Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits

• URL: http://arxiv.org/abs/2410.00953v2
• Date: Thu, 3 Oct 2024 05:53:29 GMT
• Title: Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits
• Authors: Menghan Song, Zhaoyi Zeng, Ting-Tung Wang, Yi-Zhuang You, Zi Yang Meng, Pengfei Zhang,
• Abstract summary: We investigate operator dynamics and entanglement growth in dual-unitary circuits. Our work offers a scalable computational framework for studying long-time operator evolution and entanglement.
• Score: 3.8572128827057255
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate operator dynamics and entanglement growth in dual-unitary circuits, a class of locally scrambled quantum systems that enables efficient simulation beyond the exponential complexity of the Hilbert space. By mapping the operator evolution to a classical Markov process,we perform Monte Carlo simulations to access the time evolution of local operator density and entanglement with polynomial computational cost. Our results reveal that the operator density converges exponentially to a steady-state value, with analytical bounds that match our simulations. Additionally, we observe a volume-law scaling of operator entanglement across different subregions,and identify a critical transition from maximal to sub-maximal entanglement growth, governed by the circuit's gate parameter. This transition, confirmed by both mean-field theory and Monte Carlo simulations, provides new insights into operator entanglement dynamics in quantum many-body systems. Our work offers a scalable computational framework for studying long-time operator evolution and entanglement, paving the way for deeper exploration of quantum information dynamics.

Related papers

• Gauge-Fixing Quantum Density Operators At Scale [0.0]
  We provide theory, algorithms, and simulations of non-equilibrium quantum systems. We analytically and numerically examine the virtual freedoms associated with the representation of quantum density operators.
  arXiv  Detail & Related papers  (2024-11-05T22:56:13Z)
• Truncated Gaussian basis approach for simulating many-body dynamics [0.0]
  The approach constructs an effective Hamiltonian within a reduced subspace, spanned by fermionic Gaussian states, and diagonalizes it to obtain approximate eigenstates and eigenenergies. Symmetries can be exploited to perform parallel computation, enabling to simulate systems with much larger sizes. For quench dynamics we observe that time-evolving wave functions in the truncated subspace facilitates the simulation of long-time dynamics.
  arXiv  Detail & Related papers  (2024-10-05T15:47:01Z)
• Improved precision scaling for simulating coupled quantum-classical dynamics [0.17126708168238122]
  We present a super-polynomial improvement in the precision scaling of quantum simulations for coupled classical-quantum systems. By employing a framework based on the Koopman-von Neumann formalism, we express the Liouville equation of motion as unitary dynamics. We demonstrate that these simulations can be performed in both microcanonical and canonical ensembles.
  arXiv  Detail & Related papers  (2023-07-24T18:00:03Z)
• Dynamical Triplet Unravelling: A quantum Monte Carlo algorithm for reversible dynamics [0.0]
  We introduce a quantum Monte Carlo method to simulate the dynamics of correlated many-body systems. Our method is based on the Laplace transform of the time-evolution operator which, as opposed to most quantum Monte Carlo methods, makes it possible to access the dynamics at longer times.
  arXiv  Detail & Related papers  (2022-06-21T12:09:51Z)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)
• Quantum Markov Chain Monte Carlo with Digital Dissipative Dynamics on Quantum Computers [52.77024349608834]
  We develop a digital quantum algorithm that simulates interaction with an environment using a small number of ancilla qubits. We evaluate the algorithm by simulating thermal states of the transverse Ising model.
  arXiv  Detail & Related papers  (2021-03-04T18:21:00Z)
• 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)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)
• 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)
• Autoregressive Transformer Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation [5.668795025564699]
  We present an approach for tackling open quantum system dynamics. We compactly represent quantum states with autoregressive transformer neural networks. Efficient algorithms have been developed to simulate the dynamics of the Liouvillian superoperator.
  arXiv  Detail & Related papers  (2020-09-11T18:00:00Z)
• Simulating nonnative cubic interactions on noisy quantum machines [65.38483184536494]
  We show that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware. On noisy devices without error correction, we show that simulation results are significantly improved when the quantum program is compiled using modular gates.
  arXiv  Detail & Related papers  (2020-04-15T05:16:24Z)

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.