Related papers: QMA-complete problems
Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…
I assess the potential of quantum computation. Broad and important applications must be found to justify construction of a quantum computer; I review some of the known quantum algorithms and consider the prospects for finding new ones.…
The rapid development of quantum computer hardware has laid the hardware foundation for the realization of QNN. Due to quantum properties, QNN shows higher storage capacity and computational efficiency compared to its classical…
Quantum computers are expected to surpass the computational capabilities of classical computers and have a transformative impact on numerous industry sectors. We present a comprehensive summary of the state of the art of quantum computing…
We show that the lambda-q calculus can efficiently simulate quantum Turing machines by showing how the lambda-q calculus can efficiently simulate a class of quantum cellular automaton that are equivalent to quantum Turing machines. We…
For decades, computational chemistry has been posited as one of the areas in which quantum computing would revolutionize. However, the algorithmic advantages that fault-tolerant quantum computers have for chemistry can be overwhelmed by…
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…
An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke here analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is…
Although quantum circuits have been ubiquitous for decades in quantum computing, the first complete equational theory for quantum circuits has only recently been introduced. Completeness guarantees that any true equation on quantum circuits…
In this work, we are interested in the detailed analysis of complexity aspects of both time and space that arises from the implementation of a quantum algorithm on a quantum based hardware. In particular, some steps of the implementation,…
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…
Previously, all known variants of the Quantum Satisfiability (QSAT) problem, i.e. deciding whether a $k$-local ($k$-body) Hamiltonian is frustration-free, could be classified as being either in $\mathsf{P}$; or complete for $\mathsf{NP}$,…
This thesis studies three topics in quantum computation and information: The approximability of quantum problems, quantum proof systems, and non-classical correlations in quantum systems. In the first area, we demonstrate a polynomial-time…
Quantum computing is the process of performing calculations using quantum mechanics. This field studies the quantum behavior of certain subatomic particles for subsequent use in performing calculations, as well as for large-scale…
The number of qubits used by a quantum algorithm will be a crucial computational resource for the foreseeable future. We show how to obtain the classical query complexity for continuous problems. We then establish a simple formula for a…
This paper presents stronger methods of achieving perfect completeness in quantum interactive proofs. First, it is proved that any problem in QMA has a two-message quantum interactive proof system of perfect completeness with constant…
Quantum algorithms are demonstrated to outperform classical algorithms for certain problems and thus are promising candidates for efficient information processing. Herein we aim to provide a brief and popular introduction to quantum…
Fuelled by increasing computer power and algorithmic advances, machine learning techniques have become powerful tools for finding patterns in data. Since quantum systems produce counter-intuitive patterns believed not to be efficiently…
The question of whether or not quantum computers can efficiently solve NP-complete problems is open, although indications are that BQP does not contain NP. Still, many of these problems are natural candidates for solution on quantum…
The purpose of this paper is to explore the applications of quantum computing to energy systems optimization problems and discuss some of the challenges faced by quantum computers with techniques to overcome them. The basic concepts…