Always-on Gapless Exchange Qubits with Baseband Control

We propose an implementation of exchange-only spin qubits that allows for baseband control of an always-on, gapless system using a four electron, singlet-only encoding. The spin state of the four electrons forms a qubit subspace that is protected from local magnetic field gradients---a leading source of error in exchange-only systems. Leakage out of this computational subspace is energetically suppressed by ensuring that the exchange coupling between the four electrons is always nonzero. Single qubit gates are performed by decreasing the appropriate couplings using static pulses, tuning the system away from a gapless regime---achieved when each exchange coupling is set to the same value. Two-qubit gates are performed with a single interqubit exchange pulse, greatly simplifying the complex pulse sequences used in conventional gapless exchange-only qubits. A similar architecture can be implemented using only three electrons, though this system lacks protection against local magnetic field gradients.