Three-electron spin qubits

Abstract

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 Phys. Rev. Lett. 85 1758-61, DiVincenzo et al 2000 Nature 408 339) 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 Phys. Rev. B 94 165411). Introducing the various qubit implementations, we begin with the exchange-only qubit (DiVincenzo et al 2000 Nature 408 339, Laird et al 2010 Phys. Rev. B 82 075403), followed by the RX qubit (Medford et al 2013 Phys. Rev. Lett. 111 050501, Taylor et al 2013 Phys. Rev. Lett. 111 050502), the spin-charge qubit (Kyriakidis and Burkard 2007 Phys. Rev. B 75 115324), and the hybrid qubit (Shi et al 2012 Phys. Rev. Lett. 108 140503, Koh et al 2012 Phys. Rev. Lett. 109 250503, Cao et al 2016 Phys. Rev. Lett. 116 086801, Thorgrimsson et al 2016 arXiv:1611.04945). 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 Nature 408 339, Fong and Wandzura 2011 Quantum Inf. Comput. 11 1003, Setiawan et al 2014 Phys. Rev. B 89 085314, Zeuch et al 2014 Phys. Rev. B 90 045306, Doherty and Wardrop 2013 Phys. Rev. Lett. 111 050503, Shim and Tahan 2016 Phys. Rev. B 93 121410), 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 Phys. Rev. B 92 205412, Srinivasa et al 2016 Phys. Rev. B 94 205421). 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 Nature 408 339, Taylor et al 2013 Phys. R...

Quantum information density scaling and qubit operation time constraints of CMOS silicon-based quantum computer architectures

“…39 In single spin physical qubits, the two spin states of an electron in a QD are Zeeman-split by an external magnetic field and manipulated by means of microwave pulses. 32,40 A S-T virtual qubit architecture is based on two electron spins in a double QD and it does not require microwave pulses.…”

“…Both architecture are extensively reviewed in ref. 39. In contrast to previous architectures, only a small magnetic field is required during the virtual qubit initialization, provided externally.…”

“…The surface code implementation proposal based on a spinprobe controlled two-dimensional array of donors 69 considers a distance of about 400 nm between neighboring donors, which represents an intermediate scale between QDs and superconductor qubits. Regardless of the chosen physical implementation, besides the desirable improvements concerning the single qubit specifications to achieve fault-tolerant fidelity for one-qubit and two-qubit gates, the practical demonstration of two-qubit devices and more complex circuits involves additional issues 39,45 : the need for long range quantum communication, QEC, and the demanding requirements related to the massive integration of classical control electronics at the quantum chip level. In the following, we focus on the double QD design for hybrid qubits, which could also be naturally adapted to charge qubits 51 and S-T architectures 43 if the issue of adding a local magnetic field gradient can be addressed with no cost in terms of additional space requirements.…”

“…39,43 The first experimental demonstration of the exchangeonly double QD qubit showed T 2 of 10 ns with operation time of the order of 100 ps with Si-SiGe QD. More in detail, 5.2 GHz Xrotations and 11.5 GHz Z-rotations were coherently driven with fidelity of 85 and 94%, respectively.…”

High-fidelity non-adiabatic cutting and stitching of a spin chain via local control

“…In general, such a spin system can be realized in an ensemble of quantum dots, proposed as hardware elements for quantum information processing [22] as well as in other spin-based systems with a similar prospective [23]. The single spin manipulation in a quantum dot has become a well-controllable procedure [24,25] by now. The spin-spin interaction, strongly dependent on the electron tunneling rate between the dots can be controlled electrically by a fast gating of the tunneling channels [26].…”