Nanofabricated quantum bits permit large-scale integration but usually suffer from short coherence times due to interactions with their solid-state environment 1 . The outstanding challenge is to engineer the environment so that it minimally affects the qubit, but still allows qubit control and scalability. Here we demonstrate a long-lived single-electron spin qubit in a Si/SiGe quantum dot with all-electrical two-axis control. The spin is driven by resonant microwave electric fields in a transverse magnetic field gradient from a local micromagnet 2,3 , and the spin state is read out in single-shot mode 4 . Electron spin resonance occurs at two closely spaced frequencies, which we attribute to two valley states. Thanks to the weak hyperfine coupling in silicon, Ramsey and Hahn echo decay timescales of s µ 1 and s µ 40 , respectively, are observed. This is almost two orders of magnitude longer than the intrinsic timescales in III-V quantum dots 5,6 , while gate operation times are comparable to those achieved in GaAs 3,7,8 . This places the single-qubit rotations in the fault-tolerant regime 9 and strongly raises the prospects of quantum information processing based on quantum dots.The proposal by Loss and DiVincenzo 10 to define quantum bits by the state of a single electron spin in a gate-defined semiconductor quantum dot has guided research for the past 15 years 7 . Most progress was made in well-controlled III-V quantum dots, where spin manipulation with two 6,11 , three 12 and four 13 dots has been realized, but gate fidelities and spin coherence times are limited by the unavoidable interaction with the fluctuating nuclear spins in the host substrate 5,6 . While the randomness of the nuclear spin bath could be mitigated to some extent by feedback techniques 14 , eliminating the nuclear spins by using group IV host materials offers the potential for extremely long electron spin coherence times that exceed one second in P impurities in bulk 28 Si 15,16 .Much effort has been made to develop stable spin qubits in quantum dots defined in carbon nanotubes 17,18 , Ge/Si core/shell nanowires 19 , Si MOSFETs 20,21 and Si/SiGe 2D electron gases 16,22,23 . However, coherent control in these group IV quantum dots is so far limited to a Si/SiGe singlet-triplet qubit with only single-axis control 23 and a carbon nanotube single-electron spin qubit, with a Hahn echo decay time of 65 ns 17 .Our device is based on an undoped Si/SiGe heterostructure with two layers of electrostatic gates (Fig. 1a). Compared to conventional, doped heterostructures, this technology strongly improves charge stability 23 . First, accumulation gates ( mV 150 a + V ) are used to induce a twodimensional electron gas (2DEG) in a 12 nm wide Si quantum well 37 nm below the surface. Second, a set of depletion gates, labelled 1-12 in Fig. 1a, is used to form a single or double quantum dot in the 2DEG, flanked by a quantum point contact and another dot intended as charge sensors. Two μm 1 -wide, 200 nm-thick, and μm 5 . 1 -long Co magnets are placed...

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Controlling long-distance quantum correlations is central to quantum computation and simulation. In quantum dot arrays, experiments so far rely on nearest-neighbour couplings only, and inducing long-distance correlations requires sequential local operations. Here, we show that two distant sites can be tunnel-coupled directly. The coupling is mediated by virtual occupation of an intermediate site, with a strength that is controlled via the energy detuning of this site. It permits a single charge to oscillate coherently between the outer sites of a triple dot array without passing through the middle, as demonstrated through the observation of Landau-Zener-Stückelberg interference. The long-distance coupling significantly improves the prospects of fault-tolerant quantum computation using quantum dot arrays, and opens up new avenues for performing quantum simulations in nanoscale devices.

Self-assembled nanowire (NW) crystals can be grown into nearly defect-free nanomechanical resonators with exceptional properties, including small motional mass, high resonant frequency and low dissipation. Furthermore, by virtue of slight asymmetries in geometry, a NW's flexural modes are split into doublets oscillating along orthogonal axes. These characteristics make bottom-up grown NWs extremely sensitive vectorial force sensors. Here, taking advantage of its adaptability as a scanning probe, we use a single NW to image a sample surface. By monitoring the frequency shift and direction of oscillation of both modes as we scan above the surface, we construct a map of all spatial tip-sample force derivatives in the plane. Finally, we use the NW to image electric force fields distinguishing between forces arising from the NW charge and polarizability. This universally applicable technique enables a form of atomic force microscopy particularly suited to mapping the size and direction of weak tip-sample forces.