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Tensor network states and parton wave functions are two pivotal methods for studying quantum many-body systems. This work connects these two subjects as we demonstrate that a variety of parton wave functions, such as projected Fermi sea and…
In this study we employ a feed-forward artificial neural network (FFNN) architecture to perform tomography of quantum states and processes obtained from noisy experimental data. To evaluate the performance of the FFNN, we use a heavily…
The study of many-body quantum systems out of equilibrium remains a significant challenge with complexity barriers arising in both state and operator-based representations. In this work, we review recent approaches based on finding better…
Changes in the entanglement structure and critical phenomena are hallmarks of quantum phase transitions. Here, we discuss how they appear in transitions between classes of states with distinct entanglement patterns beyond the paradigm of…
We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based…
A novel algorithm based on the optimized decimation of tensor networks with super-orthogonalization (ODTNS) that can be applied to simulate efficiently and accurately not only the thermodynamic but also the ground state properties of…
We study the statistical behaviour of quantum entanglement in bipartite systems over fermionic Gaussian states as measured by von Neumann entropy. The formulas of average von Neumann entropy with and without particle number constrains have…
Numerically simulating spinful, fermionic systems is of great interest from the perspective of condensed matter physics. However, the exponential growth of the Hilbert space dimension with system size renders an exact parameterization of…
As large-scale multimode Gaussian states begin to become accessible in the laboratory, their representation and analysis become a useful topic of research in their own right. The graphical calculus for Gaussian pure states provides powerful…
A quantum simulator is a well controlled quantum system that can simulate the behavior of another quantum system which may require exponentially large classical computing resources to understand otherwise. In the 1980s, Feynman proposed the…
Tensor network states, and in particular Projected Entangled Pair States (PEPS) have been a strong ansatz for the variational study of complicated quantum many-body systems, thanks to their built-in entanglement entropy area law. In this…
A new numerical approach to entanglement entropies of the Renyi type is proposed for one-dimensional quantum field theories. The method extends the truncated conformal spectrum approach and we will demonstrate that it is especially suited…
We present a tree-tensor-network-based method to study strongly correlated systems with nonlocal interactions in higher dimensions. Although the momentum-space and quantum-chemistry versions of the density matrix renormalization group…
Along the way initiated by Carleo and Troyer [1], we construct the neural-network quantum state of transverse-field Ising model(TFIM) by an unsupervised machine learning method. Such a wave function is a map from the spin-configuration…
Tensor networks were developed in the context of many-body physics as compressed representations of multiparticle quantum states. These representations mitigate the exponential complexity of many-body systems by capturing only the most…
The real- and imaginary-time evolution of quantum states are powerful tools in physics, chemistry, and beyond, to investigate quantum dynamics, prepare ground states or calculate thermodynamic observables. On near-term devices, variational…
Ultra-cold atoms in optical lattices provide one of the most promising platforms for analog quantum simulations of complex quantum many-body systems. Large-size systems can now routinely be reached and are already used to probe a large…
It is well established that neural networks with deep architectures perform better than shallow networks for many tasks in machine learning. In statistical physics, while there has been recent interest in representing physical data with…
We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not…
Despite the omnipresence of tensors and tensor operations in modern deep learning, the use of tensor mathematics to formally design and describe neural networks is still under-explored within the deep learning community. To this end, we…