arXiv subjects

Qian-Rui Lee

Publications and source records attributed to Qian-Rui Lee.

3 recordsLinked to original sources

arXiv2026

Channel concentration of critical quantum geometry

The quantum metric quantifies the total ground-state response along a parameter direction, but does not resolve how excitations share that response. We define channel concentration (CC) as the sum of squared normalized response weights over specified excitation channels, such as momentum blocks. An exact finite-size theorem yields thermodynamic CCs of 2/3 for the field response of the critical transverse-field Ising model and 1/3 for the half-filled XX pairing response, despite the same leading metric scaling. In finite-size approaches to the XY Lifshitz point, field and anisotropy perturbations yield different concentrations despite a common limiting Hamiltonian with quadratic dispersion. In a unitary 1+1-dimensional conformal field theory (CFT) on a circle, we consider a nondegenerate vacuum in a fixed sector perturbed by one spatially integrated scalar primary. We derive complete zero-momentum energy-level response weights, including descendants. For scaling dimension $0<Δ<3/2$, these weights determine the normalized response distribution and an exact universal concentration function. The expression reproduces the exact Ising lattice limit 2/3 and gives approximately 0.8515 for the three-state Potts thermal field, compared with approximately 0.800 from an exponent-only approximation. Finite-size interacting calculations compare concentrations and ranked response weights over many-body energy levels. These exact benchmarks show which response distinctions total metric scaling misses and guide comparisons with finite-size interacting spectra.

cond-mat.stat-mech↗

arXiv2026

Efficient identification of critical regions via Flow Matching-based Monte Carlo initialization

Markov chain Monte Carlo (MCMC) is a standard tool for studying many-body systems, but its practical cost can become substantial, especially when simulations must be repeated across temperatures and lattice sizes or near transition regions where equilibration becomes increasingly difficult. In this work, we introduce a Flow Matching (FM) framework. It is not a standalone replacement for equilibrium Monte Carlo. Instead, we present it as a scalable, physically informed initializer for downstream MCMC simulations. We use a U-Net architecture. The FM model is trained on small-system configurations of the 2D XY model and then deployed across unseen temperatures and larger lattice sizes. FM-generated configurations preserve the correct qualitative physical trends across temperature and system size. This makes them suitable warm-start states for subsequent Monte Carlo refinement. Observables computed from FM-generated samples primarily serve as diagnostics of initializer quality, not as precision equilibrium estimates. The regression-based $L_2$ objective suppresses variance and limits the accuracy of fluctuation-sensitive observables. Examples include susceptibility and spin stiffness. Still, the model captures sufficient local statistical structure to yield physically aligned initial states across a broad range of conditions. These results support a reusable hybrid FM--MCMC workflow. The one-time FM training cost can be amortized across temperatures and lattice sizes. The generated warm-start configurations then reduce the burden of initializing large-scale Monte Carlo simulations. Our findings show that Flow Matching can support efficient exploration of transition regions in many-body systems by providing reusable warm-start configurations for downstream Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2025

Automatic Characterization of Fluxonium Superconducting Qubits Parameters with Deep Transfer Learning

Accurate determination of qubit parameters is critical for the successful implementation of quantum information and computation applications. In solid state systems, the parameters of individual qubits vary across the entire system, requiring time consuming measurements and manual fitting processes for characterization. Recent developed superconducting qubits, such as fluxonium or 0-pi qubits, offer improved fidelity operations but exhibit a more complex physical and spectral structure, complicating parameter extraction. In this work, we propose a machine learning (ML)based methodology for the automatic and accurate characterization of fluxonium qubit parameters. Our approach utilized the energy spectrum calculated by a model Hamiltonian with various magnetic fields, as training data for the ML model. The output consists of the essential fluxonium qubit energy parameters, EJ, EC, and EL in Hamiltonian. The ML model achieves remarkable accuracy (with an average accuracy 95.6%) as an initial guess, enabling the development of an automatic fitting procedure for direct application to realistic experimental data. Moreover, we demonstrate that similar accuracy can be retrieved even when the input experimental spectrum is noisy or incomplete, highlighting the model robustness. These results suggest that our automated characterization method, based on a transfer learning approach, provides a reliable framework for future extensions to other superconducting qubits or different solid-state systems. Ultimately, we believe this methodology paves the way for the construction of large-scale quantum processors.

quant-ph↗