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We show that combining randomized measurement protocols with importance sampling allows for characterizing entanglement in significantly larger quantum systems and in a more efficient way than in previous work. A drastic reduction of…
Tensor network algorithms seek to minimize correlations to compress the classical data representing quantum states. Tensor network algorithms and similar tools---called tensor network methods---form the backbone of modern numerical methods…
The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This…
In some cases the state of a quantum system with a large number of subsystems can be approximated efficiently by the density matrix renormalization group, which makes use of redundancies in the description of the state. Here we show that…
The resources needed to conventionally characterize a quantum system are overwhelmingly large for high- dimensional systems. This obstacle may be overcome by abandoning traditional cornerstones of quantum measurement, such as general…
In quantum many-body systems, measurements can induce qualitative new features, but their simulation is hindered by the exponential complexity involved in sampling the measurement results. We propose to use machine learning to assist the…
We develop a density matrix renormalization group (DMRG) algorithm for constrained quantum lattice models that successfully {\it{implements the local constraints as symmetries in the contraction of the matrix product states and matrix…
The density matrix renormalization group (DMRG) algorithm is a cornerstone computational method for studying quantum many-body systems, renowned for its accuracy and adaptability. Despite DMRG's broad applicability across fields such as…
Suppose you receive a sequence of qubits where each qubit is guaranteed to be in one of two pure states, but you do not know what those states are. Your task is to determine the states. This can be viewed as a kind of quantum state learning…
Quantum computing's promise lies in its intrinsic complexity, with entanglement initially heralded as its hallmark. However, the quest for quantum advantage extends beyond entanglement, encompassing the realm of nonstabilizer (magic)…
Entangled multipartite states are resources for universal quantum computation, but they can also give rise to ensembles of unitary transformations, a topic usually studied in the context of random quantum circuits. Using several graph state…
Entanglement is a fundamental feature of quantum mechanics, playing a crucial role in quantum information processing. However, classifying entangled states, particularly in the mixed-state regime, remains a challenging problem, especially…
We introduce a class of states, called minimally entangled typical thermal states (METTS), designed to resemble a typical state of a quantum system at finite temperature with a bias towards classical (minimally entangled) properties. These…
Characterizing correlations in a quantum system on the basis of the results of the projective measurements can be performed with different means including the calculation of the classical mutual information. Generally, estimating such…
Learning probability distribution is an essential framework in classical learning theory. As a counterpart, quantum state learning has spurred the exploration of quantum machine learning theory. However, as dimensionality increases,…
We introduce a new approach for quantum linear algebra based on quantum subspace states and present three new quantum machine learning algorithms. The first is a quantum determinant sampling algorithm that samples from the distribution…
In quantum mechanics, wave functions and density matrices represent our knowledge about a quantum system and give probabilities for the outcomes of measurements. If the combined dynamics and measurements on a system lead to a density matrix…
This paper introduces the quantum deep sets model, expanding the quantum machine learning tool-box by enabling the possibility of learning variadic functions using quantum systems. A couple of variants are presented for this model. The…
We introduce a picture to analyze the density matrix renormalization group (DMRG) numerical method from a quantum information perspective. This leads us to introduce some modifications for problems with periodic boundary conditions in which…
Quantum circuits for loading probability distributions into quantum states are essential subroutines in quantum algorithms used in physics, finance engineering, and machine learning. The ability to implement these with high accuracy in…