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Quantum computation requires many qubits that can be coherently controlled and coupled to each other1. Qubits that are defined using lithographic techniques have been suggested to enable the development of scalable quantum systems because they can be implemented using semiconductor fabrication technology2–5. However, leading solid-state approaches function only at temperatures below 100 millikelvin, where cooling power is extremely limited, and this severely affects the prospects of practical quantum computation. Recent studies of electron spins in silicon have made progress towards a platform that can be operated at higher temperatures by demonstrating long spin lifetimes6, gate-based spin readout7and coherent single-spin control8. However, a high-temperature two-qubit logic gate has not yet been demonstrated. Here we show that silicon quantum dots can have sufficient thermal robustness to enable the execution of a universal gate set at temperatures greater than one kelvin. We obtain single-qubit control via electron spin resonance and readout using Pauli spin blockade. In addition, we show individual coherent control of two qubits and measure single-qubit fidelities of up to 99.3 per cent. We demonstrate the tunability of the exchange interaction between the two spins from 0.5 to 18 megahertz and use it to execute coherent two-qubit controlled rotations. The demonstration of ‘hot’ and universal quantum logic in a semiconductor platform paves the way for quantum integrated circuits that host both the quantum hardware and its control circuitry on the same chip, providing a scalable approach towards practical quantum information processing.

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 decades2,3. Here we use a quantum simulator consisting of a four-electron-site square plaquette of quantum dots4to demonstrate Nagaoka ferromagnetism5. This form of itinerant magnetism has been rigorously studied theoretically6–9but 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.

Extremely long coherence times, excellent single-qubit gate fidelities, and two-qubit logic have been demonstrated with silicon metal-oxide-semiconductor spin qubits, making it one of the leading platforms for quantum information processing. Despite this, a long-standing challenge in this system has been the demonstration of tunable tunnel coupling between single electrons. Here we overcome this hurdle with gate-defined quantum dots and show couplings that can be tuned on and off for quantum operations. We use charge sensing to discriminate between the (2,0) and (1,1) charge states of a double quantum dot and show excellent charge sensitivity. We demonstrate tunable coupling up to 13 GHz, obtained by fitting charge polarization lines, and tunable tunnel rates down to <1 Hz, deduced from the random telegraph signal. The demonstration of tunable coupling between single electrons in a silicon metal-oxide-semiconductor device provides significant scope for high-fidelity two-qubit logic toward quantum information processing with standard manufacturing.

Graphene and few-layer graphene at high bias expose a wealth of phenomena due to the high temperatures reached. With in situ transmission electron microscopy, we observe directly how the current modifies the structure, and vice versa. In some samples, cracks propagate from the edges of the flakes, leading to the formation of narrow constrictions or to nanometer spaced gaps after breakdown. In other samples, we find layer-by-layer evaporation of few-layer graphene, which could be exploited for the controlled production of single layer graphene from multilayered samples. Surprisingly, we even find that two pieces of graphene that overlap can heal out at high bias and form one continuous sheet. These findings open up new avenues to structure graphene for specific device applications.

Now that it is possible to achieve measurement and control fidelities for individual quantum bits (qubits) above the threshold for fault tolerance, attention is moving towards the difficult task of scaling up the number of physical qubits to the large numbers that are needed for fault-tolerant quantum computing. In this context, quantum-dot-based spin qubits could have substantial advantages over other types of qubit owing to their potential for all-electrical operation and ability to be integrated at high density onto an industrial platform. Initialization, readout and single- and two-qubit gates have been demonstrated in various quantum-dot-based qubit representations. However, as seen with small-scale demonstrations of quantum computers using other types of qubit, combining these elements leads to challenges related to qubit crosstalk, state leakage, calibration and control hardware. Here we overcome these challenges by using carefully designed control techniques to demonstrate a programmable two-qubit quantum processor in a silicon device that can perform the Deutsch–Josza algorithm and the Grover search algorithm—canonical examples of quantum algorithms that outperform their classical analogues. We characterize the entanglement in our processor by using quantum-state tomography of Bell states, measuring state fidelities of 85–89 per cent and concurrences of 73–82 per cent. These results pave the way for larger-scale quantum computers that use spins confined to quantum dots.

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.

Spin-based electronics or spintronics relies on the ability to store, transport and manipulate electron spin polarization with great precision. In its ultimate limit, information is stored in the spin state of a single electron, at which point quantum information processing also becomes a possibility. Here, we demonstrate the manipulation, transport and readout of individual electron spins in a linear array of three semiconductor quantum dots. First, we demonstrate single-shot readout of three spins with fidelities of 97% on average, using an approach analogous to the operation of a charge-coupled device (CCD). Next, we perform site-selective control of the three spins, thereby writing the content of each pixel of this ‘single-spin charge-coupled device’. Finally, we show that shuttling an electron back and forth in the array hundreds of times, covering a cumulative distance of 80 μm, has negligible influence on its spin projection. Extrapolating these results to the case of much larger arrays points at a diverse range of potential applications, from quantum information to imaging and sensing.