Researchers have long sought to control quantum states in materials for use in a next generation of high-speed computing—so-called quantum computing that scientists predict could one day lead to operations beyond the realm of classical computers.

But quantum computing—performing operations by employing quantum states such as nuclear spins, Josephson-junction arrays, and nitrogen-vacancy centers in diamonds—has run up against a range of barriers that restrict achieving true functionality.

What is needed is a quiet place—a platform free of the quantum-phase disruptions posed by noise and decoherence and other errors that derail quantum operations.

That quiet place may be found in a new arena—topological quantum states. Researchers posit that these states can be used to construct topological qubits—zones protected from noise and decoherence provoked by local perturbations. These zones are central to a relatively new interdisciplinary field focused on producing fault-tolerant topological quantum computing, or TQC.

Researchers from Boston College and Hong Kong University of Science and Technology report in the journal *Physical Review X* that they have developed a new theory of Quantum Anomalous Vortices (QAVs) that shows how these quiet zones can be created using these unusual topological defects in superconducting materials.

The team demonstrated through theoretical calculations that it is possible to construct QAVs to realize robust Majorana zero modes (MZMs)—exotic topological quantum states within in a mysterious particle proposed by Italian physicist Ettore Majorana in 1937.

Today, the researchers say quantum information can be stored in a pair of spatially separated MZMs—a Majorana qubit—which is resistant to fault disruptions caused by noise and decoherence.

But a MZM exists in a vortex, a tornado-like swirl of electrons in the topological defects of a superconducting material. Research to date has insisted that such vortices can only be generated by applying a large external magnetic field, which creates instability and limits the control required to conduct computing operations, or make devices.

Boston College Professor of Physics Ziqiang Wang, postdoctoral fellow Kun Jian, and Hong Kong University of Science and Technology Professor Xi Dai say their calculations reveal that a certain class of superconductors may solve this vexing vortex problem.

Much as in topological insulators and Weyl semimetals, superconductors made of heavy atoms possess strong spin-orbital coupling that locks the electron spin—the tiny magnetic moment carried by an electron—and its kinetic momentum so that vortices can spontaneously form around magnetic ions without applying an external magnetic field. Instead, magnetic control comes from the interaction between magnetic ions and superconducting electrons that flow in these materials, the team reported in the article titled “Quantum Anomalous Vortex and Majorana Zero Mode in Iron-Based Superconductor Fe(Te,Se).”.

These Quantum Anomalous Vortices can produce MZMs at their center that are free of the “contamination” found in conventional vortices powered by the application of external magnetic fields, the team reported.

For these remarkably unusual properties, as well as the relative ease to manipulate the magnetic ions, the QAV provides an unprecedented and advantageous platform for controlled study of the entanglement and correlations of the MZMs in topological quantum computing, said Wang.

“This is a good example of how basic research is connected to potential applications,” said Wang. “By advancing the fundamental knowledge of topological defect excitations in superconductors, we discovered a new zero-field platform for making Majorana-qubits in the QAVs, which paves the way for a new direction of research in fault-tolerant quantum information storage and topological quantum computing.”

Members of the team happened upon this game-changing theory as they collaborated with experimental physicists and studied a magnetic impurity iron atom in an iron-based superconductor (FeTeSe) using scanning tunneling microscopy. To the researchers’ surprise, the investigation found a zero-energy bound state on top of the magnetic impurity iron atom, which defied prior theoretical predictions.

“It took us three years to realize that the resolution of the puzzle requires new understanding of the possible topological defect excitations in superconductors,” said Wang. “Indeed, the zero-energy bound state can now be understood as a genuine MZM localized in a quantum anomalous vortex nucleated spontaneously at the magnetic iron atom.”

Wang and his colleagues are currently exploring the emergence of QAVs in other physical settings, part of a new direction of “vortex engineering in superconductors.”

Wang’s research was supported in part by a grant from the U.S. Department of Energy, Basic Energy Sciences, and an Ignite award from Boston College.

*—Ed Hayward | University Communications | July 2019*