Quantum simulation of a Fermi–Hubbard model using a semiconductor quantum dot array

A quantum simulation platform based on quantum dots is reported that can operate at relatively low temperatures, and its utility is shown by simulating a Fermi–Hubbard model. Quantum simulations on quantum dots Quantum simulations have been performed on various different platforms, for example using vacancies in diamond or ultracold quantum gases. Quantum dots have been regarded as a promising constituent of quantum simulation platforms for some time, but owing to difficulties in calibrating them it has so far been impossible to run a successful simulation. Here, the authors overcome these difficulties and demonstrate a quantum simulation of a Fermi–Hubbard model, which is a famous model in condensed matter physics. Quantum simulation platforms based on quantum dots are predicted to be able to reach lower temperatures than atomic-physics-based platforms. This could help to clarify puzzles in condensed matter physics, such as high-temperature superconductivity. Interacting fermions on a lattice can develop strong quantum correlations, which are the cause of the classical intractability of many exotic phases of matter 1 , 2 , 3 . Current efforts are directed towards the control of artificial quantum systems that can be made to emulate the underlying Fermi–Hubbard models 4 , 5 , 6 . 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 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 . 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 18 , 19 . 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 20 , which is the finite-size analogue of the interaction-driven Mott metal-to-insulator transition 1 . As automation and device fabrication of semiconductor quantum dots continue to improve, the ideas presented here will enable the investigation of the physic