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A two-qubit quantum processor in a silicon device is demonstrated, which can perform the Deutsch–Josza algorithm and the Grover search algorithm. Taken for a spin in silicon The development of platforms for spin-based quantum computing continues apace. The individual components of such a system have been the subject of much investigation, and they have been assembled to implement specific quantum-computational algorithms. Thomas Watson and colleagues have now taken such component integration and control to the next level. Using two single-electron-spin qubits in a silicon-based double quantum dot, they realize a system that can be simply programmed to perform different quantum algorithms on demand. 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 1 , 2 . 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 3 , 4 , 5 . Initialization, readout and single- and two-qubit gates have been demonstrated in various quantum-dot-based qubit representations 6 , 7 , 8 , 9 . However, as seen with small-scale demonstrations of quantum computers using other types of qubit 10 , 11 , 12 , 13 , 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.

Semiconductor nanomembranes: the next small thing? Nanomembranes are a new and exciting class of materials for electronics applications. They are monocrystalline two-dimensional structures less than a few hundred nanometres thick. Unlike thin films, nanomembranes are self-standing and can be isolated from the substrate. Their geometry makes these materials particularly suitable for integration with electronic devices using existing technology. In this Review, the synthetic challenges, the multi-layer assembly procedures and applications of semiconductor nanomembranes in electronics and optoelectronics are reviewed. It covers both those inorganic semiconductive materials that can be reduced to a nanomembrane, and the two-dimensional organic carbon structures that are an alternative to graphene. Research in electronic nanomaterials, historically dominated by studies of nanocrystals/fullerenes and nanowires/nanotubes, now incorporates a growing focus on sheets with nanoscale thicknesses, referred to as nanomembranes. Such materials have practical appeal because their two-dimensional geometries facilitate integration into devices, with realistic pathways to manufacturing. Recent advances in synthesis provide access to nanomembranes with extraordinary properties in a variety of configurations, some of which exploit quantum and other size-dependent effects. This progress, together with emerging methods for deterministic assembly, leads to compelling opportunities for research, from basic studies of two-dimensional physics to the development of applications of heterogeneous electronics.

Large-scale arrays of quantum-dot spin qubits in Si/SiGe quantum wells require large or tunable energy splittings of the valley states associated with degenerate conduction band minima. Existing proposals to deterministically enhance the valley splitting rely on sharp interfaces or modifications in the quantum well barriers that can be difficult to grow. Here, we propose and demonstrate a new heterostructure, the “Wiggle Well”, whose key feature is Ge concentration oscillations inside the quantum well. Experimentally, we show that placing Ge in the quantum well does not significantly impact our ability to form and manipulate single-electron quantum dots. We further observe large and widely tunable valley splittings, from 54 to 239 μ eV. Tight-binding calculations, and the tunability of the valley splitting, indicate that these results can mainly be attributed to random concentration fluctuations that are amplified by the presence of Ge alloy in the heterostructure, as opposed to a deterministic enhancement due to the concentration oscillations. Quantitative predictions for several other heterostructures point to the Wiggle Well as a robust method for reliably enhancing the valley splitting in future qubit devices. Quantum-dot spin qubits in Si/SiGe quantum wells require a large and uniform valley splitting for robust operation and scalability. Here the authors introduce and characterize a new heterostructure with periodic oscillations of Ge atoms in the quantum well, which could enhance the valley splitting.

A simply prepared quantum bit that is a hybrid of spin and charge enables full control on the Bloch sphere with π-rotation times of less than 100 picoseconds in two orthogonal directions; the speed arises from the charge-like characteristics, and the spin-like features result in increased quantum coherence. A controllable hybrid qubit In many quantum bit or qubit systems, speed and coherence have opposing roles, with specific devices optimized for one or the other. Here Mark Eriksson and colleagues describe a hybrid qubit combining high speed, arising from its charge-like characteristics, with quantum coherence, arising from its spin-like features. This new device, made up of three electrons in two dots, is simple to prepare using standard silicon fabrication technology and exhibits gate fidelities between 85% and 95%, the highest so far reported in an electrically gated semiconductor quantum dot qubit. The similarities between gated quantum dots and the transistors in modern microelectronics 1 , 2 —in fabrication methods, physical structure and voltage scales for manipulation—have led to great interest in the development of quantum bits (qubits) in semiconductor quantum dots 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 . Although quantum dot spin qubits have demonstrated long coherence times, their manipulation is often slower than desired for important future applications, such as factoring 19 . Furthermore, scalability and manufacturability are enhanced when qubits are as simple as possible. Previous work has increased the speed of spin qubit rotations by making use of integrated micromagnets 11 , dynamic pumping of nuclear spins 12 or the addition of a third quantum dot 17 . Here we demonstrate a qubit that is a hybrid of spin and charge. It is simple, requiring neither nuclear-state preparation nor micromagnets. Unlike previous double-dot qubits, the hybrid qubit enables fast rotations about two axes of the Bloch sphere. We demonstrate full control on the Bloch sphere with π-rotation times of less than 100 picoseconds in two orthogonal directions, which is more than an order of magnitude faster than any other double-dot qubit. The speed arises from the qubit’s charge-like characteristics, and its spin-like features result in resistance to decoherence over a wide range of gate voltages. We achieve full process tomography in our electrically controlled semiconductor quantum dot qubit, extracting high fidelities of 85 per cent for X  rotations (transitions between qubit states) and 94 per cent for Z  rotations (phase accumulation between qubit states).

