Abstract Indistinguishability of particles is a fundamental principle of quantum mechanics 1 . For all elementary and quasiparticles observed to date—including fermions, bosons and Abelian anyons—this principle guarantees that the braiding of identical particles leaves the system unchanged 2,3 . However, in two spatial dimensions, an intriguing possibility exists: braiding of non-Abelian anyons causes rotations in a space of topologically degenerate wavefunctions 4–8 . Hence, it can change the observables of the system without violating the principle of indistinguishability. Despite the well-developed mathematical description of non-Abelian anyons and numerous theoretical proposals 9–22 , the experimental observation of their exchange statistics has remained elusive for decades. Controllable many-body quantum states generated on quantum processors offer another path for exploring these fundamental phenomena. Whereas efforts on conventional solid-state platforms typically involve Hamiltonian dynamics of quasiparticles, superconducting quantum processors allow for directly manipulating the many-body wavefunction by means of unitary gates. Building on predictions that stabilizer codes can host projective non-Abelian Ising anyons 9,10 , we implement a generalized stabilizer code and unitary protocol 23 to create and braid them. This allows us to experimentally verify the fusion rules of the anyons and braid them to realize their statistics. We then study the prospect of using the anyons for quantum computation and use braiding to create an entangled state of anyons encoding three logical qubits. Our work provides new insights about non-Abelian braiding and, through the future inclusion of error correction to achieve topological protection, could open a path towards fault-tolerant quantum computing.
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Geometrically incompatible confinement of solids
The complex morphologies exhibited by spatially confined thin objects have long challenged human efforts to understand and manipulate them, from the representation of patterns in draped fabric in Renaissance art to current-day efforts to engineer flexible sensors that conform to the human body. We introduce a theoretical principle, broadly generalizing Euler’s
- NSF-PAR ID:
- 10082295
- Publisher / Repository:
- Proceedings of the National Academy of Sciences
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 116
- Issue:
- 5
- ISSN:
- 0027-8424
- Page Range / eLocation ID:
- p. 1483-1488
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract 5
d transition metal oxides, such as iridates, have attracted significant interest in condensed matter physics throughout the past decade owing to their fascinating physical properties that arise from intrinsically strong spin-orbit coupling (SOC) and its interplay with other interactions of comparable energy scales. Among the rich family of iridates, iridium dioxide (IrO2), a simple binary compound long known as a promising catalyst for water splitting, has recently been demonstrated to possess novel topological states and exotic transport properties. The strong SOC and the nonsymmorphic symmetry that IrO2possesses introduce symmetry-protected Dirac nodal lines (DNLs) within its band structure as well as a large spin Hall effect in the transport. Here, we review recent advances pertaining to the study of this unique SOC oxide, with an emphasis on the understanding of the topological electronic structures, syntheses of high crystalline quality nanostructures, and experimental measurements of its fundamental transport properties. In particular, the theoretical origin of the presence of the fourfold degenerate DNLs in band structure and its implications in the angle-resolved photoemission spectroscopy measurement and in the spin Hall effect are discussed. We further introduce a variety of synthesis techniques to achieve IrO2nanostructures, such as epitaxial thin films and single crystalline nanowires, with the goal of understanding the roles that each key parameter plays in the growth process. Finally, we review the electrical, spin, and thermal transport studies. The transport properties under variable temperatures and magnetic fields reveal themselves to be uniquely sensitive and modifiable by strain, dimensionality (bulk, thin film, nanowire), quantum confinement, film texture, and disorder. The sensitivity, stemming from the competing energy scales of SOC, disorder, and other interactions, enables the creation of a variety of intriguing quantum states of matter. -
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