Harnessing Exceptional Points for Enhanced Quantum Control and Information Processing

• Applicants: Dr. Ioan Pop; Professor Dr. Bernd Rosenow; Professor Dr. Alexander Shnirman
• Subject Area: Theoretical Condensed Matter Physics ; Experimental Condensed Matter Physics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 536777080

Understanding the dynamics of open quantum systems is central to numerous aspects of quantum physics, including quantum information processing platforms, quantum state stabilization, and dephasing of interference phenomena. One major instrument to discuss the dynamics of such quantum systems is to describe them employing non-Hermitian Hamiltonians. This leads to a plethora of effects, one of which is the emergence of exceptional points. Exceptional points (EPs), the degeneracies of non-Hermitian operators where degenerate eigenvalues share the same eigenvector, emerge as a significant phenomenon in the dynamics of quantum systems. While the study of EPs arising in non-Hermitian Hamiltonians has revealed a multitude of fascinating phenomena and has the advantage of simplicity, the use of non-Hermitian Hamiltonians raises difficulties, such as non-conservation of probability. More recently, EPs have been examined within the context of the Liouville equation, a framework that transcends non-Hermitian Hamiltonian limitations. Exceptional points have been extensively researched in the classical many-photon regime, e.g. mode switching in microwave billards or sensing in photonic systems. More recently, a first experimental demonstration of EPs was achieved in a superconducting qubit. Our objective is to study the functionalities associated with EPs (including Liouvillian and post-selected non-Hermitian Hamiltonian EPs) and utilize them for improving the speed and fidelity of quantum control and quantum information processing. There is a growing body of evidence suggesting that performance can indeed be optimized by tuning to the vicinity of an EP, an aspect we plan to further explore. Autonomous error correction protocols, such as blind steering, have shown potential to make quantum state preparation faster and more reliable when tuned to an EP. Our research will investigate how the robustness of such protocols to static and dynamic errors can be improved by similar tuning. Our research approach combines theoretical investigation with experimental implementation, employing state-of-the-art chips with several superconducting transmon qubits. These offer sufficiently long coherence times, alongside with the full tunability of each individual qubit and the coupling connectivity ideal for performing quantum measurements of collective observables. We aim to progress from single qubit state engineering to demonstration of simple error correction as well as quantum steering to any collective state of several qubits. Our goal is to realize “blind measurements” and investigate whether the vicinity of a Liouvillian EP enables optimal steering and how such optimal steering compares with active steering protocols.

• DFG Programme: Research Grants