1,668 research outputs found
Transforming Bell's Inequalities into State Classifiers with Machine Learning
Quantum information science has profoundly changed the ways we understand,
store, and process information. A major challenge in this field is to look for
an efficient means for classifying quantum state. For instance, one may want to
determine if a given quantum state is entangled or not. However, the process of
a complete characterization of quantum states, known as quantum state
tomography, is a resource-consuming operation in general. An attractive
proposal would be the use of Bell's inequalities as an entanglement witness,
where only partial information of the quantum state is needed. The problem is
that entanglement is necessary but not sufficient for violating Bell's
inequalities, making it an unreliable state classifier. Here we aim at solving
this problem by the methods of machine learning. More precisely, given a family
of quantum states, we randomly picked a subset of it to construct a
quantum-state classifier, accepting only partial information of each quantum
state. Our results indicated that these transformed Bell-type inequalities can
perform significantly better than the original Bell's inequalities in
classifying entangled states. We further extended our analysis to three-qubit
and four-qubit systems, performing classification of quantum states into
multiple species. These results demonstrate how the tools in machine learning
can be applied to solving problems in quantum information science
On the correction of anomalous phase oscillation in entanglement witnesses using quantum neural networks
Entanglement of a quantum system depends upon relative phase in complicated
ways, which no single measurement can reflect. Because of this, entanglement
witnesses are necessarily limited in applicability and/or utility. We propose
here a solution to the problem using quantum neural networks. A quantum system
contains the information of its entanglement; thus, if we are clever, we can
extract that information efficiently. As proof of concept, we show how this can
be done for the case of pure states of a two-qubit system, using an
entanglement indicator corrected for the anomalous phase oscillation. Both the
entanglement indicator and the phase correction are calculated by the quantum
system itself acting as a neural network
Discriminative Cooperative Networks for Detecting Phase Transitions
The classification of states of matter and their corresponding phase
transitions is a special kind of machine-learning task, where physical data
allow for the analysis of new algorithms, which have not been considered in the
general computer-science setting so far. Here we introduce an unsupervised
machine-learning scheme for detecting phase transitions with a pair of
discriminative cooperative networks (DCN). In this scheme, a guesser network
and a learner network cooperate to detect phase transitions from fully
unlabeled data. The new scheme is efficient enough for dealing with phase
diagrams in two-dimensional parameter spaces, where we can utilize an active
contour model -- the snake -- from computer vision to host the two networks.
The snake, with a DCN "brain", moves and learns actively in the parameter
space, and locates phase boundaries automatically
Neural network setups for a precise detection of the many-body localization transition: finite-size scaling and limitations
Determining phase diagrams and phase transitions semi-automatically using
machine learning has received a lot of attention recently, with results in good
agreement with more conventional approaches in most cases. When it comes to
more quantitative predictions, such as the identification of universality class
or precise determination of critical points, the task is more challenging. As
an exacting test-bed, we study the Heisenberg spin-1/2 chain in a random
external field that is known to display a transition from a many-body localized
to a thermalizing regime, which nature is not entirely characterized. We
introduce different neural network structures and dataset setups to achieve a
finite-size scaling analysis with the least possible physical bias (no assumed
knowledge on the phase transition and directly inputing wave-function
coefficients), using state-of-the-art input data simulating chains of sizes up
to L=24. In particular, we use domain adversarial techniques to ensure that the
network learns scale-invariant features. We find a variability of the output
results with respect to network and training parameters, resulting in
relatively large uncertainties on final estimates of critical point and
correlation length exponent which tend to be larger than the values obtained
from conventional approaches. We put the emphasis on interpretability
throughout the paper and discuss what the network appears to learn for the
various used architectures. Our findings show that a it quantitative analysis
of phase transitions of unknown nature remains a difficult task with neural
networks when using the minimally engineered physical input.Comment: v2: published versio
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