Related papers: An Introduction to Quantum Computing for Non-Physi…
A flagship application of quantum computers is the simulation of other quantum systems, including quantum field theories. In this article, we show how quantum computers can be employed to naturally calculate Feynman diagrams and their…
A quantum computer based on an asymmetric coupled dot system has been proposed and shown to operate as the controlled-NOT-gate. The basic idea is (1) the electron is localized in one of the asymmetric coupled dots. (2)The electron transfer…
Contribution: In this study, an alternative educational approach for introducing quantum computing to a wider audience is highlighted. The proposed methodology considers quantum computing as a generalized probability theory rather than a…
Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we're dealing with a numerical approximation to the solution. There are two…
The security of messages encoded via the widely used RSA public key encryption system rests on the enormous computational effort required to find the prime factors of a large number N using classical (i.e., conventional) computers. In 1994,…
This article introduces quantum computation by analogy with probabilistic computation. A basic description of the quantum search algorithm is given by representing the algorithm as a C program in a novel way.
The number of steps any classical computer requires in order to find the prime factors of an $l$-digit integer $N$ increases exponentially with $l$, at least using algorithms known at present. Factoring large integers is therefore…
With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical…
These notes begin in Chapter 1 with a review of linear algebra and the postulates of quantum mechanics, leading to an explanation of single- and multi-qubit gates. Chapter 2 explores the challenge of constructing arbitrary quantum states…
Quantum computers provide a fundamentally new computing paradigm that promises to revolutionize our ability to solve broad classes of problems. Surprisingly, the basic mathematical structures of gate-based quantum computing, such as unitary…
An efficient quantum algorithm is proposed to solve in polynomial time the parity problem, one of the hardest problems both in conventional quantum computation and in classical computation, on NMR quantum computers. It is based on the…
Quantum computing's potential is immense, promising super-polynomial reductions in execution time, energy use, and memory requirements compared to classical computers. This technology has the power to revolutionize scientific applications…
Quantum computing is one of the most enticing computational paradigms with the potential to revolutionize diverse areas of future-generation computational systems. While quantum computing hardware has advanced rapidly, from tiny laboratory…
Quantum computers offer an intriguing path for a paradigmatic change of computing in the natural sciences and beyond, with the potential for achieving a so-called quantum advantage, namely a significant (in some cases exponential) speed-up…
The fundamental principles of quantum mechanics, such as its probabilistic nature, allow for the theoretical ability of quantum computers to generate statistically random numbers, as opposed to classical computers which are only able to…
Quantum computation is a rapidly progressing field today. What are its principles? In what sense is it distinct from conventional computation? What are its advantages and disadvantages? What type of problems can it address? How practical is…
The primordial model of quantum computation was introduced over thirty years ago and the first quantum algorithms have appeared for over twenty years. Yet the exact architectures for quantum computer seem foreign to an undergraduate student…
In the last couple of decades, the world has seen several stunning instances of quantum algorithms that provably outperform the best classical algorithms. For most problems, however, it is currently unknown whether quantum algorithms can…
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…
Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable…