Zhiyan Ding

We establish new theoretical results demonstrating the efficiency and robustness of system–bath interaction models for quantum thermal and ground state preparation. Unlike prior analyses, which typically relies on the Lindblad limit and require vanishing coupling strengths $o(1)$, we rigorously show that efficient state preparation remains possible far beyond this regime, even when the cumulative coupling strength is $\Theta(1)$. We first prove that even with constant cumulative coupling strength, the induced quantum channel still approximately fixes the target state. For thermal state preparation, we then develop a general perturbative framework that yields end-to-end complexity bounds outside weak coupling, and in particular proves that the mixing time scales as the inverse square of the coupling strength. This framework extends to broad Hamiltonian for which KMS detailed balance Lindbladians are known to mix. These bounds substantially improve upon prior results, and numerical simulations further confirm the robustness of the system–bath interaction framework across both weak and strong coupling regimes.

Fine-grained spectral properties of quantum Hamiltonians, including both eigenvalues and their multiplicities, provide useful information for characterizing many-body quantum systems as well as for understanding phenomena such as topological order. Extracting such information with small additive error is BQP-complete in the worst case. In this work, we introduce QFAMES (Quantum Filtering and Analysis of Multiplicities in Eigenvalue Spectra), a quantum algorithm that efficiently identifies clusters of closely spaced dominant eigenvalues and determines their multiplicities under physically motivated assumptions, which allows us to bypass worst-case complexity barriers. QFAMES also enables the estimation of observable expectation values within targeted energy clusters, providing a powerful tool for studying quantum phase transitions and other physical properties. We validate the effectiveness of QFAMES through numerical demonstrations, including its applications to characterizing quantum phases in the transverse-field Ising model and estimating the ground-state degeneracy of a topologically ordered phase in the two-dimensional toric code model. We also generalize QFAMES to the setting of mixed initial states. Our approach offers rigorous theoretical guarantees and significant advantages over existing subspace-based quantum spectral analysis methods, particularly in terms of the sample complexity and the ability to resolve degeneracies.