• Physicists in Germany demonstrate superconducting electrical flow that runs only along the edges of certain materials
• Could presage the arrival of ‘flying qubits’ in quantum computing
• They seek them here, they seek them there, those damned elusive Majorana fermions
• Is error-free quantum computing within reach? Microsoft thinks it might be

A team of physicists at the University of Cologne in Germany have made advances in quantum materials that could well enable the construction of much more stable, robust and efficient quantum computers.

The researchers have demonstrated the possibility of creating superconducting electrical flow only along the edges of certain materials rather than it spreading throughout the entire material. The results of the experiments are published as the article, “Induced superconducting correlations in a quantum anomalous Hall insulator”, in the latest edition of the journal Nature Physics.

Superconductivity permits the transmission of electricity with zero resistance in some materials. The scientists at Cologne University used what is called the “quantum anomalous Hall effect”, which can also institute a state of zero resistance. The original Hall effect was discovered by Edwin Hall back in 1879 at the Johns Hopkins University, in Baltimore, Maryland in the US. It is founded in the production of a potential difference (the Hall voltage) across an electrical conductor that is transverse to an electric current in the conductor and to an applied magnetic field perpendicular to the current. Hall’s research led him to speculate whether magnetic fields interacted with the conductors or with the electric current itself and reasoned that if the force was acting specifically on the current, it should force that current to one side of the wire and the effect would produce a small but measurable voltage.

This became known as the Hall voltage and, considering that the breakthrough happened 18 years before the discovery of the electron, it was quite remarkable. 

Then, in 1880, the scientist also showed that Hall voltage was ten times larger in ferromagnetic materials than it was in nonmagnetic conductors. In due course this came to be known as the “anomalous Hall effect”.

Today, the quantum anomalous Hall effect is defined as “the quantisation of the Hall effect in the absence of an applied (external) magnetic field” and was first observed and defined by Chinese scientists in 2013. Its nature is topological and is regarded as having attributes very well suited to information processing.

Topology is a branch of mathematics dating back to the 17^th century. It is concerned with the properties of two geometric objects, deemed to be equivalent, that remain intact even while being continuously deformed by being stretched, twisted, crumpled or bent – all without closing holes, opening holes, tearing, glueing, cutting or passing through themselves. It is also called “rubber sheet geometry” because the geometric objects can be stretched or contracted like rubber but cannot be broken. The most common example given for rubber sheet geometry is that while a square can be deformed into a circle without breaking it, a figure 8 cannot because it will always break.

The geometrics of topological materials demonstrate that the same geometries exist on the molecular scale and this phenomenon gives rise to novel mechanical and electrical properties. Research shows that the materials could be of great use in the development of future technologies, such as ultra-low-energy transistors, cancer-scanning lasers and free-space communications systems beyond 5G and even beyond the mythical 6G.

Topological insulators, which exist today, actually insulate on the inside whilst being conductive, and thus able to carry electricity on the outside. The electricity flows in one direction only and can easily flow around corners and around defects with absolutely minimal backscattering and loss. In “topologically protected states”, a surface electron of a given momentum is unable to scatter into a state with an opposite momentum as that would involve “flipping” its spin – and this property makes them of great interest to the future of quantum computing.

The physicists at Cologne (working in collaboration with the University of Basel in Switzerland) have now shown that superconductive effects can be created in a material known to possess unique edge-only electrical properties. In this experimental case, the team used “thin films of the quantum anomalous Hall insulator contacted by a superconducting Niobium electrode”. The intent was to induce what are called ‘chiral Majorana states’ at its edges.

The paper claims that “after five years of hard work, we were finally able to achieve this goal: When we inject an electron into one terminal of the insulator material, it reflects at another terminal, not as an electron but as a hole, which is essentially a phantom of an electron with opposite charge. We call this phenomenon crossed Andreev reflection, and it enables us to detect the induced superconductivity in the topological edge state.” This could later lead to the realisation of topologically protected “flying qubits” that are regarded as being key to the production of resilient, and hence highly efficient, quantum computers because stable qubits are much less likely to decohere, and lose their quantum state and the data being computed along with it. Further experiments will look into Majorana fermions, particles so elusive that critics hitherto have dismissed them as illusory. Now it seems they may be real after all.

The quantum quadrille: The endless dance of the quasiparticles

Current quantum computers are incredibly fragile and subject to random interference from a myriad of sources that, forcing them to propagate errors that, practically instantaneously, can cause decoherence of the quantum state and stop computations in their tracks – hence the enormous amount of resource and overheads that have to be devoted to error correction. Research is now being undertaken to confirm the reality and predictability of the emergence of ‘chiral Majorana fermions’ and explain their strange existence with the aim of constructing future qubits from configurations of electrons called Majorana zero-mode (MZM) quasiparticles. (The word ‘chiral’ is used to describe the asymmetry of an object or system if it can be distinguished from its mirror image and cannot be superposed (not superimposed) onto it.

Each zero-mode quasiparticle comprises an electron state at both ends of the chain. It is not possible to interrogate or even disturb an MZM by looking at one end. Were it possible to manipulate the electron chain and force them together, they link to become an electron or a vacuum state – literally nothing at all. However, whilst they are separated, they are in quantum superposition of both states and could thus become a two-state bit for encoding a qubit.

When the two halves of the electron chain are mixed up so that the information encoded in each pair can be guaranteed to be completely hidden and unable to cause any decoherence, that mixing up can weave the trajectories of the particles together in a process called ‘braiding’. As long as a braid remains in motion, it is impossible to determine whether it will become an electron or a vacuum. Thus, while braided Majorana pairs stay apart and keep moving, the information they contain remains non-localised and any local attempts to measure their state will be of no effect or reveal the information.

Thus, to carry out a quantum computation with MZM qubits, braided threads are continually moved and then pairs brought together to find out if they form an electron or vacuum and the computation is completed – error-free.

Time will tell if such a technology will be possible but Microsoft, for one, is making a big bet that it will. Microsoft Azure Quantum is developing a fault-tolerant quantum computer based on topological qubits. It is the only major company currently following what many regard as a high-risk strategy, but it is one that will generate enormous rewards should it come to fruition.

Meanwhile, researchers are exploring other quasiparticles that could be used to engineer qubits. For example, scientists at the California Institute of Technology are working with Nanyang Technological University in Singapore on skyrmions, topologically stable, swirling quasiparticles that have been described as being like “subatomic hurricanes”. These cannot smoothly be transformed to a uniform state stabilised via interactions with magnetic materials. They may have application in spintronics technology and memory devices, as well as the potential to encode and manipulate topological protected quantum data.

- Martyn Warwick, Editor in Chief, TelecomTV