Related papers: Quantum Query Algorithm Constructions for Computin…
Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. However, due to the noise and the limited scale of current quantum…
Quantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum…
We introduce hybrid classical-quantum algorithms for problems involving a large classical data set X and a space of models Y such that a quantum computer has superposition access to Y but not X. These algorithms use data reduction…
The main ideas of quantum error correction are introduced. These are encoding, extraction of syndromes, error operators, and code construction. It is shown that general noise and relaxation of a set of 2-state quantum systems can always be…
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…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…
Quantum computation and quantum information are of great current interest in computer science, mathematics, physical sciences and engineering. They will likely lead to a new wave of technological innovations in communication, computation…
We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem…
We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem…
Quantum computing holds the potential to revolutionize various fields by efficiently tackling complex problems. At its core are quantum circuits, sequences of quantum gates manipulating quantum states. The selection of the right quantum…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
We present novel algorithms for design and design space exploration. The designs discovered by these algorithms are compositions of function types specified in component libraries. Our algorithms reduce the design problem to quantified…
Functions are a fundamental object in mathematics, with countless applications to different fields, and are usually classified based on certain properties, given their domains and images. An important property of a real-valued function is…
Quantum computers exhibit an inherent randomness, so it seems natural to consider them for procedural content generation. In this work, a quantum version of the famous (classical) wave function collapse algorithm is proposed. This quantum…
In mathematical aspect, we introduce quantum algorithm and the mathematical structure of quantum computer. Quantum algorithm is expressed by linear algebra on a finite dimensional complex inner product space. The mathematical formulations…
Quantum computation has received great attention in recent years for its possible application to difficult problem in classical calculation. Despite the experimental problems of implementing quantum devices, theoretical physicists have…
Quantum computing is a promising approach of computation that is based on equations from Quantum Mechanics. A simulator for quantum algorithms must be capable of performing heavy mathematical matrix transforms. The design of the simulator…
It is usually assumed that a quantum computation is performed by applying gates in a specific order. One can relax this assumption by allowing a control quantum system to switch the order in which the gates are applied. This provides a more…
Quantum computation is based on implementing selected unitary transformations which represent algorithms. A generalized optimal control theory is used to find the driving field that generates a prespecified unitary transformation. The…
We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…