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Register a new userA learning algorithm with emergent scaling behavior for classifying phase transitions
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Machine learning-inspired techniques have emerged as a new paradigm for analysis of phase transitions in quantum matter. In this work, we introduce a supervised learning algorithm for studying critical phenomena from measurement data, which is based on iteratively training convolutional networks of increasing complexity, and test it on the transverse field Ising chain and q=6 Potts model. At the continuous Ising transition, we identify scaling behavior in the classification accuracy, from which we infer a characteristic classification length scale. It displays a power-law divergence at the critical point, with a scaling exponent that matches with the diverging correlation length. Our algorithm correctly identifies the thermodynamic phase of the system and extracts scaling behavior from projective measurements, independently of the basis in which the measurements are performed. Furthermore, we show the classification length scale is absent for the $q=6$ Potts model, which has a first order transition and thus lacks a divergent correlation length. The main intuition underlying our finding is that, for measurement patches of sizes smaller than the correlation length, the system appears to be at the critical point, and therefore the algorithm cannot identify the phase from which the data was drawn.
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We numerically investigate the structure of many-body wave functions of 1D random quantum circuits with local measurements employing the participation entropies. The leading term in system size dependence of participation entropies indicates a multifractal scaling of the wave-functions at any non-zero measurement rate. The sub-leading term contains universal information about measurement--induced phase transitions and plays the role of an order parameter, being non-zero in the error-correcting phase and vanishing in the quantum Zeno phase. We provide an analytical interpretation of this behavior expressing the participation entropy in terms of partition functions of classical statistical models in 2D.
Machine learning has emerged as a promising approach to study the properties of many-body systems. Recently proposed as a tool to classify phases of matter, the approach relies on classical simulation methods$-$such as Monte Carlo$-$which are known to experience an exponential slowdown when simulating certain quantum systems. To overcome this slowdown while still leveraging machine learning, we propose a variational quantum algorithm which merges quantum simulation and quantum machine learning to classify phases of matter. Our classifier is directly fed labeled states recovered by the variational quantum eigensolver algorithm, thereby avoiding the data reading slowdown experienced in many applications of quantum enhanced machine learning. We propose families of variational ansatz states that are inspired directly by tensor networks. This allows us to use tools from tensor network theory to explain properties of the phase diagrams the presented method recovers. Finally, we propose a nearest-neighbour (checkerboard) quantum neural network. This majority vote quantum classifier is successfully trained to recognize phases of matter with $99%$ accuracy for the transverse field Ising model and $94%$ accuracy for the XXZ model. These findings suggest that our merger between quantum simulation and quantum enhanced machine learning offers a fertile ground to develop computational insights into quantum systems.
We demonstrate that a machine learning technique with a simple feedforward neural network can sensitively detect two successive phase transitions associated with the Berezinskii-Kosterlitz-Thouless (BKT) phase in q-state clock models simultaneously by analyzing the weight matrix components connecting the hidden and output layers. We find that the method requires only a data set of the raw spatial spin configurations for the learning procedure. This data set is generated by Monte-Carlo thermalizations at selected temperatures. Neither prior knowledge of, for example, the transition temperatures, number of phases, and order parameters nor processed data sets of, for example, the vortex configurations, histograms of spin orientations, and correlation functions produced from the original spin-configuration data are needed, in contrast with most of previously proposed machine learning methods based on supervised learning. Our neural network evaluates the transition temperatures as T_2/J=0.921 and T_1/J=0.410 for the paramagnetic-to-BKT transition and BKT-to-ferromagnetic transition in the eight-state clock model on a square lattice. Both critical temperatures agree well with those evaluated in the previous numerical studies.
A quantum many-body system whose dynamics includes local measurements at a nonzero rate can be in distinct dynamical phases, with differing entanglement properties. We introduce theoretical approaches to measurement-induced phase transitions (MPT) and also to entanglement transitions in random tensor networks. Many of our results are for all-to-all quantum circuits with unitaries and measurements, in which any qubit can couple to any other, and related settings where some of the complications of low-dimensional models are reduced. We also propose field theory descriptions for spatially local systems of any finite dimensionality. To build intuition, we first solve the simplest minimal cut toy model for entanglement dynamics in all-to-all circuits, finding scaling forms and exponents within this approximation. We then show that certain all-to-all measurement circuits allow exact results by exploiting local tree-like structure in the circuit geometry. For this reason, we make a detour to give general universal results for entanglement phase transitions random tree tensor networks, making a connection with classical directed polymers on a tree. We then compare these results with numerics in all-to-all circuits, both for the MPT and for the simpler Forced Measurement Phase Transition (FMPT). We characterize the two different phases in all-to-all circuits using observables sensitive to the amount of information propagated between initial and final time. We demonstrate signatures of the two phases that can be understood from simple models. Finally we propose Landau-Ginsburg-Wilson-like field theories for the MPT, the FMPT, and entanglement transitions in random tensor networks. This analysis shows a surprising difference between the MPT and the other cases. We discuss measurement dynamics with additional structure (e.g. free-fermion structure), and questions for the future.
URh_2Ge_2 occupies an extraordinary position among the heavy-electron 122-compounds, by exhibiting a previously unidentified form of magnetic correlations at low temperatures, instead of the usual antiferromagnetism. Here we present new results of ac and dc susceptibilities, specific heat and neutron diffraction on single-crystalline as-grown URh_2Ge_2. These data clearly indicate that crystallographic disorder on a local scale produces spin glass behavior in the sample. We therefore conclude that URh_2Ge_2 is a 3D Ising-like, random-bond, heavy-fermion spin glass.
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