相关论文: The Variational Power of Quantum Circuit Tensor Ne…
We characterize the expressive power of quantum circuits with the pseudo-dimension, a measure of complexity for probabilistic concept classes. We prove pseudo-dimension bounds on the output probability distributions of quantum circuits; the…
The noisy intermediate-scale quantum (NISQ) devices enable the implementation of the variational quantum circuit (VQC) for quantum neural networks (QNN). Although the VQC-based QNN has succeeded in many machine learning tasks, the…
Renormalization group ideas and effective operators are used to efficiently determine localized unitaries for preparing the ground states of non-interacting scalar field theories on digital quantum devices. With these methods, classically…
In this work, we propose novel families of positional encodings tailored to graph neural networks obtained with quantum computers. These encodings leverage the long-range correlations inherent in quantum systems that arise from mapping the…
In this paper, we develop a Lie group theoretic approach for parametric representation of unitary matrices. This leads to develop a quantum neural network framework for quantum circuit approximation of multi-qubit unitary gates. Layers of…
Designing superconducting quantum hardware requires simulation tools that can account for various deviations from ideal scenarios. This, in turn, requires approaches that automatically detect certain structures and leverage them to make the…
We give an algorithm that converts any tensor network (TN) into a sequence of local unitaries whose composition block-encodes the network contraction, suitable for Quantum Eigenvalue / Singular Value Transformation (QET/QSVT). The…
Modern deep learning has enabled unprecedented achievements in various domains. Nonetheless, employment of machine learning for wave function representations is focused on more traditional architectures such as restricted Boltzmann machines…
The challenge of quantum many-body problems comes from the difficulty to represent large-scale quantum states, which in general requires an exponentially large number of parameters. Recently, a connection has been made between quantum…
In many cases, Neural networks can be mapped into tensor networks with an exponentially large bond dimension. Here, we compare different sub-classes of neural network states, with their mapped tensor network counterpart for studying the…
In this paper, we extend past work done on the application of the mathematics of category theory to quantum information science. Specifically, we present a realization of a dagger-compact category that can model finite-dimensional quantum…
As in the density matrix renormalization group (DMRG) method, approximating many-body wave function of electrons using a matrix product state (MPS) is a promising way to solve electronic structure problems. The expressibility of an MPS is…
Despite the huge theoretical potential of neural quantum states, their use in describing generic, highly-correlated quantum many-body systems still often poses practical difficulties. Customized network architectures are under active…
Although tensor networks are powerful tools for simulating low-dimensional quantum physics, tensor network algorithms are very computationally costly in higher spatial dimensions. We introduce quantum gauge networks: a different kind of…
Neural quantum states (NQS) have gained prominence in variational quantum Monte Carlo methods in approximating ground-state wavefunctions. Despite their success, they face limitations in optimization, scalability, and expressivity in…
Tensor networks are a powerful tool for many-body ground states with limited entanglement. These methods can nonetheless fail for certain time-dependent processes - such as quantum transport or quenches - where entanglement growth is linear…
The rapid pace of recent advancements in numerical computation, notably the rise of GPU and TPU hardware accelerators, have allowed tensor network (TN) algorithms to scale to even larger quantum simulation problems, and to be employed more…
Transport through correlated nanoscale systems underpins the operation of quantum-dot and molecular-scale devices, yet accurate simulations of large open quantum systems remain computationally challenging as system size increases.…
Across all scales of the physical world, dynamical systems can often be usefully represented as abstract networks that encode the system's units and inter-unit interactions. Understanding how physical rules shape the topological structure…
In the rapidly evolving field of quantum computing, tensor networks serve as an important tool due to their multifaceted utility. In this paper, we review the diverse applications of tensor networks and show that they are an important…