Three-electron spin qubits.

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 exchange-only qubit (Bacon et al 2000  ) and its derived versions, e.g. the resonant exchange (RX) qubit, but we also discuss other qubit implementations using three electron spins. For each three-spin qubit we describe the qubit model, the envisioned 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 quantum computation for a viable candidate qubit implementation. We start by describing the full system of three electrons in a triple quantum dot, then discuss the charge-stability diagram, restricting ourselves to the relevant subsystem, introduce the qubit states, and discuss important transitions to other charge states (Russ et al 2016 ). Introducing the various qubit implementations, we begin with the exchange-only qubit (DiVincenzo et al 2000  339, Laird et al 2010 Phys. Rev. B 82 075403), followed by the RX qubit (Medford et al 2013  ), the spin-charge qubit (Kyriakidis and Burkard 2007 ), and the hybrid qubit (Shi et al 2012  Koh et al 2012  250503, Cao et al 2016  Thorgrimsson et al 2016 ). The main focus will be on the exchange-only qubit and its modification, 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 qubits which can be divided into short-ranged and long-ranged interactions. Both of these interaction types are expected to be necessary in a large-scale quantum computer. The short-ranged interactions use the exchange coupling by placing qubits next to each other and applying exchange-pulses (DiVincenzo et al 2000  339, Fong and Wandzura 2011  1003, Setiawan et al 2014 , Zeuch et al 2014  Doherty and Wardrop 2013  Shim and Tahan 2016 ), while the long-ranged interactions use the photons of a superconducting microwave cavity as a mediator in order to couple two qubits over long distances (Russ and Burkard 2015  205412, Srinivasa et al 2016 . The nature of the three-electron qubit states each having the same total spin and total spin in z-direction (same Zeeman energy) provides a natural protection against several sources of noise (DiVincenzo et al 2000  339, Taylor et al 2013 , Kempe et al 2001  Russ and Burkard 2015 ). The price to pay for this advantage is an increase in gate complexity. We also take into account the decoherence of the qubit through the influence of magnetic noise (  ), in particular dephasing due to the presence of nuclear spins, as well as dephasing due to charge noise (Medford et al 2013  , Shim and Tahan 2016  Russ and Burkard 2015  ), fluctuations of the energy levels on each dot due to noisy gate voltages or the environment. Several techniques are discussed which partly decouple the qubit from magnetic noise (Setiawan et al 2014 , West and Fong 2012 , Rohling and Burkard 2016 ) while for charge noise it is shown that it is favorable to operate the qubit on the so-called '(double) sweet spots' (Taylor et al 2013 , Shim and Tahan 2016  Russ and Burkard 2015   ), which are least susceptible to noise, thus providing a longer lifetime of the qubit.