Scientists crack the code on quantum system breakdowns—with real-world applications
Researchers have developed a mathematical framework to classify and predict when quantum systems fail in specific ways, solving a decades-old problem in physics. The discovery could accelerate development of more stable quantum computers and advanced materials by helping engineers design systems that harness these critical points rather than avoid them.
Originaltitel: Winding topology of multifold exceptional points
<p>Despite their ubiquity, a systematic classification of multifold exceptional points, n-fold spectral degeneracies (EPns), remains a significant unsolved problem. In this article, we characterize the Abelian eigenvalue topology of generic EPns and symmetry-protected EP <em>ns</em> for arbitrary <em>n</em>. The former and the latter emerge in (2<em>n</em> - 2)- and (<em>n</em> - 1)-dimensional parameter spaces, respectively. By introducing topological invariants called resultant winding numbers, we elucidate that these EPns are stable due to topology of a map from a base space (momentum or parameter space) to a sphere defined by resultants. In a D-dimensional parameter space (D c), the resultant winding numbers topologically characterize (D ≥ c)-dimensional manifolds of generic (symmetry-protected) EP <em>ns</em>, whose codimension is c = 2<em>n</em> - 2 (c = <em>n</em> - 1). Our framework implies fundamental doubling theorems for both generic EP <em>ns</em> and symmetry-protected EP <em>ns</em> in <em>n</em>-band models.</p>