Comparing bipartite entropy growth in open-system matrix-product simulation methods

• URL: http://arxiv.org/abs/2303.09426v2
• Date: Thu, 3 Aug 2023 15:37:19 GMT
• Title: Comparing bipartite entropy growth in open-system matrix-product simulation methods
• Authors: Guillermo Preisser, David Wellnitz, Thomas Botzung, Johannes Schachenmayer
• Abstract summary: We compare the entropy growth relevant to the complexity of matrix-product representations in open-system simulations. We show that the bipartite entropy in the MPDO description (operator entanglement, OE) generally scales more favorably with time than the entropy in QT+MPS.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The dynamics of one-dimensional quantum many-body systems is often numerically simulated with matrix-product states (MPSs). The computational complexity of MPS methods is known to be related to the growth of entropies of reduced density matrices for bipartitions of the chain. While for closed systems the entropy relevant for the complexity is uniquely defined by the entanglement entropy, for open systems it depends on the choice of the representation. Here, we systematically compare the growth of different entropies relevant to the complexity of matrix-product representations in open-system simulations. We simulate an XXZ spin-1/2 chain in the presence of spontaneous emission and absorption, and dephasing. We compare simulations using a representation of the full density matrix as a matrix-product density operator (MPDO) with a quantum trajectory unraveling, where each trajectory is itself represented by an MPS (QT+MPS). We show that the bipartite entropy in the MPDO description (operator entanglement, OE) generally scales more favorably with time than the entropy in QT+MPS (trajectory entanglement, TE): i) For spontaneous emission and absorption the OE vanishes while the TE grows and reaches a constant value for large dissipative rates and sufficiently long times; ii) for dephasing the OE exhibits only logarithmic growth while the TE grows polynomially. Although QT+MPS requires a smaller local state space, the more favorable entropy growth can thus make MPDO simulations fundamentally more efficient than QT+MPS. Furthermore, MPDO simulations allow for easier exploitation of higher-order Trotter decompositions and translational invariance, allowing for larger time steps and system sizes.

Related papers

• Tensor product random matrix theory [39.58317527488534]
  We introduce a real-time field theory approach to the evolution of correlated quantum systems. We describe the full range of such crossover dynamics, from initial product states to a maximum entropy ergodic state.
  arXiv  Detail & Related papers  (2024-04-16T21:40:57Z)
• On Entropy Growth in Perturbative Scattering [0.0]
  We study the change in subsystem entropy generated by dynamical unitary evolution of a product state in a bipartite system. Remarkably, for the case of particle scattering, the circuit diagrams corresponding to $n$-Tsallis entropy are the same as the on-shell diagrams.
  arXiv  Detail & Related papers  (2023-04-25T18:00:01Z)
• Local Intrinsic Dimensional Entropy [29.519376857728325]
  Most entropy measures depend on the spread of the probability distribution over the sample space $mathcalX|$. In this work, we question the role of cardinality and distribution spread in defining entropy measures for continuous spaces. We find that the average value of the local intrinsic dimension of a distribution, denoted as ID-Entropy, can serve as a robust entropy measure for continuous spaces.
  arXiv  Detail & Related papers  (2023-04-05T04:36:07Z)
• Non-Markovian Stochastic Schr\"odinger Equation: Matrix Product State Approach to the Hierarchy of Pure States [65.25197248984445]
  We derive a hierarchy of matrix product states (HOMPS) for non-Markovian dynamics in open finite temperature. The validity and efficiency of HOMPS is demonstrated for the spin-boson model and long chains where each site is coupled to a structured, strongly non-Markovian environment.
  arXiv  Detail & Related papers  (2021-09-14T01:47:30Z)
• HEMP: High-order Entropy Minimization for neural network comPression [20.448617917261874]
  We formulate the entropy of a quantized artificial neural network as a differentiable function that can be plugged as a regularization term into the cost function minimized by descent. We show that HEMP is able to work in synergy with other approaches aiming at pruning or quantizing the model itself, delivering significant benefits in terms of storage size compressibility without harming the model's performance.
  arXiv  Detail & Related papers  (2021-07-12T10:17:53Z)
• Out-of-time-order correlations and the fine structure of eigenstate thermalisation [58.720142291102135]
  Out-of-time-orderors (OTOCs) have become established as a tool to characterise quantum information dynamics and thermalisation. We show explicitly that the OTOC is indeed a precise tool to explore the fine details of the Eigenstate Thermalisation Hypothesis (ETH) We provide an estimation of the finite-size scaling of $omega_textrmGOE$ for the general class of observables composed of sums of local operators in the infinite-temperature regime.
  arXiv  Detail & Related papers  (2021-03-01T17:51:46Z)
• 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)
• Scaling properties of a spatial one-particle density-matrix entropy in many-body localized systems [0.0]
  We investigate a quantum entropy extracted from the one-particle density matrix (OPDM) in one-dimensional interacting fermions. We numerically show that the OPDM entropy of the eigenstates obeys an area law.
  arXiv  Detail & Related papers  (2020-11-04T09:48:46Z)
• Holographic quantum algorithms for simulating correlated spin systems [0.0]
  We present a suite of "holographic" quantum algorithms for efficient ground-state preparation and dynamical evolution of correlated spin-systems. The algorithms exploit the equivalence between matrix-product states (MPS) and quantum channels, along with partial measurement and qubit re-use. As a demonstration of the potential resource savings, we implement a holoVQE simulation of the antiferromagnetic Heisenberg chain on a trapped-ion quantum computer.
  arXiv  Detail & Related papers  (2020-05-06T18:00:01Z)

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.