Parallel window decoding enables scalable fault tolerant quantum computation.

Large-scale quantum computers have the potential to hold computational capabilities beyond conventional computers. However, the physical qubits are prone to noise which must be corrected in order to perform fault-tolerant quantum computations. Quantum Error Correction (QEC) provides the path for realizing such computations. QEC generates a continuous stream of data that decoders must process at the rate it is received, which can be as fast as 1 µs per QEC round in superconducting quantum computers. If the decoder infrastructure cannot keep up, a data backlog problem is encountered and the computation runs exponentially slower. Today's leading approaches to quantum error correction are not scalable as existing decoders typically run slower as the problem size is increased, inevitably hitting the backlog problem. Here, we show how to parallelize decoding to achieve almost arbitrary speed, removing this roadblock to scalability. Our parallelization requires some classical feed forward decisions to be delayed, slowing-down the logical clock speed. However, the slow-down is now only polynomial in the size of the QEC code, averting the exponential slowdown. We numerically demonstrate our parallel decoder for the surface code, showing no noticeable reduction in logical fidelity compared to previous decoders and demonstrating the predicted speedup.

Domain Wall Automotion in Three-Dimensional Magnetic Helical Interconnectors.

The fundamental limits currently faced by traditional computing devices necessitate the exploration of ways to store, compute, and transmit information going beyond the current CMOS-based technologies. Here, we propose a three-dimensional (3D) magnetic interconnector that exploits geometry-driven automotion of domain walls (DWs), for the transfer of magnetic information between functional magnetic planes. By combining state-of-the-art 3D nanoprinting and standard physical vapor deposition, we prototype 3D helical DW conduits. We observe the automotion of DWs by imaging their magnetic state under different field sequences using X-ray microscopy, observing a robust unidirectional motion of DWs from the bottom to the top of the spirals. From experiments and micromagnetic simulations, we determine that the large thickness gradients present in the structure are the main mechanism for 3D DW automotion. We obtain direct evidence of how this tailorable magnetic energy gradient is imprinted in the devices, and how it competes with pinning effects that are due to local changes in the energy landscape. Our work also predicts how this effect could lead to high DW velocities, reaching the Walker limit during automotion. This work demonstrates a possible mechanism for efficient transfer of magnetic information in three dimensions.

How Reproducible are Surface Areas Calculated from the BET Equation?

Porosity and surface area analysis play a prominent role in modern materials science. At the heart of this sits the Brunauer-Emmett-Teller (BET) theory, which has been a remarkably successful contribution to the field of materials science. The BET method was developed in the 1930s for open surfaces but is now the most widely used metric for the estimation of surface areas of micro- and mesoporous materials. Despite its widespread use, the calculation of BET surface areas causes a spread in reported areas, resulting in reproducibility problems in both academia and industry. To prove this, for this analysis, 18 already-measured raw adsorption isotherms were provided to sixty-one labs, who were asked to calculate the corresponding BET areas. This round-robin exercise resulted in a wide range of values. Here, the reproducibility of BET area determination from identical isotherms is demonstrated to be a largely ignored issue, raising critical concerns over the reliability of reported BET areas. To solve this major issue, a new computational approach to accurately and systematically determine the BET area of nanoporous materials is developed. The software, called "BET surface identification" (BETSI), expands on the well-known Rouquerol criteria and makes an unambiguous BET area assignment possible.

Complex free-space magnetic field textures induced by three-dimensional magnetic nanostructures.

The design of complex, competing effects in magnetic systems-be it via the introduction of nonlinear interactions1-4, or the patterning of three-dimensional geometries5,6-is an emerging route to achieve new functionalities. In particular, through the design of three-dimensional geometries and curvature, intrastructure properties such as anisotropy and chirality, both geometry-induced and intrinsic, can be directly controlled, leading to a host of new physics and functionalities, such as three-dimensional chiral spin states7, ultrafast chiral domain wall dynamics8-10 and spin textures with new spin topologies7,11. Here, we advance beyond the control of intrastructure properties in three dimensions and tailor the magnetostatic coupling of neighbouring magnetic structures, an interstructure property that allows us to generate complex textures in the magnetic stray field. For this, we harness direct write nanofabrication techniques, creating intertwined nanomagnetic cobalt double helices, where curvature, torsion, chirality and magnetic coupling are jointly exploited. By reconstructing the three-dimensional vectorial magnetic state of the double helices with soft-X-ray magnetic laminography12,13, we identify the presence of a regular array of highly coupled locked domain wall pairs in neighbouring helices. Micromagnetic simulations reveal that the magnetization configuration leads to the formation of an array of complex textures in the magnetic induction, consisting of vortices in the magnetization and antivortices in free space, which together form an effective B field cross-tie wall14. The design and creation of complex three-dimensional magnetic field nanotextures opens new possibilities for smart materials15, unconventional computing2,16, particle trapping17,18 and magnetic imaging19.

Fabrication of a 3D Nanomagnetic Circuit with Multi-Layered Materials for Applications in Spintronics.

