Many-body Liouvillian dynamics with a non-Hermitian tensor-network kernel polynomial algorithm

• URL: http://arxiv.org/abs/2407.06282v2
• Date: Sun, 24 Nov 2024 16:21:33 GMT
• Title: Many-body Liouvillian dynamics with a non-Hermitian tensor-network kernel polynomial algorithm
• Abstract summary: We put forward a method for solving the many-body Liouvillian spectrum and dynamics based on the non-Hermitian kernel method. We show that our method allows us to characterize the quantum Zeno crossover and the reduction of relaxation rate due to Stark localization. Our method provides an efficient solution to many-body Liouvillian spectrum and dynamics, a methodology to explore large open quantum many-body systems.
• Score: 1.2119651475015631
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Understanding the dynamics of open quantum many-body systems is a major problem in quantum matter. Specifically, efficiently solving the spectrum of the Liouvillian superoperator governing such dynamics remains a critical open challenge. Here, we put forward a method for solving the many-body Liouvillian spectrum and dynamics based on the non-Hermitian kernel polynomial method and tensor-network techniques. We demonstrate the faithfulness of our method by computing the dynamics of the dephasing quantum compass model with a gradient magnetic field and comparing it with exact results. In particular, we show that our method allows us to characterize the quantum Zeno crossover and the reduction of relaxation rate due to Stark localization in this model. We further demonstrate the ability of our method to go beyond exact results by exploring nearest-neighbor interaction effects on the Liouvillian dynamics, elucidating the interplay between Stark localization and many-body interactions. Our method provides an efficient solution to many-body Liouvillian spectrum and dynamics, establishing a methodology to explore large open quantum many-body systems.

Related papers

• Towards Quantum Enhanced Adversarial Robustness with Rydberg Reservoir Learning [45.92935470813908]
  Quantum computing reservoir (QRC) leverages the high-dimensional, nonlinear dynamics inherent in quantum many-body systems.<n>Recent studies indicate that perturbation quantums based on variational circuits remain susceptible to adversarials.<n>We investigate the first systematic evaluation of adversarial robustness in a QR based learning model.
  arXiv  Detail & Related papers  (2025-10-15T12:17:23Z)
• Variational approach to open quantum systems with long-range competing interactions [0.0]
  We introduce an efficient and scalable approach to dissipative quantum lattices in one and two dimensions.<n>We showcase the versatility, effectiveness, and unique methodological advantages of our algorithm by simulating the non-equilibrium dynamics and steady states of spin-$frac12$ lattices.<n>This approach offers promising prospects for advancing our understanding of the complex non-equilibrium properties of a diverse variety of experimentally-realizable quantum systems with long-ranged interactions.
  arXiv  Detail & Related papers  (2025-10-02T00:29:00Z)
• Efficient Variational Dynamics of Open Quantum Bosonic Systems via Automatic Differentiation [0.0]
  We introduce a scalable variational method for simulating the dynamics of interacting quantum bosonic systems deep in the quantum regime.<n>As a key application, we study a driven-dissipative two-dimensional Bose-Hubbard lattice with two-boson coherent driving and two-body losses.<n>Our results reveal critical slowing down with dynamical exponents of the 2D quantum Ising universality class.
  arXiv  Detail & Related papers  (2025-07-18T16:53:01Z)
• Grassmann Variational Monte Carlo with neural wave functions [45.935798913942904]
  We formalize the framework introduced by Pfau et al.citepfau2024accurate in terms of Grassmann geometry of the Hilbert space.<n>We validate our approach on the Heisenberg quantum spin model on the square lattice, achieving highly accurate energies and physical observables for a large number of excited states.
  arXiv  Detail & Related papers  (2025-07-14T13:53:13Z)
• Restricted Monte Carlo wave function method and Lindblad equation for identifying entangling open-quantum-system dynamics [0.0]
  Our algorithm performs tangential projections onto the set of separable states, leading to classically correlated quantum trajectories. Applying this method is equivalent to solving the nonlinear master equation in Lindblad form introduced in citePAH24 for two-qubit systems. We identify the impact of dynamical entanglement in open systems by applying our approach to several correlated decay processes.
  arXiv  Detail & Related papers  (2024-12-11T19:05:34Z)
• Hybrid Stabilizer Matrix Product Operator [44.99833362998488]
  We introduce a novel hybrid approach combining tensor network methods with the stabilizer formalism to address the challenges of simulating many-body quantum systems. We demonstrate the effectiveness of our method through applications to random Clifford T-doped circuits and Random Clifford Floquet Dynamics.
  arXiv  Detail & Related papers  (2024-05-09T18:32:10Z)
• Ab-initio variational wave functions for the time-dependent many-electron Schrödinger equation [41.94295877935867]
  We introduce a variational approach for fermionic time-dependent wave functions, surpassing mean-field approximations. We use time-dependent Jastrow factors and backflow transformations, which are enhanced through neural networks parameterizations. The results showcase the ability of our variational approach to accurately capture the time evolution, providing insight into the quantum dynamics of interacting electronic systems.
  arXiv  Detail & Related papers  (2024-03-12T09:37:22Z)
• Variational dynamics of open quantum systems in phase space [0.0]
  We present a method to simulate the dynamics of large driven-dissipative many-body open quantum systems. We present a proof of principle investigation into the physics of the driven-dissipative Bose-Hubbard model with weak nonlinearity.
  arXiv  Detail & Related papers  (2023-07-14T15:48:31Z)
• Estimating Eigenenergies from Quantum Dynamics: A Unified Noise-Resilient Measurement-Driven Approach [0.0]
  Ground state energy estimation is one of the most promising applications of quantum computing. We introduce a new hybrid approach that finds the eigenenergies by collecting real-time measurements and post-processing them.
  arXiv  Detail & Related papers  (2023-06-02T18:27:16Z)
• Quantum variational embedding for ground-state energy problems: sum of squares and cluster selection [12.151998897427012]
  We introduce a sum-of-squares SDP hierarchy approximating the ground-state energy from below for quantum many-body problems. We propose efficient strategies for optimizing cluster selection to tighten SDP relaxations while staying within a computational budget. As a byproduct of our investigation, we find that quantum entanglement has the potential to capture the underlying graph of the many-body Hamiltonian.
  arXiv  Detail & Related papers  (2023-05-29T19:19:03Z)
• Numerical simulations of long-range open quantum many-body dynamics with tree tensor networks [0.0]
  We introduce a numerical method for open quantum systems, based on tree tensor networks. Such a structure is expected to improve the encoding of many-body correlations. We adopt an integration scheme suited for long-range interactions and applications to dissipative dynamics.
  arXiv  Detail & Related papers  (2023-04-12T18:00:03Z)
• Dynamics with autoregressive neural quantum states: application to critical quench dynamics [41.94295877935867]
  We present an alternative general scheme that enables one to capture long-time dynamics of quantum systems in a stable fashion. We apply the scheme to time-dependent quench dynamics by investigating the Kibble-Zurek mechanism in the two-dimensional quantum Ising model.
  arXiv  Detail & Related papers  (2022-09-07T15:50:00Z)
• 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)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Method of spectral Green functions in driven open quantum dynamics [77.34726150561087]
  A novel method based on spectral Green functions is presented for the simulation of driven open quantum dynamics. The formalism shows remarkable analogies to the use of Green functions in quantum field theory. The method dramatically reduces computational cost compared with simulations based on solving the full master equation.
  arXiv  Detail & Related papers  (2020-06-04T09:41:08Z)

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.