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We discuss quantum state tomography via a stepwise reconstruction of the eigenstates of the mixed states produced in experiments. Our method is tailored to the experimentally relevant class of nearly pure states or simple mixed states,…

The Non-Markovian Stochastic Schrodinger Equation (NMSSE) offers a promising approach for open quantum simulations, especially in large systems, owing to its low scaling complexity and suitability for parallel computing. However, its…

Quantum computing offers a scalable approach to solving the nuclear shell model, a highly complex and exponentially scaled many-body problem. This work presents a numerical simulation of the subspace search variational quantum eigensolver…

Quantum state tomography (QST) is plagued by the ``curse of dimensionality'' due to the exponentially-scaled complexity in measurement and data post-processing. Efficient QST schemes for large-scale mixed states are currently missing. In…

In this work, we investigate stochastic quasi-Newton methods for minimizing a finite sum of cost functions over a decentralized network. In Part I, we develop a general algorithmic framework that incorporates stochastic quasi-Newton…

Neural-network quantum states (NQS) has emerged as a powerful application of quantum-inspired deep learning for variational Monte Carlo methods, offering a competitive alternative to existing techniques for identifying ground states of…

Neural networks are a promising tool for simulating quantum many body systems. Recently, it has been shown that neural network-based models describe quantum many body systems more accurately when they are constrained to have the correct…

Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-$N$ tensor from exponential…

We initiate the study of online quantum state tomography (QST), where the matrix representation of an unknown quantum state is reconstructed by sequentially performing a batch of measurements and updating the state estimate using only the…

Quantum state tomography (QST) via local measurements on reduced density matrices (LQST) is a promising approach but becomes impractical for large systems. To tackle this challenge, we developed an efficient quantum state tomography method…

We consider sequential state and parameter learning in state-space models with intractable state transition and observation processes. By exploiting low-rank tensor train (TT) decompositions, we propose new sequential learning methods for…

Neural quantum states (NQS) have emerged as powerful tools for simulating many-body quantum systems, but their practical use is often hindered by limitations of current sampling techniques. Markov chain Monte Carlo (MCMC) methods suffer…

Nonlinearities are crucial for capturing complex input-output relationships especially in deep neural networks. However, nonlinear functions often incur various hardware and compute overheads. Meanwhile, stochastic computing (SC) has…

This paper focuses on recovering a low-rank tensor from its incomplete measurements. We propose a novel algorithm termed the Single Mode Quasi Riemannian Gradient Descent (SM-QRGD). By exploiting the benefits of both fixed-rank matrix…

Simulating the dynamics of many-body quantum systems is a significant challenge, especially in higher dimensions where entanglement grows rapidly. Neural quantum states (NQS) offer a promising tool for representing quantum wavefunctions,…

Recent research has demonstrated the usefulness of neural networks as variational ansatz functions for quantum many-body states. However, high-dimensional sampling spaces and transient autocorrelations confront these approaches with a…

Variational approaches, such as variational Monte Carlo (VMC) or the variational quantum eigensolver (VQE), are powerful techniques to tackle the ground-state many-electron problem. Often, the family of variational states is not invariant…

We propose a general strategy to develop quantum many-body approximations of primitives in linear algebra algorithms. As a practical example, we introduce a coupled-cluster inspired framework to produce approximate Hamiltonian moments, and…

Computations on a manifold often involve constructing an operator on the tangent space and computing its inverse, which can be time-consuming in many applications. In order to reduce the computational costs and preserve the benign…

In the classical Steiner tree problem, given an undirected, connected graph $G=(V,E)$ with non-negative edge costs and a set of \emph{terminals} $T\subseteq V$, the objective is to find a minimum-cost tree $E' \subseteq E$ that spans the…