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.

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...

The gate fidelity and the coherence time of a quantum bit (qubit) are important benchmarks for quantum computation. We construct a qubit using a single electron spin in an Si/SiGe quantum dot and control it electrically via an artificial spin-orbit field from a micromagnet. We measure an average single-qubit gate fidelity of ∼99% using randomized benchmarking, which is consistent with dephasing from the slowly evolving nuclear spins in the substrate. The coherence time measured using dynamical decoupling extends up to ∼400 μs for 128 decoupling pulses, with no sign of saturation. We find evidence that the coherence time is limited by noise in the 10-kHz to 1-MHz range, possibly because charge noise affects the spin via the micromagnet gradient. This work shows that an electron spin in an Si/SiGe quantum dot is a good candidate for quantum information processing as well as for a quantum memory, even without isotopic purification.T he performance of a quantum bit (qubit) is characterized by how accurately operations on the qubit are implemented and for how long its state is preserved. For improving qubit performance, it is important to identify the nature of the noise that introduces gate errors and leads to loss of qubit coherence. Ultimately, what counts is to balance the ability to drive fast qubit operations and the need for long coherence times (1).Electron spins in Si quantum dots are now known to be one of the most promising qubit realizations for their potential to scale up and their long coherence times (2-10). Using magnetic resonance on an electron spin bound to a phosphorus impurity in isotopically purified 28 Si (5) or confined in a 28 Si metal-oxidesemiconductor (MOS) quantum dot (3), ∼0.3-MHz Rabi frequencies, gate fidelities over 99.5%, and spin memory times of tens to hundreds of milliseconds have been achieved. Also, electrical control of an electron spin has been demonstrated in a (natural abundance) Si/SiGe quantum dot, which was achieved by applying an AC electric field that oscillates the electron wave function back and forth in the gradient magnetic field of a local micromagnet (7). The advantage of electrical control over magnetic control is that electric fields can be generated without the need for microwave cavities or striplines and allows better spatial selectivity, which simplifies individual addressing of qubits. However, the magnetic field gradient also makes the qubit sensitive to electrical noise, so it is important to examine whether the field gradient limits the spin coherence time and the gate fidelity.In our previous work (7), the effect of electrical noise on spin coherence and gate fidelity was overwhelmed by transitions between the lowest two valley-orbit states. Because different valleyorbit states have slightly different Larmor frequencies, such a transition will quickly randomize the phase of the electron spin. If valley-orbit transitions can be (largely) avoided, then the question becomes what limits coherence and fidelities instead.Here we measure the gate fidelity and ...