Long-range interactions play a key role in several phenomena of quantum physics and chemistry. To study these phenomena, analog quantum simulators provide an appealing alternative to classical numerical methods. Gate-defined quantum dots have been established as a platform for quantum simulation, but for those experiments the effect of long-range interactions between the electrons did not play a crucial role. Here we present a detailed experimental characterization of long-range electron-electron interactions in an array of gate-defined semiconductor quantum dots. We demonstrate significant interaction strength among electrons that are separated by up to four sites, and show that our theoretical prediction of the screening effects matches well the experimental results. Based on these findings, we investigate how long-range interactions in quantum dot arrays may be utilized for analog simulations of artificial quantum matter. We numerically show that about ten quantum dots are sufficient to observe binding for a one-dimensional H2-like molecule. These combined experimental and theoretical results pave the way for future quantum simulations with quantum dot arrays and benchmarks of numerical methods in quantum chemistry.

Quantum-mechanical correlations of interacting fermions result in the emergence of exotic phases. Magnetic phases naturally arise in the Mott-insulator regime of the Fermi-Hubbard model, where charges are localized and the spin degree of freedom remains. In this regime, the occurrence of phenomena such as resonating valence bonds, frustrated magnetism, and spin liquids is predicted. Quantum systems with engineered Hamiltonians can be used as simulators of such spin physics to provide insights beyond the capabilities of analytical methods and classical computers. To be useful, methods for the preparation of intricate many-body spin states and access to relevant observables are required. Here, we show the quantum simulation of magnetism in the Mott-insulator regime with a linear quantum-dot array. We characterize the energy spectrum for a Heisenberg spin chain, from which we can identify when the conditions for homogeneous exchange couplings are met. Next, we study the multispin coherence with global exchange oscillations in both the singlet and triplet subspace of the Heisenberg Hamiltonian. Last, we adiabatically prepare the low-energy global singlet of the homogeneous spin chain and probe it with two-spin singlet-triplet measurements on each nearest-neighbor pair and the correlations therein. The methods and control presented here open new opportunities for the simulation of quantum magnetism benefiting from the flexibility in tuning and layout of gate-defined quantum-dot arrays.

The spin of a single electron in a semiconductor quantum dot provides a well-controlled and long-lived qubit implementation. The electron charge in turn allows control of the position of individual electrons in a quantum dot array, and enables charge sensors to probe the charge configuration. Here we show that the Coulomb repulsion allows an initial charge transition to induce subsequent charge transitions, inducing a cascade of electron hops, like toppling dominoes. A cascade can transmit information along a quantum dot array over a distance that extends by far the effect of the direct Coulomb repulsion. We demonstrate that a cascade of electrons can be combined with Pauli spin blockade to read out distant spins and show results with potential for high fidelity using a remote charge sensor in a quadruple quantum dot device. We implement and analyse several operating modes for cascades and analyse their scaling behaviour. We also discuss the application of cascade-based spin readout to densely-packed two-dimensional quantum dot arrays with charge sensors placed at the periphery. The high connectivity of such arrays greatly improves the capabilities of quantum dot systems for quantum computation and simulation.

Electrostatically-defined semiconductor quantum dot arrays offer a promising platform for quantum computation and quantum simulation. However, crosstalk of gate voltages to dot potentials and interdot tunnel couplings complicates the tuning of the device parameters. To date, crosstalk to the dot potentials is routinely and efficiently compensated using so-called virtual gates, which are specific linear combinations of physical gate voltages. However, due to exponential dependence of tunnel couplings on gate voltages, crosstalk to the tunnel barriers is currently compensated through a slow iterative process. In this work, we show that the crosstalk on tunnel barriers can be efficiently characterized and compensated for, using the fact that the same exponential dependence applies to all gates. We demonstrate efficient calibration of crosstalk in a quadruple quantum dot array and define a set of virtual barrier gates, with which we show orthogonal control of all interdot tunnel couplings. Our method marks a key step forward in the scalability of the tuning process of large-scale quantum dot arrays.

The fundamental concept of light–matter interaction is routinely realized by coupling the quantized electric field in a cavity to the dipole moment of a real or an artificial atom. A recent proposal^1,2, motivated by the prospect of overcoming the decohering effects of distant charge fluctuations, suggests that introduction of and coupling to an electric quadrupole moment of a single electron can be achieved by confining it in a triple quantum dot. Here, we show an experimental realization of this concept by connecting a superconducting microwave resonator to the middle of the three dots, such that the dipole coupling becomes negligible. We demonstrate strong coupling to the electron quadrupole moment and determine that the coherence of our system is limited by short-range charge noise. Our experiment enables the construction and detection of a complex electronic state of a single electron in a solid-state environment that does not exist as such for a free electron.

Engineered, highly controllable quantum systems are promising simulators of emergent physics beyond the simulation capabilities of classical computers¹. 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 debated for decades^2,3. Here we use a quantum simulator consisting of a four-electron-site square plaquette of quantum dots⁴ to demonstrate Nagaoka ferromagnetism⁵. This form of itinerant magnetism has been rigorously studied theoretically^6–9 but has remained unattainable in experiments. We load the plaquette with three electrons and demonstrate the predicted emergence of spontaneous ferromagnetic correlations through pairwise measurements of spin. We find that the ferromagnetic ground state is remarkably robust to engineered disorder in the on-site potentials and we 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 experimental system. The work also constitutes an important step towards large-scale quantum dot simulators of correlated electron systems.

