Quantum spectroscopy of topological dynamics via a supersymmetric Hamiltonian

• URL: http://arxiv.org/abs/2511.23169v1
• Date: Fri, 28 Nov 2025 13:25:26 GMT
• Title: Quantum spectroscopy of topological dynamics via a supersymmetric Hamiltonian
• Authors: Hiroshi Yamauchi, Satoshi Kanno, Yuki Sato, Hiroyuki Tezuka, Yoshi-aki Shimada, Eriko Kaminishi, Naoki Yamamoto,
• Abstract summary: We estimate topological descriptors through quantum spectroscopy.<n>We show that low-lying excited states quantify the stability of topological features.<n>This framework suggests that quantum hardware can function as a spectrometer for data topologies beyond classical reach.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Topological data analysis (TDA) characterizes complex dynamics through global invariants, but classical computation becomes prohibitive for high-dimensional data. We reinterpret time-domain dynamics as the eigenvalue spectrum of a supersymmetric (SUSY) Hamiltonian and thereby estimate topological descriptors through quantum spectroscopy. While zero modes correspond to Betti numbers, we show that low-lying excited states quantify the stability of topological features. Using a Takens embedding of the Lorenz system together with a resource-efficient quantum phase estimation implemented on IBM quantum hardware, we observe that the spectral gap of the SUSY Laplacian tracks the persistence of homological structures. Notably, the minimum of this spectral gap coincides with the onset of chaos, whereas its reopening reflects the geometric maturation of the attractor. Validated on small complexes yet offering an exponential advantage over classical diagonalization (from $O(N^3)$ to $\mathrm{poly}(\log N)$), this framework suggests that quantum hardware can function as a spectrometer for data topologies beyond classical reach.

Related papers

• Quantum Filtering and Analysis of Multiplicities in Eigenvalue Spectra [4.081730190778995]
  We introduce QFAMES, a quantum algorithm that efficiently identifies clusters of eigenvalues and determines their multiplicities.<n>QFAMES also enables the estimation of observable expectation values within targeted energy clusters.<n>We validate the effectiveness of QFAMES through numerical demonstrations.
  arXiv  Detail & Related papers  (2025-10-08T18:37:36Z)
• Classical feature map surrogates and metrics for quantum control landscapes [0.0]
  We derive and analyze three feature maps of parametrized quantum dynamics, which generalize variational quantum circuits.<n>The Lie-Fourier representation is shown to have a dense spectrum with discrete peaks, that reflects control Hamiltonian properties, but that is compressible in typically found symmetric systems.
  arXiv  Detail & Related papers  (2025-09-30T08:24:13Z)
• Dissipation-Driven Topological Phase Transition in Quantum Open Systems Independent of system Hamiltonian [2.28437033297544]
  We investigate dissipation-driven topological phase transitions in one-dimensional quantum open systems governed by the Lindblad equation with linear dissipation operators.<n>By employing the modular Hamiltonian framework, we rigorously demonstrate that the $rmZ$ topological invariant characterizing steady states in one-dimensional class D systems is exclusively dependent on the dissipation operators.
  arXiv  Detail & Related papers  (2025-08-22T10:16:11Z)
• Grassmann Variational Monte Carlo with neural wave functions [45.935798913942904]
  We formalize the framework introduced by Pfau et al.citepfau2024accurate in terms of Grassmann geometry of the Hilbert space.<n>We validate our approach on the Heisenberg quantum spin model on the square lattice, achieving highly accurate energies and physical observables for a large number of excited states.
  arXiv  Detail & Related papers  (2025-07-14T13:53:13Z)
• Quantum and Semi-Classical Signatures of Dissipative Chaos in the Steady State [0.40498500266986387]
  We investigate the quantum-classical correspondence in open quantum many-body systems using the SU(3) Bose-Hubbard trimer as a minimal model.<n>We show that classical dynamical behavior, as quantified by the sign of the Lyapunov exponent, governs the level statistics of the steady-state density matrix.
  arXiv  Detail & Related papers  (2025-06-17T20:21:06Z)
• Avoided-crossings, degeneracies and Berry phases in the spectrum of quantum noise through analytic Bloch-Messiah decomposition [49.1574468325115]
  "analytic Bloch-Messiah decomposition" provides approach for characterizing dynamics of quantum optical systems.<n>We show that avoided crossings arise naturally when a single parameter is varied, leading to hypersensitivity of the singular vectors.<n>We highlight the possibility of programming the spectral response of photonic systems through the deliberate design of avoided crossings.
  arXiv  Detail & Related papers  (2025-04-29T13:14:15Z)
• Hierarchical analytical approach to universal spectral correlations in Brownian Quantum Chaos [44.99833362998488]
  We develop an analytical approach to the spectral form factor and out-of-time ordered correlators in zero-dimensional Brownian models of quantum chaos.
  arXiv  Detail & Related papers  (2024-10-21T10:56:49Z)
• Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems [77.88054335119074]
  We use FNOs to model the evolution of random quantum spin systems. We apply FNOs to a compact set of Hamiltonian observables instead of the entire $2n$ quantum wavefunction.
  arXiv  Detail & Related papers  (2024-09-05T07:18:09Z)
• Meson content of entanglement spectra after integrable and nonintegrable quantum quenches [0.0]
  We calculate the time evolution of the lower part of the entanglement spectrum and return rate functions after global quantum quenches in the Ising model. Our analyses provide a deeper understanding on the role of quantum information quantities for the dynamics of emergent phenomena reminiscent to systems in high-energy physics.
  arXiv  Detail & Related papers  (2022-10-27T18:00:01Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.