Classifying Topology via Edge-State Pure Thermalization

Technical Summary: Classifying Topology via Edge-State Pure Thermalization

Problem Statement
Repeated-interaction architectures, such as micromasers, utilize streams of ancillary states ("quantum fuels") to drive target systems toward steady states. A critical distinction in quantum thermodynamics exists between "heat-like" resources, which induce entropy production and Gibbs relaxation, and "work-like" resources, which exhibit coherence (displacement or squeezing) and enable ordered energy extraction. While prior research has identified structured dimers and multi-qubit clusters as fuels capable of pure thermalization, it remains unknown whether the topological degree of freedom—specifically the symmetry-protected structure of topological edge states—can be operationally utilized to isolate heat from work. The central question addressed is whether topological edge states can serve as robust "pure-thermalization fuels" that suppress coherent channels more effectively than traditional candidates.

Methodology
The authors propose a protocol utilizing an open Su–Schrieffer–Heeger (SSH) chain as the source of quantum fuel. The workflow consists of four stages:

1. Initialization: A single-excitation eigenstate is prepared within a physical 16-site (8-dimer) SSH chain. The system Hamiltonian includes intra-cell ($t_1$) and inter-cell ($t_2$) hopping amplitudes.
2. Unitary Compression: The selected 16-site eigenstate is deterministically compressed into a compact four-qubit register. This mapping preserves the topological signature of the original state within a reduced Hilbert space, making it compatible with current superconducting-qubit hardware.
3. Interaction: These four-qubit "fuel" registers are injected into a lossy cavity at Poissonian arrival times. They interact with a single cavity mode via a Tavis–Cummings Hamiltonian before exiting.
4. Diagnostics: The steady-state response of the cavity is analyzed via homodyne/heterodyne quadrature readout. The system monitors two coherent-channel indicators: displacement ($\lambda$) and squeezing ($\xi$).

The study evaluates the system under realistic conditions, including generalized amplitude damping (GADC) during the flight time ($t_{tr}$), cavity loss ($\kappa$), and various forms of disorder (bond and onsite).

Key Contributions

• Topological Edge-State Fuel: The paper identifies topological edge eigenstates of the SSH chain as a novel class of pure-thermalization fuels.
• Edge-Bulk Thermodynamic Dichotomy: The authors demonstrate a sharp operational distinction:
  • Edge Fuels: Eigenstates localized at the boundaries of the topological phase ($t_1 < t_2$) suppress both displacement and squeezing ($\lambda \approx 0, \xi \approx 0$). Consequently, they drive the cavity exclusively through heat-exchange channels, resulting in a purely thermal Gibbs steady state.
  • Bulk Fuels: Eigenstates extended across the bulk of the chain activate coherent channels, yielding non-zero $\lambda$ and $\xi$, and driving the system toward a thermo-mechanical steady state.
• Transport-Free Classifier: The protocol establishes a method to classify topology based solely on the thermodynamic response of the cavity, without requiring transport measurements.

Results

• Robustness: The edge-bulk dichotomy persists under realistic imperfections. Numerical simulations show that even with generalized amplitude damping during flight ($t_{tr} = 10$ ns) and cavity loss, the two edge fuels (states 15 and 16 in the 16-state spectrum) maintain vanishing coherent indicators throughout the topological phase. In contrast, all 14 bulk fuels consistently activate coherent channels.
• Physical Mechanism: The suppression of coherent channels in edge fuels arises from the exponential localization and constrained amplitude patterns of the boundary modes. When compressed into the four-qubit register, these structures suppress the density-matrix elements responsible for one- and two-quantum coherence channels. Bulk states, being spatially extended, populate the register broadly, sustaining the coherences necessary for displacement and squeezing.
• Trivial Lattices: Control simulations on trivial lattice models across broad parameter ranges failed to produce an analogous pure-thermalization regime, confirming that the effect is specific to the topological edge structure.
• Implementation Feasibility: The authors outline a concrete superconducting implementation where a 16-site SSH eigenstate is prepared via adiabatic evolution or spectroscopic synthesis and transferred to a four-qubit register using calibrated exchange interactions and local single-qubit controls. This pipeline remains within coherence limits of current transmon hardware.

Significance
The paper claims to uncover a direct operational bridge between topology and quantum thermodynamics. By demonstrating that topological edge states naturally function as pure-thermalization resources, the work provides a robust mechanism for engineering Gibbs states and isolating heat transfer in quantum systems. The proposed scheme serves as a "transport-free classifier of topology," where the binary signature of the cavity response (pure thermal vs. thermo-mechanical) identifies the topological nature of the fuel. This link extends beyond cavity-QED platforms to general repeated-interaction settings, suggesting that edge-mode fuels can act as passive, Gibbs-stabilizing resources for autonomous quantum heat engines and thermodynamic control across diverse quantum architectures.