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.
Standard CMOS circuits are expected to be no longer able to satisfy nowadays demand for higher performances and lower power consumption. This commits to look for new solutions. Quantum computation, whose fundamental quantity of information is the qubit, is a thoroughly new way of thinking to electronics. There are at least two main reasons for which quantum computing is expected to broaden computation horizons. First, specific algorithms can be engineered, manipulating the probability amplitudes of different states, to exploit the quantum superposition principle and achieve high parallelism. Second, it is expected to be spontaneously suitable to simulate complex quantum physical systems, as large molecules. Quantum computing requires the cooperation of several scientific fields. The leading idea has been to highlight the operations and algorithms a quantum computer must be able to perform and, then, to propose a hardware solution, providing the rigorous physical treatment mandatory for a deep understanding and for an appropriate modelling, something which is hard to find in nowadays literature. Thus, the first chapters address the quantum algorithms, focusing on Grover's search algorithm and deriving, from fundamentals, the corresponding circuit. The latter is then described in Quantum Assembly (QASM), which can be seen as the quantum equivalent of VHDL, and simulated on IBM Q Experience. The following chapters deal with a possible physical implementation of quantum processors: the encoding of qubits on nuclear spins in diamagnetic molecules. When a static magnetic field is applied to a spin-1/2 nucleus, two well-defined energy eigenstates arise, as a result of the Zeeman effect. Each of them can be associated with a qubit eigenstate. Thanks to nuclear magnetic resonance principles, the probability with which one of the two eigenstates is measured can be handled by the superposition of a radio frequency field at the resonance frequency of the nucleus. This can be interpreted as a rotation of the spin, and so of the qubit, about the RF field and enables the execution of single qubit quantum gates, since they are simple rotations of the state vector. The two-qubit CNOT gate is obtained through the interaction of spins via J-coupling. Considering that these gates constitute a universal set, every quantum algorithm can theoretically be run on an NMR processor. Different nuclei have different resonant frequencies, but the addressing of a specific spin can be achieved also in homonuclear molecules, since the resonant frequency depends also on the nuclear environment (nuclear shielding). While unwanted J-couplings can be removed thanks to refocusing, spin decoherence and relaxation phenomena force an upper limit to the allowed timescale. A main advantage of NMR is that this timescale is long, even at room temperature. Conversely, scalability is still an issue. A simple heteronuclear MATLAB model, based on the relations derived from first principles in the thesis, is proposed to prove the feasibility of NMR quantum processors. The input technological parameters, as chemical shielding and J-coupling, can be computed resorting on ORCA, or obtained from experimental data. The model, able to run a universal set of quantum gates and simple algorithms, can be useful to find an optimal operating point as a compromise between molecule physical properties and the quantities which can be controlled by nowadays NMR instrumentation.
A quantum computer is a device that processes information in a quantum-mechanically coherent fashion. In principle, it can exploit coherent quantum interference and entanglement to perform computations, such as factoring large numbers or searching an unsorted database, more rapidly than classical computers. Noise, decoherence, and manufacturing problems make constructing large scale quantum computers difficult. Ion traps and optical cavities offer promising experimental approaches, but no quantum algorithm has yet been implemented with those systems. On the other hand, because of their natural isolation from the environment, nuclear spins are particularly good 'quantum bits', and their use for quantum computation is possible by applying nuclear magnetic resonance (NMR) techniques in an unconventional manner. Here, we report on the experimental implementation of a quantum algorithm using NMR to solve a purely mathematical problem in fewer steps than is possible classically. Our simple quantum computer can determine the type of an unknown function using fewer function 'calls' than is possible using a classical computer.
Abstract This personal essay recounts a misadventure in attempting to find a quantum algorithm with a “general purpose” flavor. Exact arithmetic with large integers can be conducted modulo a list of relatively prime numbers, the answer being reconstructed in conventional terms only at the last moment. Implementing this process on a molecular level would lead not to a quantum computation, but to a massively parallel classical computation. It has been observed that something similar is going on, in practice though not in principle, in the nuclear magnetic resonance implementations of the Grover search algorithm. Certain other NMR computations, which are frankly of an “ensemble” nature, are even closer to my proposal, though more practical. Comparing and contrasting these situations may cast light on the current semantic disputes over what constitutes a “quantum” computation.
Quantum information processing is the use of inherently quantum mechanical phenomena to perform information processing tasks that cannot be achieved using conventional classical information technologies. One famous example is quantum computing, which would permit calculations to be performed that are beyond the reach of any conceivable conventional computer. Initially it appeared that actually building a quantum computer would be extremely difficult, but in the last few years there has been an explosion of interest in the use of techniques adapted from conventional liquid state nuclear magnetic resonance (NMR) experiments to build small quantum computers. After a brief introduction to quantum computing I will review the current state of the art, describe some of the topics of current interest, and assess the long term contribution of NMR studies to the eventual implementation of practical quantum computers capable of solving real computational problems.