Related papers: Computational Complexity in Electronic Structure
There has been no lack of coverage in the past few years in scientific journals of the topic of quantum computation. Rightly so, as this is a novel idea with--so far--at least one very important practical application (prime factorisation)…
Computer simulation plays a central role in modern day materials science. The utility of a given computational approach depends largely on the balance it provides between accuracy and computational cost. Molecular crystals are a class of…
Complexity theory offers a variety of concise computational models for computing boolean functions - branching programs, circuits, decision trees and ordered binary decision diagrams to name a few. A natural question that arises in this…
Quantum circuit complexity is a fundamental concept whose importance permeates quantum information, computation, many-body physics and high-energy physics. While extensively studied in closed systems, its characterization and behaviors in…
We employ holography to calculate the quantum complexity of $T\bar{T}$-deformation, utilizing the complexity equals volume (CV) and the complexity equals action (CA) proposals within the bulk spacetime with a finite radius cutoff. We find…
We analyse dissipation in quantum computation and its destructive impact on efficiency of quantum algorithms. Using a general model of decoherence, we study the time evolution of a quantum register of arbitrary length coupled with an…
In this introductory review, we focus on applications of quantum computation to problems of interest in physics and chemistry. We describe quantum simulation algorithms that have been developed for electronic-structure problems,…
Silicon quantum computing has the potential to revolutionize technology with capabilities to solve real-life problems that are computationally complex or even intractable for modern computers [1] by offering sufficient high quality qubits…
Molecular biology and biochemistry interpret microscopic processes in the living world in terms of molecular structures and their interactions, which are quantum mechanical by their very nature. Whereas the theoretical foundations of these…
The previously proposed Heisenberg-type relation $ E_c t_c >> \hbar {\cal C}$ for the energy used by a quantum computer, the total computation time and the logical ("classical") complexity of the problem is verified for the following…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
Here we address the challenge of profiling causal properties and tracking the transformation of chemical compounds from an algorithmic perspective. We explore the potential of applying a computational interventional calculus based on the…
The emergence of a complex, large-scale organisation of cosmic matter into the Cosmic Web is a beautiful exemplification of how complexity can be produced by simple initial conditions and simple physical laws. In the epoch of Big Data in…
All natural things process and transform information. They receive environmental information as input, and transform it into appropriate output responses. Much of science is dedicated to building models of such systems -- algorithmic…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
Molecular science is governed by the dynamics of electrons, atomic nuclei, and their interaction with electromagnetic fields. A reliable physicochemical understanding of these processes is crucial for the design and synthesis of chemicals…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
High-throughput approximations of quantum mechanics calculations and combinatorial experiments have been traditionally used to reduce the search space of possible molecules, drugs and materials. However, the interplay of structural and…
In this note, we provide a unifying framework to investigate the computational complexity of classical spin models and give the full classification on spin models in terms of system dimensions, randomness, external magnetic fields and types…
Over the past decades, atomistic simulations of chemical, biological and materials systems have become increasingly precise and predictive thanks to the development of accurate and efficient techniques that describe the quantum mechanical…