1,231 research outputs found
Inhomogeneous quenches as state preparation in two-dimensional conformal field theories
The non-equilibrium process where the system does not evolve to the
featureless state is one of the new central objects in the non-equilibrium
phenomena. In this paper, starting from the short-range entangled state in the
two-dimensional conformal field theories (d CFTs), the boundary state with a
regularization, we evolve the system with the inhomogeneous Hamiltonians called
M\"obius/SSD ones. Regardless of the details of CFTs considered in this paper,
during the M\"obius evolution, the entanglement entropy exhibits the periodic
motion called quantum revival. During SSD time evolution, except for some
subsystems, in the large time regime, entanglement entropy and mutual
information are approximated by those for the vacuum state. We argue the time
regime for the subsystem to cool down to vacuum one is , where , , and are time, system, and
subsystem sizes. This finding suggests the inhomogeneous quench induced by the
SSD Hamiltonian may be used as the preparation for the approximately-vacuum
state. We propose the gravity dual of the systems considered in this paper,
furthermore, and generalize it. In addition to them, we discuss the relation
between the inhomogenous quenches and continuous multi-scale entanglement
renormalization ansatz (cMERA).Comment: 32+4 pages, 11 figure
Entanglement Dynamics of the Non-Unitary Holographic Channel
We study the dynamical properties of a strongly scrambling quantum circuit
involving a projective measurement on a finite-sized region by studying the
operator entanglement entropy and mutual information (OEE and BOMI) of the dual
operator state that corresponds to this quantum circuit. The time-dependence of
the OEE exhibits a new dynamical behavior of operator entanglement, namely an
additional fractional coefficient that accompanies the linear time growth of
the OEE. For a holographic system, this is equivalent to an additional
fractional coefficient that modifies the linear growth rate of the wormhole
volume. The time-dependence of the BOMI shows that the projective measurement
may destroy the non-local correlations in this dual state. We also propose a
gravity dual as well as a line-tension picture, which is an effective model,
that describe this strongly scrambling quantum circuit.Comment: 30 pages + appendices, 12 figure
Scrambling and Recovery of Quantum Information in Inhomogeneous Quenches in Two-dimensional Conformal Field Theories
We study various quantum quench processes induced by the M\"obius/sine-square
deformation of the Hamiltonian in two-dimensional conformal field theories
starting from the thermofield double state in the two copies of the Hilbert
space. These quantum quenches, some of which are directly related to the
operator entanglement of the time-evolution operators, allow us to study
scrambling and recovery of quantum information. In particular, under the SSD
time-evolution, we show from the time-dependence of mutual information that the
Bell pairs, initially shared by the subsystems of the two Hilbert spaces, may
revive even after the mutual information for small subsystems is completely
destroyed by quantum information scrambling dynamics. This mutual information
is robust against the strong scrambling dynamics. As a consequence, the steady
state has a non-local correlation shared not by any of two parties but by three
parties. In the holographic dual description, a wormhole connecting the two
Hilbert spaces may non-linearly grow with time during the quantum quenches. We
also propose effective pictures that describe the dynamics of mutual
information during the time-evolution by inhomogeneous Hamiltonians.Comment: 36+26 pages, 23 figure
Bridging two quantum quench problems -- local joining quantum quench and M\"obius quench -- and their holographic dual descriptions
We establish an equivalence between two different quantum quench problems,
the joining local quantum quench and the M\"obius quench, in the context of
-dimensional conformal field theory (CFT). Here, in the former, two
initially decoupled systems (CFTs) on finite intervals are joined at . In
the latter, we consider the system that is initially prepared in the ground
state of the regular homogeneous Hamiltonian on a finite interval and, after
, let it time-evolve by the so-called M\"obius Hamiltonian that is
spatially inhomogeneous. The equivalence allows us to relate the time-dependent
physical observables in one of these problems to those in the other. As an
application of the equivalence, we construct a holographic dual of the M\"obius
quench from that of the local quantum quench. The holographic geometry involves
an end-of-the-world brane whose profile exhibits non-trivial dynamics.Comment: 13 pages, 9 figure
Rethinking the Open-Loop Evaluation of End-to-End Autonomous Driving in nuScenes
Modern autonomous driving systems are typically divided into three main
tasks: perception, prediction, and planning. The planning task involves
predicting the trajectory of the ego vehicle based on inputs from both internal
intention and the external environment, and manipulating the vehicle
accordingly. Most existing works evaluate their performance on the nuScenes
dataset using the L2 error and collision rate between the predicted
trajectories and the ground truth. In this paper, we reevaluate these existing
evaluation metrics and explore whether they accurately measure the superiority
of different methods. Specifically, we design an MLP-based method that takes
raw sensor data (e.g., past trajectory, velocity, etc.) as input and directly
outputs the future trajectory of the ego vehicle, without using any perception
or prediction information such as camera images or LiDAR. Our simple method
achieves similar end-to-end planning performance on the nuScenes dataset with
other perception-based methods, reducing the average L2 error by about 20%.
Meanwhile, the perception-based methods have an advantage in terms of collision
rate. We further conduct in-depth analysis and provide new insights into the
factors that are critical for the success of the planning task on nuScenes
dataset. Our observation also indicates that we need to rethink the current
open-loop evaluation scheme of end-to-end autonomous driving in nuScenes. Codes
are available at https://github.com/E2E-AD/AD-MLP.Comment: Technical report. Code is availabl
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