Nagaoka ferromagnetism observed in a quantum dot plaquette

Engineered, highly-controllable quantum systems hold promise as simulators of emergent physics beyond the capabilities of classical computers. An important problem in many-body physics is itinerant magnetism, which originates purely from long-range interactions of free electrons and whose existence in real systems has been subject to debate for decades. Here we use a quantum simulator consisting of a four-site square plaquette of quantum dots to demonstrate Nagaoka ferromagnetism. This form of itinerant magnetism has been rigorously studied theoretically but has remained unattainable in experiment. We load the plaquette with three electrons and demonstrate the predicted emergence of spontaneous ferromagnetic correlations through pairwise measurements of spin. We find the ferromagnetic ground state is remarkably robust to engineered disorder in the on-site potentials and can induce a transition to the low-spin state by changing the plaquette topology to an open chain. This demonstration of Nagaoka ferromagnetism highlights that quantum simulators can be used to study physical phenomena that have not yet been observed in any system before. The work also constitutes an important step towards large-scale quantum dot simulators of correlated electron systems.Comment: This version: main (8 pages, 6 figures) + supplementary (15 pages, 8 figures

High-fidelity adiabatic inversion of a 31P^{31}\mathrm{P} electron spin qubit in natural silicon

The main limitation to the high-fidelity quantum control of spins in semiconductors is the presence of strongly fluctuating fields arising from the nuclear spin bath of the host material. We demonstrate here a substantial improvement in single-qubit gate fidelities for an electron spin qubit bound to a $^{31}$P atom in natural silicon, by applying adiabatic inversion instead of narrow-band pulses. We achieve an inversion fidelity of 97%, and we observe signatures in the spin resonance spectra and the spin coherence time that are consistent with the presence of an additional exchange-coupled donor. This work highlights the effectiveness of adiabatic inversion techniques for spin control in fluctuating environments.Comment: 4 pages, 2 figure

Bell's inequality violation with spins in silicon

Bell's theorem sets a boundary between the classical and quantum realms, by providing a strict proof of the existence of entangled quantum states with no classical counterpart. An experimental violation of Bell's inequality demands simultaneously high fidelities in the preparation, manipulation and measurement of multipartite quantum entangled states. For this reason the Bell signal has been tagged as a single-number benchmark for the performance of quantum computing devices. Here we demonstrate deterministic, on-demand generation of two-qubit entangled states of the electron and the nuclear spin of a single phosphorus atom embedded in a silicon nanoelectronic device. By sequentially reading the electron and the nucleus, we show that these entangled states violate the Bell/CHSH inequality with a Bell signal of 2.50(10). An even higher value of 2.70(9) is obtained by mapping the parity of the two-qubit state onto the nuclear spin, which allows for high-fidelity quantum non-demolition measurement (QND) of the parity. Furthermore, we complement the Bell inequality entanglement witness with full two-qubit state tomography exploiting QND measurement, which reveals that our prepared states match the target maximally entangled Bell states with $>$96\% fidelity. These experiments demonstrate complete control of the two-qubit Hilbert space of a phosphorus atom, and show that this system is able to maintain its simultaneously high initialization, manipulation and measurement fidelities past the single-qubit regime.Comment: 10 pages, 3 figures, 1 table, 4 extended data figure

Electrically controlling single spin qubits in a continuous microwave field

Large-scale quantum computers must be built upon quantum bits that are both highly coherent and locally controllable. We demonstrate the quantum control of the electron and the nuclear spin of a single 31P atom in silicon, using a continuous microwave magnetic field together with nanoscale electrostatic gates. The qubits are tuned into resonance with the microwave field by a local change in electric field, which induces a Stark shift of the qubit energies. This method, known as A-gate control, preserves the excellent coherence times and gate fidelities of isolated spins, and can be extended to arbitrarily many qubits without requiring multiple microwave sources.Comment: Main paper: 13 pages, 4 figures. Supplementary information: 25 pages, 13 figure

Storing quantum information for 30 seconds in a nanoelectronic device

The spin of an electron or a nucleus in a semiconductor(1) naturally implements the unit of quantum information-the qubit. In addition, because semiconductors are currently used in the electronics industry, developing qubits in semiconductors would be a promising route to realize scalable quantum information devices(2). The solid-state environment, however, may provide deleterious interactions between the qubit and the nuclear spins of surrounding atoms(3), or charge and spin fluctuations arising from defects in oxides and interfaces(4). For materials such as silicon, enrichment of the spin-zero Si-28 isotope drastically reduces spin-bath decoherence(5). Experiments on bulk spin ensembles in Si-28 crystals have indeed demonstrated extraordinary coherence times(6-8). However, it remained unclear whether these would persist at the single-spin level, in gated nanostructures near amorphous interfaces. Here, we present the coherent operation of individual P-31 electron and nuclear spin qubits in a top-gated nanostructure, fabricated on an isotopically engineered Si-28 substrate. The P-31 nuclear spin sets the new benchmark coherence time (>30 s with Carr-Purcell-Meiboom-Gill (CPMG) sequence) of any single qubit in the solid state and reaches >99.99% control fidelity. The electron spin CPMG coherence time exceeds 0.5 s, and detailed noise spectroscopy(9) indicates that-contrary to widespread belief-it is not limited by the proximity to an interface. Instead, decoherence is probably dominated by thermal and magnetic noise external to the device, and is thus amenable to further improvement