Implementation of a Quantum Search Algorithm on a Nuclear Magnetic Resonance Quantum Computer

The simulation of quantum mechanical systems with classical computers appears to be a computationally intractable problem. In 1982 Feynman reversed this observation, suggesting that quantum mechanical systems have an information processing capability much greater than that of corresponding classical systems, and thus could be used to implement a new type of powerful computer. In 1985 Deutsch described a quantum mechanical Turing machine, showing that quantum computers could indeed be constructed. Since then there has been extensive research in this field, but while the theory is fairly well understood actually building a quantum computer has proved extremely difficult, and only two methods have been used to demonstrate quantum logic gates: ion traps, 4 and nuclear magnetic resonance (NMR). 6 NMR quantum computers have previously been used to demonstrate quantum algorithms to solve the two bit Deutsch problem. 8 Here we show how such a computer can be used to implement a fast quantum search algorithm initially developed by Grover. 10 Among other applications Grover’s algorithms enable an extremely rapid search over the domain of a binary function to find elements for which this function is satisfied (that is, the function has the value 1). This approach is simpler if the number of satisfying values is known beforehand, and is particularly simple when precisely one quarter of the elements in the domain satisfy the function. The algorithm can be demonstrated using a computer with two quantum bits (qubits) to search a two bit domain in which one of the four elements satisfies the function. A classical search of this domain would require between 1 and 3