Quantum Hall edge channels offer an efficient and controllable platform to study quantum transport in one dimension. Such channels are a prospective tool for the efficient transfer of quantum information at the nanoscale, and play a vital role in exposing intriguing physics. Electric current along the edge carries energy and heat leading to inelastic scattering, which may impede coherent transport. Several experiments attempting to probe the concomitant energy redistribution along the edge reported energy loss via unknown mechanisms of inelastic scattering. Here we employ quantum dots to inject and extract electrons at specific energies, to spectrally analyse inelastic scattering inside quantum Hall edge channels. We show that the missing energy puzzle could be untangled by incorporating non-local Auger-like processes, in which energy is redistributed between spatially separate parts of the sample. Our theoretical analysis, accounting for the experimental results, challenges common-wisdom analyses which ignore such non-local decay channels.

Increasing the number of quantum bits while preserving precise control of their quantum electronic properties is a significant challenge in materials design for the development of semiconductor quantum computing devices. Semiconductor heterostructures can host multiple quantum dots that are electrostatically defined by voltages applied to an array of metallic nanoelectrodes. The structural distortion of multiple-quantum-dot devices due to elastic stress associated with the electrodes has been difficult to predict because of the large micrometer-scale overall sizes of the devices, the complex spatial arrangement of the electrodes, and the sensitive dependence of the magnitude and spatial variation of the stress on processing conditions. Synchrotron X-ray nanobeam Bragg diffraction studies of a GaAs/AlGaAs heterostructure reveal the magnitude and nanoscale variation of these distortions. Investigations of individual linear electrodes reveal lattice tilts consistent with a 28-MPa compressive residual stress in the electrodes. The angular magnitude of the tilts varies by up to 20% over distances of less than 200 nm along the length of the electrodes, consistent with heterogeneity in the metal residual stress. A similar variation of the crystal tilt is observed in multiple-quantum-dot devices, due to a combination of the variation of the stress and the complex electrode arrangement. The heterogeneity in particular can lead to significant challenges in the scaling of multiple-quantum-dot devices due to differences between the charging energies of dots and uncertainty in the potential energy landscape. Alternatively, if incorporated in design, stress presents a new degree of freedom in device fabrication.

Quantum devices formed in high-electron-mobility semiconductor heterostructures provide a route through which quantum mechanical effects can be exploited on length scales accessible to lithography and integrated electronics. The electrostatic definition of quantum dots in semiconductor heterostructure devices intrinsically involves the lithographic fabrication of intricate patterns of metallic electrodes. The formation of metal/semiconductor interfaces, growth processes associated with polycrystalline metallic layers, and differential thermal expansion produce elastic distortion in the active areas of quantum devices. Understanding and controlling these distortions present a significant challenge in quantum device development. We report synchrotron X-ray nanodiffraction measurements combined with dynamical X-ray diffraction modeling that reveal lattice tilts with a depth-averaged value up to 0.04° and strain on the order of 10^-4 in the two-dimensional electron gas (2DEG) in a GaAs/AlGaAs heterostructure. Elastic distortions in GaAs/AlGaAs heterostructures modify the potential energy landscape in the 2DEG due to the generation of a deformation potential and an electric field through the piezoelectric effect. The stress induced by metal electrodes directly impacts the ability to control the positions of the potential minima where quantum dots form and the coupling between neighboring quantum dots.

The interaction between electrons in arrays of electrostatically defined quantum dots is naturally described by a Fermi-Hubbard Hamiltonian. Moreover, the high degree of tunability of these systems makes them a powerful platform to simulate different regimes of the Hubbard model. However, most quantum dot array implementations have been limited to one-dimensional linear arrays. In this letter, we present a square lattice unit cell of 2 × 2 quantum dots defined electrostatically in an AlGaAs/GaAs heterostructure using a double-layer gate technique. We probe the properties of the array using nearby quantum dots operated as charge sensors. We show that we can deterministically and dynamically control the charge occupation in each quantum dot in the single- to few-electron regime. Additionally, we achieve simultaneous individual control of the nearest-neighbor tunnel couplings over a range of 0-40 μeV. Finally, we demonstrate fast (∼1 μs) single-shot readout of the spin state of electrons in the dots through spin-to-charge conversion via Pauli spin blockade. These advances pave the way for analog quantum simulations in two dimensions, not previously accessible in quantum dot systems.

Coherent interactions at a distance provide a powerful tool for quantum simulation and computation. The most common approach to realize an effective long-distance coupling on-chip' is to use a quantum mediator, as has been demonstrated for superconducting qubits and trapped ions. For quantum dot arrays, which combine a high degree of tunability with extremely long coherence times, the experimental demonstration of the time evolution of coherent spin-spin coupling via an intermediary system remains an important outstanding goal. Here, we use a linear triple-quantum-dot array to demonstrate a coherent time evolution of two interacting distant spins via a quantum mediator. The two outer dots are occupied with a single electron spin each, and the spins experience a superexchange interaction through the empty middle dot, which acts as mediator. Using single-shot spin readout, we measure the coherent time evolution of the spin states on the outer dots and observe a characteristic dependence of the exchange frequency as a function of the detuning between the middle and outer dots. This approach may provide a new route for scaling up spin qubit circuits using quantum dots, and aid in the simulation of materials and molecules with non-nearest-neighbour couplings such as MnO (ref. 27), high-temperature superconductors and DNA. The same superexchange concept can also be applied in cold atom experiments.