Machine-learned, finite temperature Fermi-operator expansions suitable for GPUs and AI-hardware

• URL: http://arxiv.org/abs/2605.08523v1
• Date: Fri, 08 May 2026 22:15:11 GMT
• Title: Machine-learned, finite temperature Fermi-operator expansions suitable for GPUs and AI-hardware
• Abstract summary: We present several finite-temperature recursive Fermi-operator expansion schemes based on the second-order spectral projection (SP2) method.<n>We construct machine learning models to determine optimized expansion coefficients.<n>Compared to state-of-the-art diagonalization, we achieve an order-of-magnitude speedup in the single-particle finite-temperature density matrix calculation.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: We present several finite-temperature recursive Fermi-operator expansion schemes based on the second-order spectral projection (SP2) method. Our approach builds on a previous observation that the electronic structure problem, as formulated through a recursive SP2 expansion, can be mapped onto the architecture of a deep neural network. Using this perspective, we generalize SP2 to finite electronic temperatures and construct machine learning models to determine optimized expansion coefficients. These coefficients are trained for a specified chemical potential and electronic temperature and are not available in closed analytical form. However, by employing an appropriate affine rescaling strategy to the Hamiltonian matrix, we eliminate the need to retrain the model during a simulation if the temperature and chemical potential change. Our approach avoids explicit diagonalization and relies solely on highly optimized matrix-matrix multiplication kernels. Compared to state-of-the-art diagonalization, we achieve an order-of-magnitude speedup in the single-particle finite-temperature density matrix calculation for small and moderately sized matrices on modern GPUs and dense matrix multiply units.

Related papers

• Spectral and thermodynamic properties of supersymmetric quantum systems with self-adjoint deformed momentum [0.0]
  We build a rigorous framework for quantum systems with geometric deformations by constructing a strictly self-adjoint deformed momentum operator.<n>We provide the first complete thermodynamic characterization of such systems by analytically evaluating the partition function.<n>These results establish geometric deformation as a tunable parameter for engineering quantum thermodynamic responses in curved nanostructures.
  arXiv  Detail & Related papers  (2026-06-20T15:43:06Z)
• Quantum Ising Model on $(2+1)-$Dimensional Anti$-$de Sitter Space using Tensor Networks [37.108493798440655]
  We study the quantum Ising model on (2+1)-dimensional anti-de Sitter space using Matrix Product States (MPS) and Matrix Product Operators (MPOs)<n>Our spatial lattices correspond to regular tessellations of hyperbolic space with coordination number seven.<n>We find the ground state of this model using the Density Matrix Renormalization Group (DMRG) algorithm which allowed us to probe lattices that range in size up to 232 sites.
  arXiv  Detail & Related papers  (2025-12-23T23:29:39Z)
• Fundamental Limits of Matrix Sensing: Exact Asymptotics, Universality, and Applications [34.781211988554425]
  We provide rigorous equations characterizing the Bayes-optimal learning performance from a number of samples.<n>We mathematically establish predictions obtained via non-rigorous methods from statistical physics.
  arXiv  Detail & Related papers  (2025-03-18T10:36:30Z)
• Machine learning approach for vibronically renormalized electronic band structures [3.3312479395168455]
  We present a machine learning (ML) method for efficient computation of vibrational thermal expectation values of physical properties from first principles. A deep-learning neural network is trained to accurately predict physical properties associated with sampled phonon configurations. We show that, with less than a hundred DFT calculations for training the neural network model, an order of magnitude of sampling can be achieved for the computation of the vibrational thermal expectation values.
  arXiv  Detail & Related papers  (2024-09-03T01:39:18Z)
• Neutron-nucleus dynamics simulations for quantum computers [49.369935809497214]
  We develop a novel quantum algorithm for neutron-nucleus simulations with general potentials. It provides acceptable bound-state energies even in the presence of noise, through the noise-resilient training method. We introduce a new commutativity scheme called distance-grouped commutativity (DGC) and compare its performance with the well-known qubit-commutativity scheme.
  arXiv  Detail & Related papers  (2024-02-22T16:33:48Z)
• Two dimensional quantum lattice models via mode optimized hybrid CPU-GPU density matrix renormalization group method [0.0]
  We present a hybrid numerical approach to simulate quantum many body problems on two spatial dimensional quantum lattice models. We demonstrate for the two dimensional spinless fermion model and for the Hubbard model on torus geometry that several orders of magnitude in computational time can be saved.
  arXiv  Detail & Related papers  (2023-11-23T17:07:47Z)
• Non-Markovian Stochastic Schr\"odinger Equation: Matrix Product State Approach to the Hierarchy of Pure States [65.25197248984445]
  We derive a hierarchy of matrix product states (HOMPS) for non-Markovian dynamics in open finite temperature. The validity and efficiency of HOMPS is demonstrated for the spin-boson model and long chains where each site is coupled to a structured, strongly non-Markovian environment.
  arXiv  Detail & Related papers  (2021-09-14T01:47:30Z)
• Positivity Preserving Density Matrix Minimization at Finite Temperatures via Square Root [0.0]
  We present a method for calculating the Fermi-Dirac density matrix for electronic structure problems at finite temperature. We consider both the grand canonical (constant chemical potential) and canonical (constant number of electrons) ensembles. We show that the number of steps required for convergence is independent of the number of atoms in the system.
  arXiv  Detail & Related papers  (2021-03-12T04:30:31Z)
• Mixed Precision Fermi-Operator Expansion on Tensor Cores From a Machine Learning Perspective [0.20011494166747584]
  A performance of over 100 teraFLOPs is achieved for half-precision floating point operations on Nvidia's A100 tensor core units. A differentiable deep neural network structure is formulated to solve the quantum mechanical electronic structure problem.
  arXiv  Detail & Related papers  (2021-01-16T06:55:20Z)
• Generative Flows with Matrix Exponential [25.888286821451562]
  Generative flows models enjoy the properties of tractable exact likelihood and efficient sampling. We incorporate matrix exponential into generative flows. Our model achieves great performance on density estimation amongst generative flows models.
  arXiv  Detail & Related papers  (2020-07-19T11:18:47Z)
• Learning Composable Energy Surrogates for PDE Order Reduction [28.93892833892805]
  We use parametric modular structure to learn component-level surrogates, enabling cheaper high-fidelity simulation. We use a neural network to model the stored potential energy in a component given boundary conditions. Composable energy surrogates permit simulation in the reduced basis of component boundaries.
  arXiv  Detail & Related papers  (2020-05-13T19:41:24Z)

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.