RQC Seminar

294th RQC Seminar

• Speaker

  Mr. Ilyes Degardin
  ( Ecole Polytechnique, France )

• Date

  16:00-17:00, (4:00 p.m.- 5:00 p.m.) Wednesday, July 22, 2026

• Venue

  Hybrid( Zoom,
  345-347 Seminar Room, 3F, Main Research Building, Wako Campus / 和光地区 研究本館3階 セミナー室 (345-347) (C01))

• Title

  Sample-based Krylov Algorithm for Open Quantum Systems

• Inquiries

  norilab_rqc_assist[at]ml.riken.jp

Abstract
Determining the ground states of many-body Hamiltonians or the steady states of many-body Liouvillians through numerically exact diagonalization rapidly becomes prohibitive due to the exponential growth of the Hilbert space. Krylov subspace methods tackle this challenge by projecting the Hamiltonian or Liouvillian onto a physically relevant subspace, generated from a judicious initial state subjected to a sequence of time evolutions. Sample-based Krylov methods use a quantum computer to sample the computational basis states that dominate the Krylov basis states and consider the subspace they generate. Knowledge of the subspace basis allows to project, and subsequently diagonalize, the Hamiltonian or Liouvillian classically. Sample-based Krylov Diagonalization has already been successfully demonstrated for Hamiltonians of closed quantum systems. In this talk, I will show how this method can be extended to the Liouvillians of open quantum systems. I will argue that this is best achieved by simulating the open-system dynamics with pure-state quantum trajectories. I will demonstrate along examples that this generalized framework can be used to retrieve approximations of the steady state, the spectral gap, as well as the dynamics of observables of interest. Convergence guarantees can be proven under some sparsity hypotheses.