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arXiv:2508.10122 · PRX Quantum

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

Serra Erdamar, Maryam Abbasi, Weijian Chen, Niklas Hörnedal, Aurélia Chenu, Kater W. Murch

Published Jan 2, 2026• 2 citations
arXivHTMLPDF

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.

DOI
10.1103/7gtf-4tbh

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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.
As quantum systems are understood better from a fundamental physics perspective, we are gaining more insight and ideas for their many applications. Among them are quantum computation, sensing, and materials. Some difficulties that have been encountered are short lifetimes and coupling to unwanted modes while attempting to control these systems, resulting in error propagation. Previously, physicists have pursued Hermitian descriptions of systems to preserve unitary evolution and real-valued measurements. However, non-Hermitian systems not only provide a realistic description of physical systems within larger environments, but also a rich topological landscape from their complex energy spectrum. In this thesis, we will explore how to control a non-Hermitian qubit to utilize its complex spectrum and the role of its Hamiltonian in energetics and time dynamics. Because superconducting qubits offer flexibility in parameter tuning, we can tune the values of the non-Hermitian Hamiltonian to explore this complex spectrum across regions of both $\PT$-symmetry and $\PT$-symmetry breaking. This complex energy spectrum forms a Riemann surface that has a branch cut and branch points (exceptional points). Encircling these exceptional points adiabatically allows for state transport that can non-trivially convert between eigenstates. Previous experimental studies of this process revealed a chirality: eigenstate conversion occurs when following the state with higher gain, but breaks down when following the state with higher loss. We explore how the interplay between gain and loss in modes of the system results in the breakdown of this adiabaticity and how we can use a method based on shortcuts to adiabaticity to circumvent this. Finally, we leverage this tunability to further investigate how the components of the non-Hermitian Hamiltonian relate to classical thermodynamic notions of internal energy and work in time-dependent protocols via the Jarzynski equality.
We study the quantum evolution of a non-Hermitian qubit realized as a submanifold of a dissipative superconducting transmon circuit. Real-time tuning of the system parameters to encircle an exceptional point results in nonreciprocal quantum state transfer. We further observe chiral geometric phases accumulated under state transport, verifying the quantum coherent nature of the evolution in the complex energy landscape and distinguishing between coherent and incoherent effects associated with exceptional point encircling. Our work demonstrates an entirely new method for control over quantum state vectors, highlighting new facets of quantum bath engineering enabled through dynamical non-Hermitian control.
We study the quantum evolution of a non-Hermitian qubit realized as a sub-manifold of a dissipative superconducting transmon circuit. Real-time tuning of the system parameters results in non-reciprocal quantum state transfer associated with proximity to the exceptional points of the effective Floquet Hamiltonian. We observe chiral geometric phases accumulated under state transport, verifying the quantum coherent nature of the evolution in the complex energy landscape and distinguishing between coherent and incoherent effects associated with exceptional point encircling. Our work demonstrates an entirely new method for control over quantum state vectors, highlighting new facets of quantum bath engineering enabled through time-periodic (Floquet) non-Hermitian control.
We study the dynamics of a driven non-Hermitian superconducting qubit which is perturbed by quantum jumps between energy levels, a purely quantum effect with no classical correspondence. The quantum jumps mix the qubit states leading to decoherence. We observe that this decoherence rate is enhanced near the exceptional point, owing to the cube-root topology of the non-Hermitian eigenenergies. Together with the effect of non-Hermitian gain or loss, quantum jumps can also lead to a breakdown of adiabatic evolution under the slow-driving limit. Our study shows the critical role of quantum jumps in generalizing the applications of classical non-Hermitian systems to open quantum systems for sensing and control.
Topological phenomena are fundamentally underlain by the geometric phase of eigenstates. Time-varying Hamiltonians furthermore allow for a dynamical topological invariant associated with continuous flows. We study chiral and nonreciprocal dynamics by encircling the exceptional points (EPs) of non-Hermitian Hamiltonians in a trapped ion system. We find that these dynamics are topologically robust against external perturbations even in the presence of dissipation-induced nonadiabatic transitions. Furthermore, our results indicate that these behaviors are protected by dynamical vorticity—an emerging topological invariant associated with the energy dispersion of non-Hermitian band structures in a parallel transported eigenbasis. Through the quantum state tomography, the symmetry breaking and other key features of topological dynamics are directly verified. These results mark a significant step towards exploring topological properties of open quantum systems. The complex energy surface of a non-Hermitian system is not single-valued, and windings around its so-called exceptional branching points lead to the chiral and non-reciprocal transfer of eigenstates. Here, the authors experimentally demonstrate such topological state transfers in trapped ion systems, which are being established as promising platforms for quantum simulation.
Non-Hermitian systems exhibit a variety of unique features rooted in the presence of exceptional points (EPs). The distinct topological structure in the proximity of an EP gives rise to counterintuitive behaviors absent in Hermitian systems, which emerge after encircling the EP either quasistatically or dynamically. However, experimental exploration of EP encirclement in quantum systems, particularly those involving high-order EPs, remains challenging due to the difficulty of coherently controlling more degrees of freedom. In this work, we experimentally investigate the eigenvalue braiding and state transfer arising from the encirclement of EP in a three-dimensional non-Hermitian quantum system using superconducting circuits. We characterize the second- and third-order EPs through the coalescence of eigenvalues. Then we reveal the topological structure near the EP3 by quasistatically encircling it along various paths with three independent parameters, which yields the eigenvalue braiding described by the braid group B 3 . Additionally, we observe chiral state transfer between three eigenstates under a fast driving scheme when no EPs are enclosed, while time-symmetric behavior occurs when at least one EP is encircled. Our findings offer insights into understanding non-Hermitian topological structures and the manipulation of quantum states through dynamic operations.