Solving the Transient Dyson Equation with Quasilinear Complexity via Matrix Compression

• URL: http://arxiv.org/abs/2410.11057v1
• Date: Mon, 14 Oct 2024 20:05:05 GMT
• Title: Solving the Transient Dyson Equation with Quasilinear Complexity via Matrix Compression
• Authors: Baptiste Lamic,
• Abstract summary: We introduce a numerical strategy to efficiently solve the out-of-equilibrium Dyson equation in the transient regime. We achieve significant improvements in computational efficiency, which result in quasi-linear scaling of both time and space complexity with propagation time.
• Score: 0.0
• License:
• Abstract: We introduce a numerical strategy to efficiently solve the out-of-equilibrium Dyson equation in the transient regime. By discretizing the equation into a compact matrix form and applying state-of-the-art matrix compression techniques, we achieve significant improvements in computational efficiency, which result in quasi-linear scaling of both time and space complexity with propagation time. This enables to compute accurate solutions even for systems with multiple and disparate time scales. We benchmark our solver by simulating a voltage-biased Josephson junction formed by a quantum dot connected to two superconducting leads.

Related papers

• Quantum Iterative Methods for Solving Differential Equations with Application to Computational Fluid Dynamics [14.379311972506791]
  We propose quantum methods for solving differential equations based on a gradual improvement of the solution via an iterative process. We benchmark the approach on paradigmatic fluid dynamics problems.
  arXiv  Detail & Related papers  (2024-04-12T17:08:27Z)
• 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)
• Quantum algorithms for linear and non-linear fractional reaction-diffusion equations [3.409316136755434]
  We investigate efficient quantum algorithms for nonlinear fractional reaction-diffusion equations with periodic boundary conditions. We present a novel algorithm that combines the linear combination of Hamiltonian simulation technique with the interaction picture formalism.
  arXiv  Detail & Related papers  (2023-10-29T04:48:20Z)
• A hybrid quantum-classical algorithm for multichannel quantum scattering of atoms and molecules [62.997667081978825]
  We propose a hybrid quantum-classical algorithm for solving the Schr"odinger equation for atomic and molecular collisions. The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes the fundamental scattering $S$-matrix. We show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules.
  arXiv  Detail & Related papers  (2023-04-12T18:10:47Z)
• A quantum algorithm for the linear Vlasov equation with collisions [0.0]
  We present a quantum algorithm that simulates the linearized Vlasov equation with and without collisions. We show that a quadratic speedup in system size is attainable.
  arXiv  Detail & Related papers  (2023-03-06T19:19:30Z)
• Calculating non-linear response functions for multi-dimensional electronic spectroscopy using dyadic non-Markovian quantum state diffusion [68.8204255655161]
  We present a methodology for simulating multi-dimensional electronic spectra of molecular aggregates with coupling electronic excitation to a structured environment. A crucial aspect of our approach is that we propagate the NMQSD equation in a doubled system Hilbert space but with the same noise.
  arXiv  Detail & Related papers  (2022-07-06T15:30:38Z)
• Continuous-time dynamics and error scaling of noisy highly-entangling quantum circuits [58.720142291102135]
  We simulate a noisy quantum Fourier transform processor with up to 21 qubits. We take into account microscopic dissipative processes rather than relying on digital error models. We show that depending on the dissipative mechanisms at play, the choice of input state has a strong impact on the performance of the quantum algorithm.
  arXiv  Detail & Related papers  (2021-02-08T14:55:44Z)
• 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)
• Low rank compression in the numerical solution of the nonequilibrium Dyson equation [0.0]
  We propose a method to improve the computational and memory efficiency of numerical solvers for the nonequilibrium Dyson equation in the Keldysh formalism. It is based on the empirical observation that the nonequilibrium Green's functions and self energies arising in many problems of physical interest, discretized as matrices, have low rank off-diagonal blocks. We describe an efficient algorithm to build this compressed representation on the fly during the course of time stepping, and use the representation to reduce the cost of computing history integrals.
  arXiv  Detail & Related papers  (2020-10-13T16:09:20Z)
• 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.