Non-Markovian Exceptional Points by Interpolating Quantum Channels

Abstract: Exceptional points (EPs) are special points in non-Hermitian systems where both eigenvalues and eigenvectors coalesce. In open quantum systems, these points are typically analyzed using effective non-Hermitian Hamiltonians or Liouvillian superoperators. While quantum channels offer the most general framework for describing state evolution in such systems, the existence and properties of EPs within this setting remain largely unexplored. In this work, we present a general strategy for generating quantum EPs for a single-qubit setting. We show that quantum channels can be separated into two distinct phases, with the transition between them marked by the presence of an EP. Based on this, we propose a systematic method to realize EPs by interpolating between quantum channels representing different phases. Experimentally, we implement these interpolated channels on a nuclear magnetic resonance (NMR) quantum computer and confirm the emergence of second-order EPs with high fidelity. Extending the interpolation to three channels further reveals third-order EPs. Our results establish quantum channel interpolation as a versatile framework for generating EPs and provide a general description of EPs in open quantum systems.