Discrete cosine transforms on quantum computers

Combining physics, mathematics and computer science, quantum computing has developed in the past two decades from a visionary idea to one of the most fascinating areas of quantum mechanics [4]. If the bits of computer are scaled down to the size of individual atom, then it can change the nature of computation itself. In that case the function of such a quantum computer may consist of a superposition of many computations carried out simultaneously. This can solve many computational problem such as factoring of large integers , tractable. This research paper gives an overview of quantum computer, description of qubit, difference between quantum and silicon computer.

International Journal of Computers and Applications, 2006

Quantum computing is an emerging technology. The clock frequency of current computer processor systems may reach about 40 GHz within the next 10 years. By then, one atom may represent one bit. Electrons under such conditions are no longer described by classical physics, and a new model of the computer may be necessary by that time. The quantum computer is one proposal that may have merit in dealing with the problems presented. Currently, there exist some algorithms utilizing the advantage of quantum computers. For example, Shor's algorithm performs factoring of a large integer in polynomial time, whereas classical factoring algorithms can do it in exponential time. In this paper we briefly survey the current status of quantum computers, quantum computer systems, and quantum simulators.

The main advantages of quantum computing are exponential computing power it provides. This exponential computing is derived from the supposition of the states, and possibility to use entanglement of particles to communicate over large distances. This paper shall attempt to identify what constitute quantum computer, its benefits, obstacle and research and in conclusion, I shall address the future direction of quantum computation.

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1998

We discuss the fundamental role of entanglement as the essential nonclassical feature providing the computational speedup in the known quantum algorithms. We review the construction of the Fourier transform on an Abelian group and the principles underlying the fast Fourier transform algorithm. We describe the implementation of the FFT algorithm for the group of integers modulo 2 n in the quantum context, showing how the group-theoretic formalism leads to the standard quantum network and identifying the property of entanglement that gives rise to the exponential speedup (compared to the classical FFT). Finally we outline the use of the Fourier transform in extracting periodicities, which underlies its utility in the known quantum algorithms.

2000

The paper is intended to be a survey of all the important aspects and results that have shaped the field of quantum computation and quantum information. The reader is first familiarized with those features and principles of quantum mechanics providing a more efficient and secure information processing. Their applications to the general theory of information, cryptography, algorithms, computational complexity and error-correction are then discussed. Prospects for building a practical quantum computer are also analyzed.

Conference on Science and Technology Development (CSTD), 2019

Quantum computing is the new field of science which uses quantum phenomena to perform operations on data at the intersection of mathematics, computer science and physics. This paper is to guide computer scientists through the barriers that separate quantum computing from conventional computing. We introduce basic principles of quantum mechanics to explain where the power of quantum computers comes from and why it is difficult to harness. We describe the differences between classical and quantum computers, bit and quantum bit and quantum operation.

A brief introduction on Quantum Compter.

Journal of Mathematical Analysis and Applications, 2002

The quantum Fourier transform (QFT) is a powerful tool in quantum computing. The main ingredients of QFT are formed by the Walsh-Hadamard transform H and phase shifts P (•), both of which are 2 × 2 unitary matrices as operators on the two-dimensional 1-qubit space. In this paper, we show that H and P (•) suffice to generate the unitary group U(2) and, consequently, through controlled-U operations and their concatenations, the entire unitary group U(2 n) on n-qubits can be generated. Since any quantum computing algorithm in an n-qubit quantum computer is based on operations by matrices in U(2 n), in this sense we have the universality of the QFT.

Today's computers work on bits that exist as either 0 or 1. Quantum computers aren't limited to two states; they encode information as quantum bits, or qubits, which can exist in superposition. Qubits represent atoms, ions, photons or electrons and their respective control devices that are working together to act as computer memory and a processor. Because a quantum computer can contain these multiple states simultaneously, it has the potential to be millions of times more powerful than today's most powerful supercomputers. A processor that can use registers of qubits will be able to perform calculations using all the possible values of the input registers simultaneously. This superposition causes a phenomenon called quantum parallelism, and is the motivating force behind the research being carried out in quantum computing. www.giapjournals.com/ijsrtm/ 628 computer could efficiently solve this problem using Shor's algorithm to find its factors. This ability would allow a quantum computer to decrypt many of the cryptographic systems in use today. In particular, most of the popular public key ciphers are based on the difficulty of factoring integers. These are used to protect secure Web pages, encrypted email, and many other types of data. Breaking these would have significant ramifications for electronic privacy and security. An example of this is a password cracker that attempts to guess the password for an encrypted file (assuming that the password has a maximum possible length).