Realizable time crystal of four silicon quantum dot qubits

We demonstrate that exciting possible realizations of quantum Floquet matter are within reach for modern silicon spin qubits based in quantum dots, most notably the discrete time crystal (DTC). This is significant given that spin qubits have fallen behind other qubit architectures in terms of size and control. However, silicon spin qubits are especially well suited to this task as the charge noise that usually foils gate operations can now be leveraged as an asset in this time-crystal realization. We illustrate differences between prethermal phenomena and true time-crystalline spatiotemporal order. We demonstrate that even for a spin chain of four qubits, rich regime structures can be established by observing signatures of the discrete time crystal and the Floquet symmetry-protected topological regime both distinct from the thermal regime. We also analyze the persistence of these signatures at longer chain lengths, showing that the DTC lifetime grows exponentially with the system length and that these signatures may even be detectable for chains as small as three qubits. We also discuss the effects of longer pulse durations and the effectiveness of pulse sequences for converting the exchange interaction to an Ising model. Our theoretical predictions are well suited for immediate experimental implementations using currently existing quantum dot spin qubit systems.