  The goal of this article is to review the progress of three-electron spin
qubits from their inception to the state of the art. We direct the main focus
towards the resonant exchange (RX) qubit and the exchange-only qubit, but we
also discuss other qubit implementations using three electron spins. For each
three-spin qubit we describe the qubit model, the physical realization, the
implementations of single-qubit operations, as well as the read-out and
initialization schemes. Two-qubit gates and decoherence properties are
discussed for the RX qubit and the exchange-only qubit, thereby, completing the
list of requirements for a viable candidate qubit implementation for quantum
computation. We start with describing the full system of three electrons in a
triple quantum dot, then discuss the charge-stability diagram and restrict
ourselves to the relevant subsystem, introduce the qubit states, and discuss
important transitions to other charge states. Introducing the various qubit
implementations, we begin with the exchange-only qubit, followed by the
spin-charge qubit, the hybrid qubit, and the RX qubit, discussing for each the
single-qubit operations, read-out, and initialization methods, whereas the main
focus will be on the RX qubit, whose single-qubit operations are realized by
driving the qubit at its resonant frequency in the microwave range similar to
electron spin resonance. Two different types of two-qubit operations are
presented for the exchange-only and the RX qubit which can be divided into
short-ranged and long-ranged interactions. Both of these interaction types can
be expected to be necessary in a large-scale quantum computer. We also take
into account the decoherence of the qubit through the influence of magnetic
noise as well as dephasing due to charge noise.

Mesoscale and Nanoscale Physics