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Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…
Quantum entanglement of identical particles is essential in quantum information theory. Yet, its correct determination remains an open issue hindering the general understanding and exploitation of many-particle systems. Operator-based…
Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a \emph{quantitative} relation…
In this research notebook in the four-part, quantum computation and applications, quantum computation and algorithms, quantum communication protocol, and universal quantum computation for quantum engineers, researchers, and scientists, we…
We will show for undergraduate and graduate students of physics that Quantum Mechanics is an incomplete and non-local theory. The problem of non-locality is discussed by analyzing the Bell's theorem where are considered correlations between…
Measurements on a single quantum system at different times reveal rich non-classical correlations similar to those observed in spatially separated multi-partite systems. Here we introduce a theory framework that unifies the description of…
Is entanglement an exclusive feature of quantum systems, or is it common to all non-classical theories? And if this is the case, how strong is quantum mechanical entanglement as compared to that exhibited by other theories? The first part…
Solving systems of linear equations is a fundamental problem, but it can be computationally intensive for classical algorithms in high dimensions. Existing quantum algorithms can achieve exponential speedups for the quantum linear system…
Although a universal quantum computer is still far from reach, the tremendous advances in controllable quantum devices, in particular with solid-state systems, make it possible to physically implement "quantum simulators". Quantum…
Entanglement of quasiclassical (coherent) states of two harmonic oscillators leads to striking quantum effects and is useful for quantum technologies. These effects and applications are closely related to nonlocal correlations inherent in…
To identify which principles characterize quantum correlations, it is essential to understand in which sense this set of correlations differs from that of almost quantum correlations. We solve this problem by invoking the so-called…
The impossibility of creating perfect identical copies of unknown quantum systems is a fundamental concept in quantum theory and one of the main non-classical properties of quantum information. This limitation imposed by quantum mechanics,…
A quantum constraint problem is a frustration-free Hamiltonian problem: given a collection of local operators, is there a state that is in the ground state of each operator simultaneously? It has previously been shown that these problems…
Pedagogical introduction into the problem of the mathematical description of the quantum correlation (entanglement) of composite quantum systems is represented. The notion is substantiated about the fact that the conventional algorithm of…
This dissertation investigates questions arising in the consistent histories formulation of the quantum mechanics of closed systems. Various criteria for approximate consistency are analysed. The connection between the Dowker-Halliwell…
This thesis examines seven topics in the areas of deterministic open-quantum-system dynamics, quantum measurements, and quantum error correction (QEC). The first topic concerns weak measurements and their universality as a means of…
Quantum simulation is a potentially powerful application of quantum computing, holding the promise to be able to emulate interesting quantum systems beyond the reach of classical computing methods. Despite such promising applications, and…
Quantum computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
In order to qualify quantum algorithms for industrial NP-Hard problems, comparing them to available polynomial approximate classical algorithms and not only to exact ones -- exponential by nature -- , is necessary. This is a great challenge…