systems, phantom spin-helix states, or formation of multi-photon bound states. To illustrate the robustness and versatility of the protocol, we tailor the transverse and longitudinal coupling independently, 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, by realizing the transverse coupling between higher levels leading to a three-qubit CCZ gate with an estimated fidelity of 96.18(5)%, we show that the interactions can be generally engineered for multilevel systems without additional hardware components. Our Floquet protocol is broadly applicable to various solid-state platforms, thereby unlocking a suite of essential interactions for hardware-efficient quantum computing and simulation using fixed-frequency architectures.