Related papers: Optimization schemes for unitary tensor-network ci…
We introduce a hybrid model combining a quantum-inspired tensor network and a variational quantum circuit to perform supervised learning tasks. This architecture allows for the classical and quantum parts of the model to be trained…
Neural-network quantum states (NQSs), variationally optimized by combining traditional methods and deep learning techniques, is a new way to find quantum many-body ground states and gradually becomes a competitor of traditional variational…
Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…
Tensor network states form a variational ansatz class widely used, both analytically and numerically, in the study of quantum many-body systems. It is known that if the underlying graph contains a cycle, e.g. as in projected entangled pair…
In this paper, we extend the analysis of random Kronecker graphs to multi-dimensional networks represented as tensors, enabling a more detailed and nuanced understanding of complex network structures. We decompose the adjacency tensor of…
Squared tensor networks (TNs) and their generalization as parameterized computational graphs -- squared circuits -- have been recently used as expressive distribution estimators in high dimensions. However, the squaring operation introduces…
In this work, we study the tensor ring decomposition and its associated numerical algorithms. We establish a sharp transition of algorithmic difficulty of the optimization problem as the bond dimension increases: On one hand, we show the…
Classically simulating quantum circuits is crucial when developing or testing quantum algorithms. Due to the underlying exponential complexity, efficient data structures are key for performing such simulations. To this end, tensor networks…
We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an…
Several variational quantum circuit approaches to machine learning have been proposed in recent years, with one promising class of variational algorithms involving tensor networks operating on states resulting from local feature maps. In…
Variational quantum algorithms are practical approaches to prepare ground states, but their potential for quantum advantage remains unclear. Here, we use differentiable 2D tensor networks (TN) to optimize parameterized quantum circuits that…
Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models…
Recurrent neural networks (RNNs) are powerful tools for sequential modeling, but typically require significant overparameterization and regularization to achieve optimal performance. This leads to difficulties in the deployment of large…
We provide a graphical calculus for computing averages of tensor network diagrams with respect to the distribution of random vectors containing independent uniform complex phases. Our method exploits the order structure of the partially…
Hybrid Tensor Networks (hTN) offer a promising solution for encoding variational quantum states beyond the capabilities of efficient classical methods or noisy quantum computers alone. However, their practical usefulness and many…
Tensor network methods are powerful and efficient tools to study the properties and dynamics of statistical and quantum systems, in particular in one and two dimensions. In recent years, these methods were applied to lattice gauge theories,…
Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension…
The tensor-entanglement renormalization group approach is applied to Hamiltonians that realize a class of topologically ordered states -- string-net condensed states. We analyze phase transitions between phases with and without string-net…
In the tensor-network framework, the expectation values of two-dimensional quantum states are evaluated by contracting a double-layer tensor network constructed from initial and final tensor-network states. The computational cost of…
The power method (or iteration) is a well-known classical technique that can be used to find the dominant eigenpair of a matrix. Here, we present a variational quantum circuit method for the power iteration, which can be used to find the…