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Although universal quantum computers ideally solve problems such as factoring integers exponentially more efficiently than classical machines, the formidable challenges in building such devices motivate the demonstration of simpler, problem-specific algorithms that still promise a quantum speedup. We constructed a quantum boson-sampling machine (QBSM) to sample the output distribution resulting from the nonclassical interference of photons in an integrated photonic circuit, a problem thought to be exponentially hard to solve classically. Unlike universal quantum computation, boson sampling merely requires indistinguishable photons, linear state evolution, and detectors. We benchmarked our QBSM with three and four photons and analyzed sources of sampling inaccuracy. Scaling up to larger devices could offer the first definitive quantum-enhanced computation.

Quantum computers are unnecessary for exponentially efficient computation or simulation if the Extended Church-Turing thesis is correct. The thesis would be strongly contradicted by physical devices that efficiently perform tasks believed to be intractable for classical computers. Such a task is boson sampling: sampling the output distributions of n bosons scattered by some passive, linear unitary process. We tested the central premise of boson sampling, experimentally verifying that three-photon scattering amplitudes are given by the permanents of submatrices generated from a unitary describing a six-mode integrated optical circuit. We find the protocol to be robust, working even with the unavoidable effects of photon loss, non-ideal sources, and imperfect detection. Scaling this to large numbers of photons should be a much simpler task than building a universal quantum computer.

A remarkable feature of modern silicon electronics is its ability to remain physically invariant, almost indefinitely for practical purposes. Although this characteristic is a hallmark of applications of integrated circuits that exist today, there might be opportunities for systems that offer the opposite behavior, such as implantable devices that function for medically useful time frames but then completely disappear via résorption by the body. We report a set of materials, manufacturing schemes, device components, and theoretical design tools for a silicon-based complementary metal oxide semiconductor (CMOS) technology that has this type of transient behavior, together with integrated sensors, actuators, power supply systems, and wireless control strategies. An implantable transient device that acts as a programmable nonantibiotic bacteriocide provides a system-level example.

A passive optical diode effect would be useful for on-chip optical information processing but has been difficult to achieve. Using a method based on optical nonlinearity, we demonstrate a forward-backward transmission ratio of up to 28 decibels within telecommunication wavelengths. Our device, which uses two silicon rings 5 micrometers in radius, is passive yet maintains optical nonreciprocity for a broad range of input power levels, and it performs equally well even if the backward input power is higher than the forward input. The silicon optical diode is ultracompact and is compatible with current complementary metal-oxide semiconductor processing.

We report classes of electronic systems that achieve thicknesses, effective elastic moduli, bending stiffnesses, and areal mass densities matched to the epidermis. Unlike traditional wafer-based technologies, laminating such devices onto the skin leads to conformal contact and adequate adhesion based on van der Waals interactions alone, in a manner that is mechanically invisible to the user. We describe systems incorporating electrophysiological, temperature, and strain sensors, as well as transistors, light-emitting diodes, photodetectors, radio frequency inductors, capacitors, oscillators, and rectifying diodes. Solar cells and wireless coils provide options for power supply. We used this type of technology to measure electrical activity produced by the heart, brain, and skeletal muscles and show that the resulting data contain sufficient information for an unusual type of computer game controller.

Microbatteries with dimensions of tens to hundreds of micrometers that are produced by common microfabrication techniques are poised to provide integration of power sources onto electronic devices, but they still suffer from poor cycle lifetime, as well as power and temperature range of operation issues that are alleviated with the use of supercapacitors. There have been a few reports on thin-film and other micro-supercapacitors, but they are either too thin to provide sufficient energy or the technology is not scalable. By etching supercapacitor electrodes into conductive titanium carbide substrates, we demonstrate that monolithic carbon films lead to a volumetric capacity exceeding that of micro- and macroscale supercapacitors reported thus far, by a factor of 2. This study also provides the framework for integration of high-performance micro-supercapacitors onto a variety of devices.

