Accelerating Real-Time Coupled Cluster Methods with Single-Precision Arithmetic and Adaptive Numerical Integration

• URL: http://arxiv.org/abs/2205.05175v1
• Date: Tue, 10 May 2022 21:21:49 GMT
• Title: Accelerating Real-Time Coupled Cluster Methods with Single-Precision Arithmetic and Adaptive Numerical Integration
• Authors: Zhe Wang, Benjamin G. Peyton and T. Daniel Crawford
• Abstract summary: We show that single-precision arithmetic reduces both the storage and multiplicative costs of the real-time simulation by approximately a factor of two. Additional speedups of up to a factor of 14 in test simulations of water clusters are obtained via a straightforward-based implementation.
• Score: 3.469636229370366
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We explore the framework of a real-time coupled cluster method with a focus on improving its computational efficiency. Propagation of the wave function via the time-dependent Schr\"odinger equation places high demands on computing resources, particularly for high level theories such as coupled cluster with polynomial scaling. Similar to earlier investigations of coupled cluster properties, we demonstrate that the use of single-precision arithmetic reduces both the storage and multiplicative costs of the real-time simulation by approximately a factor of two with no significant impact on the resulting UV/vis absorption spectrum computed via the Fourier transform of the time-dependent dipole moment. Additional speedups of up to a factor of 14 in test simulations of water clusters are obtained via a straightforward GPU-based implementation as compared to conventional CPU calculations. We also find that further performance optimization is accessible through sagacious selection of numerical integration algorithms, and the adaptive methods, such as the Cash-Karp integrator provide an effective balance between computing costs and numerical stability. Finally, we demonstrate that a simple mixed-step integrator based on the conventional fourth-order Runge-Kutta approach is capable of stable propagations even for strong external fields, provided the time step is appropriately adapted to the duration of the laser pulse with only minimal computational overhead.

Related papers

• A time-parallel multiple-shooting method for large-scale quantum optimal control [0.0]
  We introduce a multiple-shooting approach in which the time domain is divided into multiple windows and the intermediate states at window boundaries are treated as additional optimization variables. This enables parallel computation of state evolution across time-windows, significantly accelerating objective function and gradient evaluations. A quadratic penalty optimization method is used to solve the constrained optimal control problem, and an efficient adjoint technique is employed to calculate the gradients in each iteration.
  arXiv  Detail & Related papers  (2024-07-18T23:57:26Z)
• Fast, Scalable, Warm-Start Semidefinite Programming with Spectral Bundling and Sketching [53.91395791840179]
  We present Unified Spectral Bundling with Sketching (USBS), a provably correct, fast and scalable algorithm for solving massive SDPs. USBS provides a 500x speed-up over the state-of-the-art scalable SDP solver on an instance with over 2 billion decision variables.
  arXiv  Detail & Related papers  (2023-12-19T02:27:22Z)
• Self-Tuning Hamiltonian Monte Carlo for Accelerated Sampling [12.163119957680802]
  Hamiltonian Monte Carlo simulations crucially depend on the integration timestep and the number of integration steps. We present an adaptive general-purpose framework to automatically tune such parameters. We show that a good correspondence between loss and autocorrelation time can be established.
  arXiv  Detail & Related papers  (2023-09-24T09:35:25Z)
• Learning Unnormalized Statistical Models via Compositional Optimization [73.30514599338407]
  Noise-contrastive estimation(NCE) has been proposed by formulating the objective as the logistic loss of the real data and the artificial noise. In this paper, we study it a direct approach for optimizing the negative log-likelihood of unnormalized models.
  arXiv  Detail & Related papers  (2023-06-13T01:18:16Z)
• Generative modeling of time-dependent densities via optimal transport and projection pursuit [3.069335774032178]
  We propose a cheap alternative to popular deep learning algorithms for temporal modeling. Our method is highly competitive compared with state-of-the-art solvers.
  arXiv  Detail & Related papers  (2023-04-19T13:50:13Z)
• Fast Computation of Optimal Transport via Entropy-Regularized Extragradient Methods [75.34939761152587]
  Efficient computation of the optimal transport distance between two distributions serves as an algorithm that empowers various applications. This paper develops a scalable first-order optimization-based method that computes optimal transport to within $varepsilon$ additive accuracy.
  arXiv  Detail & Related papers  (2023-01-30T15:46:39Z)
• A Sublinear-Time Quantum Algorithm for Approximating Partition Functions [0.0]
  We present a novel quantum algorithm for estimating Gibbs partition functions in sublinear time. This is the first speed-up of this type to be obtained over the seminal nearly-linear time of vStefankovivc, Vempala and Vigoda.
  arXiv  Detail & Related papers  (2022-07-18T14:41:48Z)
• Efficient classical simulation of open bosonic quantum systems [0.0]
  We propose a method to solve the dynamics of operators of bosonic quantum systems coupled to their environments. The method maps the operator under interest to a set of complex-valued functions, and its adjoint master equation to a set of partial differential equations. We foresee the method to prove useful, e.g., for the verification of the operation of superconducting quantum processors.
  arXiv  Detail & Related papers  (2022-03-10T18:24:09Z)
• DiffPD: Differentiable Projective Dynamics with Contact [65.88720481593118]
  We present DiffPD, an efficient differentiable soft-body simulator with implicit time integration. We evaluate the performance of DiffPD and observe a speedup of 4-19 times compared to the standard Newton's method in various applications.
  arXiv  Detail & Related papers  (2021-01-15T00:13:33Z)
• Fast and differentiable simulation of driven quantum systems [58.720142291102135]
  We introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical methods. We show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
  arXiv  Detail & Related papers  (2020-12-16T21:43:38Z)
• Accelerating Feedforward Computation via Parallel Nonlinear Equation Solving [106.63673243937492]
  Feedforward computation, such as evaluating a neural network or sampling from an autoregressive model, is ubiquitous in machine learning. We frame the task of feedforward computation as solving a system of nonlinear equations. We then propose to find the solution using a Jacobi or Gauss-Seidel fixed-point method, as well as hybrid methods of both. Our method is guaranteed to give exactly the same values as the original feedforward computation with a reduced (or equal) number of parallelizable iterations, and hence reduced time given sufficient parallel computing power.
  arXiv  Detail & Related papers  (2020-02-10T10:11:31Z)

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.