If a computer could be built from quantum elements, which can exist in superpositions of many states rather than the 1s and 0s of conventional binary logic, then important hard problems could be solved rapidly. One example is the prime number factorization problem at the heart of modern encryption: Given the product of two large primes, find the primes themselves. Another important problem is exhaustive search: Given an unstructured list of items, quickly find the one that satisfies a certain property. A pair of Research Commentaries in this issue discuss some important new results in which simple quantum computers have been constructed with liquids probed by nuclear magnetic resonance techniques. The first, by L. K. Grover of Bell Labs, describes the theoretical situation and the implementation of an algorithm that he designed for exhaustive search. The second, by
J. A. Jones
of Oxford University, UK, discusses the recent experimental approaches to quantum computing with nuclear magnetic resonance.
If a computer could be built from quantum elements, which can exist in superpositions of many states rather than the 1s and 0s of conventional binary logic, then important hard problems could be solved rapidly. One example is the prime number factorization problem at the heart of modern encryption: Given the product of two large primes, find the primes themselves. Another important problem is exhaustive search: Given an unstructured list of items, quickly find the one that satisfies a certain property. A pair of Research Commentaries in this issue discuss some important new results in which simple quantum computers have been constructed with liquids probed by nuclear magnetic resonance techniques. The first, by L. K. Grover of Bell Labs, describes the theoretical situation and the implementation of an algorithm that he designed for exhaustive search. The second, by
J. A. Jones
of Oxford University, UK, discusses the recent experimental approaches to quantum computing with nuclear magnetic resonance.
If a computer could be built from quantum elements, which can exist in superpositions of many states rather than the 1s and 0s of conventional binary logic, then important hard problems could be solved rapidly. One example is the prime number factorization problem at the heart of modern encryption: given the product of two large primes, find the primes themselves. Another important problem is exhaustive search: given an unstructured list of items, quickly find the one that satisfies a certain property. A pair of Research Commentaries in this issue discuss some important new results in which simple quantum computers have been constructed with liquids probed by nuclear magnetic resonance techniques. The first, by
L. K. Grover
of Bell Labs, describes the theoretical situation and the implementation of an algorithm that he designed for exhaustive search. The second, by J. A. Jones of Oxford University, UK, discusses the recent experimental approaches to quantum computing with nuclear magnetic resonance.
Regarding the end of the 1900s, a small community of researchers in physics, computer science, mathematics and chemistry began to explore the fertile ground at the intersection of quantum mechanics with information theory, which led to a new and powerful paradigm of quantum computing.Quantum information processing promises to extend today's computing resources.Quantum computers, theoretically, could solve problems much more quickly than any classic computer.Intensive experimental efforts have been made to implement quantum computing since Shor and Grover developed their algorithms.In 1997, Nuclear Magnetic Resonance (NMR) emerged as one of the most promising experimental techniques for the implementation of quantum computing protocols.The isolation of nuclear spins and consequent long relaxation times, combined with the perfect dynamics implemented by radiofrequency pulses, led to important studies in the area.Therefore, nuclear spins are picked out as good candidates for quantum bits.In this scenario, quantum chemistry covers a vast field of quantum information science and can lead to advances in scientific research.
Quantum computing makes use of wave-function superposition to provide a computational system with remarkable possibilities. A computing bit is a 0 or 1, but a quantum bit, a qubit, is a superposition of two quantum states, of, say, an atom. A number n of qubits will then be in a superposition of 2n distinct states. An operation on such a state then does 2n simultaneous operations, demonstrating quantum parallelism. The possibilities of quantum computing are demonstrated via discussion of Deutch’s problem, Shor’s period-finding algorithm, and Grover’s search algorithm. Shor’s algorithm might allow the factoring of large numbers, which might enable the decoding of many encryption schemes. Details are given for the solution of Deutch’s problem. The analysis introduces certain operators, the NOT and Hadamard, that are used in computer logic.
Abstract: Quantum computers work in a fundamentally different way from classical computers. Each qubit is in a superposition of 0 and 1 and can be used to store information. Quantum computers have the potential to revolutionize many industries. They can solve exponentially more difficult problems than conventional computers in seconds. Encryption is the process of turning plain text into ciphertext using a key. By measuring the quantum register we can find the marked number. Grover's algorithm can be used to solve a variety of problems related to finding an item in an unsorted database, such as cryptography, optimization, or machine learning. The main limitation of Grover's algorithm is that it is probabilistic. This means that there is a chance that the algorithm will not find the highlighted item after a certain number of iterations. However, the probability that the algorithm does not find the highlighted element decreases exponentially with the number of iterations. The Grover algorithm is a powerful quantum algorithm with many potential applications. However, it is still only a theoretical algorithm and has not been implemented on actual quantum computers. .. Many challenges must be overcome before the Grover algorithm can be used to solve real-world problems
Over the last decade a new way to compute has been defined which, unlike conventional methods, is based on quantum mechanics rather than classical physics. This fundamental change in paradigm can, in principle, solve some important and hitherto intractable problems such as prime factorization of large numbers. This tutorial presentation will review the basics of quantum computation and the design of circuits to implement quantum algorithms. The starting point is the notion of a quantum bit or qubit. Because of the superposition property of quantum states, n qubits can store 2n numbers simultaneously, implying a type of massive parallelism. Furthermore, quantum states allow powerful forms of interaction such as entanglement that have no classical counterparts. Qubits are fragile, however, and are altered by measurement; hence quantum circuits must follow very different rules from classical ones. The differences between quantum and classical logic circuits will be discussed and illustrated. Finally, the physical implementation of quantum devices will be considered, along with the prospects for practical quantum computers.
Deutsch's algorithm and Grover's quantum search are theoretically interesting, but it is not obvious that these two algorithms are actually useful for anything important. We next consider a selection of more advanced algorithms, several of which may have real-life applications. Some of these will be too complicated to explain fully, and their properties will only be sketched briefly. The Deutsch–Jozsa algorithm Deutsch's algorithm is simple, but important, as it shows that a quantum algorithm can find a property of an unknown function (its parity) with a smaller number of queries than any possible classical algorithm (one rather than two). For this reason we can say that quantum computing is more efficient than classical computing within the oracle model of function evaluation. (It is widely believed that quantum computing is more efficient than classical computing in general, but this is a surprisingly hard thing to prove.) The simplicity of the algorithm is also an advantage, as it can be implemented on very primitive quantum computers. Beyond this, however, Deutsch's algorithm is also important as the simplest member of a large family of quantum algorithms, including most notably Shor's quantum factoring algorithm. The second simplest algorithm in the family is the Deutsch–Jozsa algorithm, which solves a very closely related problem. Consider an unknown binary function with n input bits, giving N = 2 n possible inputs, and a single output bit.