A wafer-scale graphene circuit was demonstrated in which all circuit components, including graphene field-effect transistor and inductors, were monolithically integrated on a single silicon carbide wafer. The integrated circuit operates as a broadband radio-frequency mixer at frequencies up to 10 gigahertz. These graphene circuits exhibit outstanding thermal stability with little reduction in performance (less than 1 decibel) between 300 and 400 kelvin. These results open up possibilities of achieving practical graphene technology with more complex functionality and performance.

As silicon electronics approaches the atomic scale, interconnects and circuitry become comparable in size to the active device components. Maintaining low electrical resistivity at this scale is challenging because of the presence of confining surfaces and interfaces. We report on the fabrication of wires in silicon—only one atom tall and four atoms wide—with exceptionally low resistivity (~0.3 milliohm-centimeters) and the current-carrying capabilities of copper. By embedding phosphorus atoms within a silicon crystal with an average spacing of less than 1 nanometer, we achieved a diameter-independent resistivity, which demonstrates ohmic scaling to the atomic limit. Atomistic tight-binding calculations confirm the metallicity of these atomic-scale wires, which pave the way for single-atom device architectures for both classical and quantum information processing.

Nanoelectronic devices offer substantial potential for interrogating biological systems, although nearly all work has focused on planar device designs. We have overcome this limitation through synthetic integration of a nanoscale field-effect transistor (nanoFET) device at the tip of an acute-angle kinked silicon nanowire, where nanoscale connections are made by the arms of the kinked nanostructure, and remote multilayer interconnects allow three-dimensional (3D) probe presentation. The acute-angle probe geometry was designed and synthesized by controlling eis versus trans crystal conformations between adjacent kinks, and the nanoFET was localized through modulation doping. 3D nanoFET probes exhibited conductance and sensitivity in aqueous solution, independent of large mechanical deflections, and demonstrated high pH sensitivity. Additionally, 3D nanoprobes modified with phospholipid bilayers can enter single cells to allow robust recording of intracellular potentials.

Flexible nanotube circuits Integrated circuits formed on flexible plastic sheets can be lighter and tougher than those made from conventional materials, as well as being usefully bendy. Semiconductors made from organic small molecules and polymers have shown promise in such applications, but a new carbon-based nanomaterial described in this issue — its creators say — promises higher performance in electronic applications than the currently available options. Cao et al . have developed small- to medium-scale integrated digital circuits consisting of random networks of single-walled carbon nanotubes on plastic substrates. The layouts enable both high mobilities and high on/off ratios and the resulting devices and circuits (consisting of up to 100 transistors) show excellent electronic properties. These new films should be of use for a wide range of applications such as unusual consumer electronic devices, biological sensing and optoelectronics. The ability to form integrated circuits on flexible sheets of plastic enables attributes (for example conformal and flexible formats and lightweight and shock resistant construction) in electronic devices that are difficult or impossible to achieve with technologies that use semiconductor wafers or glass plates as substrates 1 . Organic small-molecule and polymer-based materials represent the most widely explored types of semiconductors for such flexible circuitry 2 . Although these materials and those that use films or nanostructures of inorganics have promise for certain applications, existing demonstrations of them in circuits on plastic indicate modest performance characteristics that might restrict the application possibilities. Here we report implementations of a comparatively high-performance carbon-based semiconductor consisting of sub-monolayer, random networks of single-walled carbon nanotubes to yield small- to medium-scale integrated digital circuits, composed of up to nearly 100 transistors on plastic substrates. Transistors in these integrated circuits have excellent properties: mobilities as high as 80 cm 2  V -1  s -1 , subthreshold slopes as low as 140 m V dec -1 , operating voltages less than 5 V together with deterministic control over the threshold voltages, on/off ratios as high as 10 5 , switching speeds in the kilohertz range even for coarse (∼100-μm) device geometries, and good mechanical flexibility—all with levels of uniformity and reproducibility that enable high-yield fabrication of integrated circuits. Theoretical calculations, in contexts ranging from heterogeneous percolative transport through the networks to compact models for the transistors to circuit level simulations, provide quantitative and predictive understanding of these systems. Taken together, these results suggest that sub-monolayer films of single-walled carbon nanotubes are attractive materials for flexible integrated circuits, with many potential areas of application in consumer and other areas of electronics.