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Physical Review A

Experimental realization of a target-accepting quantum search by NMR

Jae‐Hyun Kim, Jae‐Seung Lee, Soonchil Lee

Published Apr 24, 2002• 9 citations
Publisher

Abstract

With a three-bit nuclear magnetic resonance quantum computer, we have experimentally realized a quantum search algorithm that can take a desired function value (or target) t as its input and give the corresponding function argument ${x}_{0}$ such that ${f(x}_{0})=t$ as a result. The function value is not retrieved from an existing table, but evaluated by the search algorithm in the manner of a typical algorithmic search. A single-query version of the quantum search algorithm is used to search for one of two function arguments.

DOI
10.1103/physreva.65.054301

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With a three-bit nuclear magnetic resonance quantum computer, we have experimentally realized a quantum search algorithm that can take a desired function value (or target) t as its input and give the corresponding function argument x0{x}_{0}x0​ such that f(x0)=t{f(x}_{0})=tf(x0​)=t as a result. The function value is not retrieved from an existing table, but evaluated by the search algorithm in the manner of a typical algorithmic search. A single-query version of the quantum search algorithm is used to search for one of two function arguments.
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.
We describe an implementation of Grover's fixed-point quantum search algorithm on a nuclear magnetic resonance quantum computer, searching for either one or two matching items in an unsorted database of four items. In this algorithm the target state (an equally weighted superposition of the matching states) is a fixed point of the recursive search operator, so that the algorithm always moves towards the desired state. The effects of systematic errors in the implementation are briefly explored.
Using nuclear magnetic resonance (NMR) techniques with a three-qubit sample, we have experimentally implemented the highly structured algorithm for the satisfiability problem with one variable in each clause proposed by Hogg. A simplified temporal averaging procedure was employed to prepare the three-qubit pseudopure state. The algorithm was completed with only a single evaluation of the structure of the problem and the solutions were found theoretically with probability 100100%,100 results that outperform both unstructured quantum and the best classical search algorithms. However, about 9090%90 of the corresponding experimental fidelities can be attributed to the imperfections of manipulations.
There has been much recent effort to realize quantum devices in many different physical systems. Among them, nuclear magnetic resonance (NMR) has been the first to demonstrate nontrivial quantum algorithms with small numbers of qubits and hence is a prototype for the key ingredients needed to build quantum computers. An important building block in many quantum applications is the scattering circuit, which can be used as a quantum multimeter to perform various quantum information processing tasks directly without recourse to quantum tomography. We implement in NMR a three-qubit version of the multimeter and also demonstrate a single-qubit fingerprinting.