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Chapman & Hall/CRC eBooks

Transgressing the boundaries of quantum computation: acontribution to the hermeneuticsof the NMR paradigm

Published Feb 14, 2002• 0 citations
Publisher

Abstract

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.

DOI
10.1201/9781420035377-16

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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.
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.
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.
Nuclear magnetic resonance offers an appealing prospect for implementation of quantum computers, because of the long coherence times associated with nuclear spins, and extensive laboratory experience in manipulating the spins with radio frequency pulses. Existing proposals, however, suffer from a signal-to-noise ratio that decays exponentially in the number of qubits in the quantum computer. This places a severe limit on the size of the computations that can be performed by such a computer; estimates of that limit are well within the range in which a conventional computer taking exponentially more steps would still be practical. We give an NMR implementation in which the signal-to-noise ratio depends only on features of NMR technology, not the size of the computer. This provides a means for NMR computation techniques to scale to sizes at which the exponential speedup enables quantum computation to solve problems beyond the capabilities of classical computers.
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.