Related papers: Quantum Tensor Product Decomposition from Choi Sta…
Quantum state tomography (QST) is a fundamental technique for estimating the state of a quantum system from measured data and plays a crucial role in evaluating the performance of quantum devices. However, standard estimation methods become…
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…
Quantifying entanglement is an important task by which the resourcefulness of a quantum state can be measured. Here, we develop a quantum algorithm that tests for and quantifies the separability of a general bipartite state by using the…
In quantum information theory, the Schmidt rank is a fundamental measure for the entanglement dimension of a pure bipartite state. Its natural definition uses the Schmidt decomposition of vectors on bipartite Hilbert spaces, which does not…
It is well known that the Schmidt decomposition exists for all pure states of a two-party quantum system. We demonstrate that there are two ways to obtain an analogous decomposition for arbitrary rank-1 operators acting on states of a…
The thesis includes the original results of our articles [30, 37, 40, 42, 51, 53, 75]. A method is developed to compute analytically entanglement measures of three-qubit pure states. Owing to it closed-form expressions are presented for the…
We use Deutsch's algorithm as a stand in for more complex quantum algorithms in order to determine how quantum properties of an environment manifest themselves in results that can be obtained on quantum computers. We model pure dephasing in…
We study the quantum entanglement caused by unitary operators that have classical limits that can range from the near integrable to the completely chaotic. Entanglement in the eigenstates and time-evolving arbitrary states is studied…
Entanglement between three or more parties exhibits a realm of properties unknown to two-party states. Bipartite states are easily classified using the Schmidt decomposition. The Schmidt coefficients of a bipartite pure state encompass all…
Characterizing entanglement is central for quantum information science. Special observables which indicate entanglement, so-called entanglement witnesses, are a widely used tool for this task. The construction of these witnesses typically…
Quantum state preparation is a fundamental component of quantum algorithms, particularly in quantum machine learning and data processing, where classical data must be encoded efficiently into quantum states. Existing amplitude encoding…
We introduce with geometric means a density matrix decomposition of a multipartite quantum system of a finite dimension into two density matrices: a separable one, also known as the best separable approximation, and an essentially entangled…
Efficient verification of multipartite quantum states is crucial to many applications in quantum information processing. By virtue of Schmidt decomposition and mutually unbiased bases, here we propose a universal protocol to verify…
With the aim of establishing a framework to efficiently perform the practical application of quantum chemistry simulation on near-term quantum devices, we envision a hybrid quantum--classical framework for leveraging problem decomposition…
Entangled quantum states can be given a separable decomposition if we relax the restriction that the local operators be quantum states. Motivated by the construction of classical simulations and local hidden variable models, we construct…
Production and verification of multipartite quantum state are an essential step in quantum information processing. In this work, we propose an efficient method to decompose symmetric multipartite observables, which are invariant under…
Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is…
Efficient sampling from ensembles of Hamiltonian cycles is critical for predicting the thermodynamic properties of compact polymers, with applications including modeling protein and RNA folding and designing soft materials. Although…
Entanglement is the key resource for quantum technologies and is at the root of exciting many-body phenomena. However, quantifying the entanglement between two parts of a real-world quantum system is challenging when it interacts with its…
This article proposes an efficient way of calculating the geometric measure of entanglement using tensor decomposition methods. The connection between these two concepts is explored using the tensor representation of the wavefunction.…