234 research outputs found
Learning phase transitions from dynamics
We propose the use of recurrent neural networks for classifying phases of
matter based on the dynamics of experimentally accessible observables. We
demonstrate this approach by training recurrent networks on the magnetization
traces of two distinct models of one-dimensional disordered and interacting
spin chains. The obtained phase diagram for a well-studied model of the
many-body localization transition shows excellent agreement with previously
known results obtained from time-independent entanglement spectra. For a
periodically-driven model featuring an inherently dynamical time-crystalline
phase, the phase diagram that our network traces in a previously-unexplored
regime coincides with an order parameter for its expected phases.Comment: 5 pages + 3 fig, appendix + 5 fi
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
Single spin probe of Many-Body Localization
We use an external spin as a dynamical probe of many body localization. The
probe spin is coupled to an interacting and disordered environment described by
a Heisenberg spin chain in a random field. The spin-chain environment can be
tuned between a thermalizing delocalized phase and non-thermalizing localized
phase, both in its ground- and high-energy states. We study the decoherence of
the probe spin when it couples to the environment prepared in three states: the
ground state, the infinite temperature state and a high energy N\'eel state. In
the non-thermalizing many body localized regime, the coherence shows scaling
behaviour in the disorder strength. The long-time dynamics of the probe spin
shows a logarithmic dephasing in analogy with the logarithmic growth of
entanglement entropy for a bi-partition of a many-body localized system. In
summary, we show that decoherence of the probe spin provides clear signatures
of many-body localization.Comment: 5 pages, 4 figure
Renormalization group approach to symmetry protected topological phases
A defining feature of a symmetry protected topological phase (SPT) in
one-dimension is the degeneracy of the Schmidt values for any given
bipartition. For the system to go through a topological phase transition
separating two SPTs, the Schmidt values must either split or cross at the
critical point in order to change their degeneracies. A renormalization group
(RG) approach based on this splitting or crossing is proposed, through which we
obtain an RG flow that identifies the topological phase transitions in the
parameter space. Our approach can be implemented numerically in an efficient
manner, for example, using the matrix product state formalism, since only the
largest first few Schmidt values need to be calculated with sufficient
accuracy. Using several concrete models, we demonstrate that the critical
points and fixed points of the RG flow coincide with the maxima and minima of
the entanglement entropy, respectively, and the method can serve as a
numerically efficient tool to analyze interacting SPTs in the parameter space.Comment: 5 pages, 3 figure
Explainable Representation Learning of Small Quantum States
Unsupervised machine learning models build an internal representation of
their training data without the need for explicit human guidance or feature
engineering. This learned representation provides insights into which features
of the data are relevant for the task at hand. In the context of quantum
physics, training models to describe quantum states without human intervention
offers a promising approach to gaining insight into how machines represent
complex quantum states. The ability to interpret the learned representation may
offer a new perspective on non-trivial features of quantum systems and their
efficient representation. We train a generative model on two-qubit density
matrices generated by a parameterized quantum circuit. In a series of
computational experiments, we investigate the learned representation of the
model and its internal understanding of the data. We observe that the model
learns an interpretable representation which relates the quantum states to
their underlying entanglement characteristics. In particular, our results
demonstrate that the latent representation of the model is directly correlated
with the entanglement measure concurrence. The insights from this study
represent proof of concept towards interpretable machine learning of quantum
states. Our approach offers insight into how machines learn to represent
small-scale quantum systems autonomously
A NEAT Quantum Error Decoder
We investigate the use of the evolutionary NEAT algorithm for the
optimization of a policy network that performs quantum error decoding on the
toric code, with bitflip and depolarizing noise, one qubit at a time. We find
that these NEAT-optimized network decoders have similar performance to
previously reported machine-learning based decoders, but use roughly three to
four orders of magnitude fewer parameters to do so.Comment: 10 pages, 7 figure
- …