Electrostatically defined quantum dot arrays offer a compelling platform for quantum computation and simulation. However, tuning up such arrays with existing techniques becomes impractical when going beyond a handful of quantum dots. Here, we present a method for systematically adding quantum dots to an array one dot at a time, in such a way that the number of electrons on previously formed dots is unaffected. The method allows individual control of the number of electrons on each of the dots, as well as of the interdot tunnel rates. We use this technique to tune up a linear array of eight GaAs quantum dots such that they are occupied by one electron each. This new method overcomes a critical bottleneck in scaling up quantum-dot based qubit registers. arXiv:1901.00426v1 [cond-mat.mes-hall]

Engineered, highly-controllable quantum systems hold promise as simulators of emergent physics beyond the capabilities of classical computers [1]. 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 [2,3]. Here we use a quantum simulator consisting of a four-site square plaquette of quantum dots [4] to demonstrate Nagaoka ferromagnetism [5]. This form of itinerant magnetism has been rigorously studied theoretically [6][7][8][9] 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.The potential impact of discovering and understanding exotic forms of magnetism and superconductivity is one of the largest motivations for research in condensedmatter physics. These quantum mechanically governed effects result from the strong correlations that arise between interacting electrons. Modelling and simulating such systems can in some instances only be achieved through the use of engineered, controllable systems that operate in the quantum regime [1]. Efforts to build quantum simulators have already demonstrated great promise at this early stage [10], mainly led by the ultracold atom * These authors contributed equally to this work. † e-mail: l.m.k.vandersypen@tudelft.nl community [11-17]. More broadly, quantum simulations of many-body fermionic systems have been carried out in a range of experimental systems such as quantum dot lattices [18], dopant atoms [19], superconducting circuits [20] and trapped ions [21]. Electrostatically defined semiconductor quantum dots [22][23][24] have been proposed as excellent candidates for quantum simulations [25][26][27]. Their ability to reach thermal energies far below the hopping and on-site interaction energies enable access to previously unexplored material phases. Quantum dot systems have already achieved success in realising simulations of Mott-insulator physics in linear arrays [28]. Additionally, the feasibility to extend these systems into 2D lattices has recently been demonstrated [4,[29][30][31][32], including the ability to perform measurements of spin correlations [4]. As a result, quantum dot systems are now prime candidates for exploring how superconductivity and magnetism emerge in strongly-correlated electron systems [33][34][35].The emergence of magnetism in purely i...

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 make 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 a 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 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 to analog quantum simulations in two dimensions, not previously accessible in quantum dot systems.