arXiv subjects

Zhe-Hao Zhang

Publications and source records attributed to Zhe-Hao Zhang.

3 recordsLinked to original sources

arXiv2026

A Restricted Boltzmann Machine with Quantum-State Visible Units

We construct a restricted Boltzmann machine (RBM) whose visible input is a quantum state rather than a classical configuration. Each hidden unit carries a trainable quantum template prepared by a parametrized circuit and converts its overlap with the input into a feature. Treating quantum states as high-dimensional continuous visible objects creates nontrivial normalization and scaling problems. We regularize the continuous likelihood and derive two controlled high-dimensional limits, yielding a Hopfield-type network with continuous Hilbert-space patterns and a data-augmented Gram likelihood. The resulting algorithms are compact and use trainable circuit-prepared templates as measurement intermediaries between quantum data and classical optimization. Numerical simulations across several many-body systems demonstrate effective quantum-phase recognition and multicomponent feature extraction.

quant-ph↗

arXiv2026

Localization Tensor Revisited: Geometric-Probabilistic Foundations and a Structure-Factor Criterion under Periodic Boundaries

We revisit the localization tensor (LT) from geometric and probabilistic perspectives and construct extensions that are naturally compatible with periodic boundary conditions (PBC), without redefining the position operator. In open boundary conditions, we show that the LT can be written exactly as the covariance of a bivariate probability distribution built from density-density correlations. This leads to two conceptually distinct extensions to PBC: (i) a geometric one based on the Riemannian center (Frechet mean) on the circle, and (ii) a metric-free one based on the mutual information I, which treats the configuration space purely as a probability space. We then relate the LT to the static structure factor by identifying the diagonal part, Cpp, as a "localization function" C(p), whose small-momentum behavior determines the LT in the thermodynamic limit. This clarifies why the LT is sensitive to transitions out of the extended phase but by itself cannot distinguish Anderson-type localization from dimerization: both share the same low-momentum asymptotics. We show that the finite-momentum behavior of C(p), together with an inverse participation ratio (IPR)-based upper bound valid in localized phases, provides a sharp criterion that discriminates localization from dimerization. These results are illustrated on the Su-Schrieffer-Heeger and Aubry-Andre models, with and without interactions, and suggest that structure factor-based probes offer robust and experimentally accessible diagnostics of localized and dimerized phases under PBC.

quant-ph↗

arXiv2024

Microscopic origin of quantum supersonic phenomenon in one dimension

Using the Bethe ansatz (BA), we rigorously obtain non-equilibrium dynamics of an impurity with a large initial momentum $Q$ in the one-dimensional (1D) interacting bosonic medium. We show that magnon and exciton-like states obtained from the BA equations drastically determine the oscillation nature of the quantum flutter with the periodicity given by $τ_{\rm QF} = 2π/(|\varepsilon_{\rm c}(0)|- |\varepsilon_{\rm s}(0)|)$. Where the charge and spin dressed energies $\varepsilon_{\rm c,s}(0)$ are precisely given by the thermodynamical BA equations. While we further find a persistent revival dynamics of the impurity with a larger periodicity $τ_{L} = L/\left(v_{\rm c}(Q-k^*)-v_{\rm s}(k^*)\right)$ than $τ_{\rm QF}$, manifesting a quantum reflection induced by the periodic boundary conditions of a finite length $L$, here $v_{\rm c,s}$ are the sound velocities of charge and spin excitations, respectively, and $k^*$ is a characteristic momentum of the impurity to the Fermi point. Finally, we study the application of such a magnon impurity as a quantum resource for measuring the gravitational force.

cond-mat.quant-gas↗