In another path towards scaling up quantum processors that we have been pursuing, superconducting resonators are used to couple distant qubits. A first hallmark goal in this direction is to show that an individual photon stored in a resonator can be coherently coupled to one of our spin qubits. This we have shown recently, as we measured the coupling strength between one of our spin qubits and a resonator-based microwave photon to exceed the relevant decoherence and dissipation rates [Science 359, 1123 (2018)]! See also our own press release. Next up is to see if we can use this mechanism to couple distant qubits in an attempt to combine the spacing and versatility of the superconducting resonator with the long-lived coherence of our single-spin qubits.

Electrons confined to quantum dot lattices are described by the same physics as those confined in material lattices. By emulating open problems in materials in which electrons become strongly-correlated, one can hope to further the understanding of their emergent electronic and magnetic properties. We show that the control of our quantum dot systems is sufficient to emulate Fermi-Hubbard physics in the relevant regime of strong interactions and low temperatures, where correlations are expected to be at their strongest [Nature 548, 70 (2017)]. The developed toolbox can also be used to calibrate extended quantum dot arrays, a topic we are currently pursuing. For a general introduction, see here (English) or here (Dutch).

The field has been long looking at alternative semiconducting materials to GaAs as hosts for more long-lived electronic spin states. In a collaboration with the Eriksson group (U. Wisconsin), we have shown how strained silicon quantum wells in undoped SiGe heterostructures are a promising future platform for spin qubits. An on-chip micromagnet induced magnetic field gradient allows for all-electrical two-axis control of a single electron spin and a Ramsey decay timescale of 1 μs is observed [Nature Nanotechnology 9, 666 (2014)]. A study of gate fidelity shows qubit control is achieved at sufficient accuracy that any remaining errors can be corrected for using error correction protocols [PNAS 113, 11738 (2016)]. Direct room for improvement lies in the employ of isotopically purified ²⁸Si substrates, which promise even longer-lived spin states.

We have realized independent, all-electrical and single-shot read-out of two electron spins in a double quantum dot, with neglegible cross-talk between the two measurements and readout fidelities of ~86% on average. This allowed us to directly probe the anticorrelations between two spins prepared in a singlet state and to demonstrate the operation of the two-qubit exchange gate as the spins on the adjacent quantum dots are made to interact [Science 333, 1269 (2011)].

We realized magnetic resonance of a single electron spin in a quantum dot, whereby spin flips are induced via an oscillating magnetic field, generated on-chip. Electron spin resonance (ESR) in one quantum dot was detected with the help of a second dot that contained a reference spin, via a spin-dependent transport measurement through the two dots in series. Coherent control of the quantum state of the electron spin was achieved by applying short bursts of the oscillating magnetic field. We observe about eight oscillations of the spin state (so-called Rabi oscillations) during a microsecond burst. See also the press release or the article [Nature 442, 766 (2006)]. Equivalently, we have shown that aside from using oscillation magnetic fields, which are cumbersome to realize on chip, we can also flip single electron spins coherently using oscillating electric fields applied on one of the gates that are on chip already. The material-dependent spin-orbit interaction allows the movement of the electronic charge to couple to its spin degree of freedom, and as such allowed us to realize electrical dipole spin resonance (EDSR) [Science 318, 1430 (2007)]. See also two general introductions into these results and the state of the field at this point, one in English and one in Dutch.

We have demonstrated single-shot read-out of single- and two-electron spin states in a quantum dot. As we allow an electron to escape from the dot or not depending on its spin state, we measure the dot occupation using a quantum point contact next to the dot. As such we transfer spin to charge information. We have demonstrated two different ways for the spin-dependent escape; one method exploits the energy difference between the two spin states [Nature 430, 431 (2004)] and the other method exploits a difference in tunnel rates [PRL 94, 196802 (2005)]. Depending on the method, we achieved single-shot spin readout fidelities from 82% to 97.5%.