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  • Open Access

Exploring the Riemann-Surface Topology of a Non-Hermitian Superconducting Qubit Using Shortcuts to Adiabaticity

Serra Erdamar1,2,*, Maryam Abbasi2,*, Weijian Chen2, Niklas Hörnedal3, Aurélia Chenu3, and Kater W. Murch2,4,5,†

  • 1Department of Electrical and Systems Engineering, Washington University, St. Louis, Missouri 63130, USA
  • 2Department of Physics, Washington University, St. Louis, Missouri 63130, USA
  • 3Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, G. D. Luxembourg
  • 4Department of Electrical Engineering and Computer Science, University of California Berkeley, Berkeley, California 94720, USA
  • 5Department of Physics, University of California Berkeley, Berkeley, California 94720, USA

  • *These authors contributed equally to this work.
  • †Contact author: katermurch@berkeley.edu
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PRX Quantum 7, 010337 – Published 23 February, 2026

DOI: https://doi.org/10.1103/7gtf-4tbh

Abstract

Open quantum systems described by a non-Hermitian Hamiltonian exhibit rich dynamics due to the topology of their complex energy spectrum. By encircling an exceptional point degeneracy, this topology allows for topological state transport, chiral geometric phases, and eigenvalue braiding. To access these topological features, it is desirable to drive the system adiabatically. However, adiabatic transport in a system with a complex spectrum is conventionally only possible for the eigenstate whose eigenenergy has the lowest loss. Previous experiments have demonstrated such adiabatic evolution for the quantum state with relative gain, yet observed a breakdown in adiabaticity for quantum states with relative loss. In this work, we harness a shortcut to adiabaticity—counterdiabatic driving—to avoid the effects of loss while maintaining trajectories that follow the instantaneous eigenstates in significantly shorter timescales. We experimentally investigate the robustness of this control method using a superconducting transmon circuit with engineered dissipation. We observe that counterdiabatic driving stabilizes quasistatic transport and preserves the complex energy spectrum’s topology.

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Popular Summary

Open quantum systems with loss are naturally described by non-Hermitian Hamiltonians whose complex energy spectra live on branched Riemann surfaces connected at exceptional points, where eigenvalues and eigenvectors coalesce. In this work, we realize such a non-Hermitian landscape using a superconducting transmon qubit with engineered dissipation and use it to explore how encircling exceptional points in parameter space reshapes quantum state evolution. Ordinarily, slow (adiabatic) encircling is spoiled by gain-loss imbalance, which exponentially favors one eigenstate and causes a breakdown of adiabatic following. We overcome this by implementing shortcut-to-adiabaticity control in the form of counterdiabatic driving fields that force the qubit to track the instantaneous eigenstate of the target non-Hermitian Hamiltonian on fast timescales. This allows us to adiabatically encircle exceptional points in both directions and to cleanly resolve the underlying Riemann-sheet topology. We further identify special parameter trajectories—Apollonius circles—along which the required counterdiabatic term is effectively Hermitian and thus experimentally accessible without additional engineered dissipation. Our results establish shortcuts to adiabaticity as a practical tool for controlling non-Hermitian quantum systems and leveraging their topological structure for robust state preparation, geometric phase manipulation, and potential sensing applications near exceptional points.

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PRX Quantum 7, 010337– Published 23 February, 2026
  • Received 7 August 2025
  • Revised 30 November 2025
  • Accepted 2 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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