Three-dimensional (3D) spintronic devices are attracting significant research interest due to their potential for both fundamental studies and computing applications. However, their implementations face great challenges regarding not only the fabrication of 3D nanomagnets with high quality materials, but also their integration into 2D microelectronic circuits. In this study, we developed a new fabrication process to facilitate the efficient integration of both non-planar 3D geometries and high-quality multi-layered magnetic materials to prototype 3D spintronic devices, as a first step to investigate new physical effects in such systems. Specifically, we exploited 3D nanoprinting, physical vapour deposition and lithographic techniques to realise a 3D nanomagnetic circuit based on a nanobridge geometry, coated with high quality Ta/CoFeB/Ta layers. The successful establishment of this 3D circuit was verified through magnetotransport measurements in combination with micromagnetic simulations and finite element modelling. This fabrication process provides new capabilities for the realisation of a greater variety of 3D nanomagnetic circuits, which will facilitate the understanding and exploitation of 3D spintronic systems.

Non-Planar Geometrical Effects on the Magnetoelectrical Signal in a Three-Dimensional Nanomagnetic Circuit.

Expanding nanomagnetism and spintronics into three dimensions (3D) offers great opportunities for both fundamental and technological studies. However, probing the influence of complex 3D geometries on magnetoelectrical phenomena poses important experimental and theoretical challenges. In this work, we investigate the magnetoelectrical signals of a ferromagnetic 3D nanodevice integrated into a microelectronic circuit using direct-write nanofabrication. Due to the 3D vectorial nature of both electrical current and magnetization, a complex superposition of several magnetoelectrical effects takes place. By performing electrical measurements under the application of 3D magnetic fields, in combination with macrospin simulations and finite element modeling, we disentangle the superimposed effects, finding how a 3D geometry leads to unusual angular dependences of well-known magnetotransport effects such as the anomalous Hall effect. Crucially, our analysis also reveals a strong role of the noncollinear demagnetizing fields intrinsic to 3D nanostructures, which results in an angular dependent magnon magnetoresistance contributing strongly to the total magnetoelectrical signal. These findings are key to the understanding of 3D spintronic systems and underpin further fundamental and device-based studies.

Writing 3D Nanomagnets Using Focused Electron Beams.

Focused electron beam induced deposition (FEBID) is a direct-write nanofabrication technique able to pattern three-dimensional magnetic nanostructures at resolutions comparable to the characteristic magnetic length scales. FEBID is thus a powerful tool for 3D nanomagnetism which enables unique fundamental studies involving complex 3D geometries, as well as nano-prototyping and specialized applications compatible with low throughputs. In this focused review, we discuss recent developments of this technique for applications in 3D nanomagnetism, namely the substantial progress on FEBID computational methods, and new routes followed to tune the magnetic properties of ferromagnetic FEBID materials. We also review a selection of recent works involving FEBID 3D nanostructures in areas such as scanning probe microscopy sensing, magnetic frustration phenomena, curvilinear magnetism, magnonics and fluxonics, offering a wide perspective of the important role FEBID is likely to have in the coming years in the study of new phenomena involving 3D magnetic nanostructures.

Layer-by-Layer Growth of Complex-Shaped Three-Dimensional Nanostructures with Focused Electron Beams.

The fabrication of three-dimensional (3D) nanostructures is of great interest to many areas of nanotechnology currently challenged by fundamental limitations of conventional lithography. One of the most promising direct-write methods for 3D nanofabrication is focused electron beam-induced deposition (FEBID), owing to its high spatial resolution and versatility. Here we extend FEBID to the growth of complex-shaped 3D nanostructures by combining the layer-by-layer approach of conventional macroscopic 3D printers and the proximity effect correction of electron beam lithography. This framework is based on the continuum FEBID model and is capable of adjusting for a wide range of effects present during deposition, including beam-induced heating, defocusing, and gas flux anisotropies. We demonstrate the capabilities of our platform by fabricating free-standing nanowires, surfaces with varying curvatures and topologies, and general 3D objects, directly from standard stereolithography (STL) files and using different precursors. Real 3D nanoprinting as demonstrated here opens up exciting avenues for the study and exploitation of 3D nanoscale phenomena.

Fabrication of Scaffold-Based 3D Magnetic Nanowires for Domain Wall Applications.

Three-dimensional magnetic nanostructures hold great potential to revolutionize information technologies and to enable the study of novel physical phenomena. In this work, we describe a hybrid nanofabrication process combining bottom-up 3D nano-printing and top-down thin film deposition, which leads to the fabrication of complex magnetic nanostructures suitable for the study of new 3D magnetic effects. First, a non-magnetic 3D scaffold is nano-printed using Focused Electron Beam Induced Deposition; then a thin film magnetic material is thermally evaporated onto the scaffold, leading to a functional 3D magnetic nanostructure. Scaffold geometries are extended beyond recently developed single-segment geometries by introducing a dual-pitch patterning strategy. Additionally, by tilting the substrate during growth, low-angle segments can be patterned, circumventing a major limitation of this nano-printing process; this is demonstrated by the fabrication of ‘staircase’ nanostructures with segments parallel to the substrate. The suitability of nano-printed scaffolds to support thermally evaporated thin films is discussed, outlining the importance of including supporting pillars to prevent deformation during the evaporation process. Employing this set of methods, a set of nanostructures tailored to precisely match a dark-field magneto-optical magnetometer have been fabricated and characterized. This work demonstrates the versatility of this hybrid technique and the interesting magnetic properties of the nanostructures produced, opening a promising route for the development of new 3D devices for applications and fundamental studies.