The electron spin in a silicon-based quantum dot can be controlled electrically for as long as several tens of microseconds, which improves the prospects for quantum information processing based on this type of quantum dot. 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 , and the spin state is read out in the single-shot mode 3 . Electron spin resonance occurs at two closely spaced frequencies, which we attribute to two valley states. Thanks to the weak hyperfine coupling in silicon, a Ramsey decay timescale of 1 μs is observed, almost two orders of magnitude longer than the intrinsic timescales in GaAs quantum dots 4 , 5 , whereas gate operation times are comparable to those reported in GaAs 6 , 7 , 8 . The spin echo decay time is ∼40 μs, both with one and four echo pulses, possibly limited by intervalley scattering. These advances strongly improve the prospects for quantum information processing based on quantum dots.

We report the first complete characterization of single-qubit and two-qubit gate fidelities in silicon-based spin qubits, including cross talk and error correlations between the two qubits. To do so, we use a combination of standard randomized benchmarking and a recently introduced method called character randomized benchmarking, which allows for more reliable estimates of the two-qubit fidelity in this system, here giving a 92% fidelity estimate for the controlled-Zgate. Interestingly, with character randomized benchmarking, the two-qubit gate fidelity can be obtained by studying the additional decay induced by interleaving the two-qubit gate in a reference sequence of single-qubit gates only. This work sets the stage for further improvements in all the relevant gate fidelities in silicon spin qubits beyond the error threshold for fault-tolerant quantum computation.

A microwave signal can be used to control semiconductor charge qubits with high fidelity. An intuitive realization of a qubit is an electron charge at two well-defined positions of a double quantum dot. This qubit is simple and has the potential for high-speed operation because of its strong coupling to electric fields. However, charge noise also couples strongly to this qubit, resulting in rapid dephasing at all but one special operating point called the ‘sweet spot’. In previous studies d.c. voltage pulses have been used to manipulate semiconductor charge qubits 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 but did not achieve high-fidelity control, because d.c. gating requires excursions away from the sweet spot. Here, by using resonant a.c. microwave driving we achieve fast (greater than gigahertz) and universal single qubit rotations of a semiconductor charge qubit. The Z -axis rotations of the qubit are well protected at the sweet spot, and we demonstrate the same protection for rotations about arbitrary axes in the X – Y plane of the qubit Bloch sphere. We characterize the qubit operation using two tomographic approaches: standard process tomography 9 , 10 and gate set tomography 11 . Both methods consistently yield process fidelities greater than 86% with respect to a universal set of unitary single-qubit operations.

The qubit is the fundamental building block of a quantum computer. We fabricate a qubit in a silicon double-quantum dot with an integrated micromagnet in which the qubit basis states are the singlet state and the spin-zero triplet state of two electrons. Because of the micromagnet, the magnetic field difference Δ B between the two sides of the double dot is large enough to enable the achievement of coherent rotation of the qubit’s Bloch vector around two different axes of the Bloch sphere. By measuring the decay of the quantum oscillations, the inhomogeneous spin coherence time [Formula] is determined. By measuring [Formula] at many different values of the exchange coupling J and at two different values of Δ B , we provide evidence that the micromagnet does not limit decoherence, with the dominant limits on [Formula] arising from charge noise and from coupling to nuclear spins.

An important goal in the manipulation of quantum systems is the achievement of many coherent oscillations within the characteristic dephasing time T 2 * . Most manipulations of electron spins in quantum dots have focused on the construction and control of two-state quantum systems, or qubits, in which each quantum dot is occupied by a single electron. Here we perform quantum manipulations on a system with three electrons per double quantum dot. We demonstrate that tailored pulse sequences can be used to induce coherent rotations between three-electron quantum states. Certain pulse sequences yield coherent oscillations fast enough that more than 100 oscillations are visible within a T 2 * time. The minimum oscillation frequency we observe is faster than 5 GHz. The presence of the third electron enables very fast rotations to all possible states, in contrast to the case when only two electrons are used, in which some rotations are slow. Electron spins in quantum dots are a promising platform for quantum information technologies. Using a double quantum dot system with three electrons, Shi et al . show that certain pulse sequences allow for fast rotations to all possible states, improving the performance compared with the two electron case.

Recent progress in laser wakefield acceleration has led to the emergence of a new generation of electron and X-ray sources that may have enormous benefits for ultrafast science. These novel sources promise to become indispensable tools for the investigation of structural dynamics on the femtosecond time scale, with spatial resolution on the atomic scale. Here, we demonstrate the use of laser-wakefield-accelerated electron bunches for time-resolved electron diffraction measurements of the structural dynamics of single-crystal silicon nano-membranes pumped by an ultrafast laser pulse. In our proof-of-concept study, we resolve the silicon lattice dynamics on a picosecond time scale by deflecting the momentum-time correlated electrons in the diffraction peaks with a static magnetic field to obtain the time-dependent diffraction efficiency. Further improvements may lead to femtosecond temporal resolution, with negligible pump-probe jitter being possible with future laser-wakefield-accelerator ultrafast-electron-diffraction schemes.