Interacting electrons on material lattices can build up strong quantum correlations, which in turn can lead to the emergence of a wide range of novel and potentially useful magnetic and electronic material properties. Our understanding of this physics, however, is severely limited by the exponential growth in complexity with system size, which leads all classical methods to fall fundamentally short. In this thesis, I show how artificial lattices of conduction band electrons in semiconductors, so-called quantum dot arrays, can be used to directly emulate and therefore elucidate such Fermi-Hubbard physics. To this end, I focus on two approaches. A top-down approach allows to scale easily, but lacks to ability to control or measure individual sites. A bottom-up approach on the other hand utilizes the small devices employed by the community for qubit experiments, in which the control of individual sites is both a blessing and a curse. We address the issue of control to the point where mapping to relevant models is possible and efficiently calibrating larger devices becomes feasible. These results open up the inherently well-suited and scalable platform of quantum dots to emulate novel quantum states of matter.@en

One of the main bottlenecks in the pursuit of a large-scale-chip-based quantum computer is the large number of control signals needed to operate qubit systems. As system sizes scale up, the number of terminals required to connect to off-chip control electronics quickly becomes unmanageable. Here, we discuss a quantum-dot spin-qubit architecture that integrates on-chip control electronics, allowing for a significant reduction in the number of signal connections at the chip boundary. By arranging the qubits in a two-dimensional array with about 12μm pitch, we create space to implement locally integrated sample-and-hold circuits. This allows us to offset the inhomogeneities in the potential landscape across the array and to globally share the majority of the control signals for qubit operations. We make use of advanced circuit modeling software to go beyond conceptual drawings of the component layout, to assess the feasibility of the scheme through a concrete floor plan, including estimates of footprints for quantum and classical electronics, as well as routing of signal lines across the chip using different interconnect layers. We make use of local demultiplexing circuits to achieve an efficient signal-connection scaling, leading to a Rent's exponent as low as p=0.43. Furthermore, we use available data from state-of-the-art spin qubit and microelectronics technology development, as well as circuit models and simulations, to estimate the operation frequencies and power consumption of a million-qubit array. This work presents a complementary approach to previously proposed architectures, focusing on a feasible scheme to integrating quantum and classical hardware, and identifying remaining challenges for achieving full fault-tolerant quantum computation. It thereby significantly closes the gap towards a fully CMOS-compatible quantum computer implementation. @en

Interacting fermions on a lattice can develop strong quantum correlations, which are the cause of the classical intractability of many exotic phases of matter. Current efforts are directed towards the control of artificial quantum systems that can be made to emulate the underlying Fermi-Hubbard models. Electrostatically confined conduction-band electrons define interacting quantum coherent spin and charge degrees of freedom that allow all-electrical initialization of low-entropy states and readily adhere to the Fermi-Hubbard Hamiltonian. Until now, however, the substantial electrostatic disorder of the solid state has meant that only a few attempts at emulating Fermi-Hubbard physics on solid-state platforms have been made. Here we show that for gate-defined quantum dots this disorder can be suppressed in a controlled manner. Using a semi-automated and scalable set of experimental tools, we homogeneously and independently set up the electron filling and nearest-neighbour tunnel coupling in a semiconductor quantum dot array so as to simulate a Fermi-Hubbard system. With this set-up, we realize a detailed characterization of the collective Coulomb blockade transition, which is the finite-size analogue of the interaction-driven Mott metal-to-insulator transition. As automation and device fabrication of semiconductor quantum dots continue to improve, the ideas presented here will enable the investigation of the physics of ever more complex many-body states using quantum dots.@en

Electrostatic confinement in semiconductors provides a flexible platform for the emulation of interacting electrons in a two-dimensional lattice, including in the presence of gauge fields. This combination offers the potential to realize a wide host of quantum phases. Capacitance spectroscopy provides a technique that allows one to directly probe the density of states of such two-dimensional electron systems. Here, we present a measurement and fabrication scheme that builds on capacitance spectroscopy and allows for the independent control of density and periodic potential strength imposed on a two-dimensional electron gas. We characterize disorder levels and (in)homogeneity and develop and optimize different gating strategies at length scales where interactions are expected to be strong. A continuation of these ideas might see to fruition the emulation of interaction-driven Mott transitions or Hofstadter butterfly physics.@en

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.@en

Current implementations of quantum computers suffer from large numbers of control lines per qubit, becoming unmanageable with system scale up. Here, we discuss a sparse spin-qubit architecture featuring integrated control electronics significantly reducing the off-chip wire count. This quantum-classical hardware integration closes the feasibility gap towards a CMOS quantum computer.@en