We discuss a simple search problem which can be pursued with different methods, either on a classical or on a quantum basis. The system is represented by a chain of trapped ions. The ion to be searched for is a member of that chain, consisting, however, of an isotopic species different from the others. It is shown that classical imaging may lead to the final result as fast as quantum imaging. However, for the discussed case the quantum method gives more flexibility and higher precision when the number of ions considered in the chain increases. In addition, interferences are observable even when the distances between the ions are smaller than half a wavelength of the incident light.We discuss a simple search problem which can be pursued with different methods, either on a classical or on a quantum basis. The system is represented by a chain of trapped ions. The ion to be searched for is a member of that chain, consisting, however, of an isotopic species different from the others. It is shown that classical imaging may lead to the final result as fast as quantum imaging. However, for the discussed case the quantum method gives more flexibility and higher precision when the number of ions considered in the chain increases. In addition, interferences are observable even when the distances between the ions are smaller than half a wavelength of the incident light.

arXiv:quant-ph/0401141Physical Review ADec 27, 20048 citations

Nonclassical Imaging for a quantum search of ions in a linear trap

G. S. Agarwal, Gombojav O. Ariunbold, Joachim von Zanthier +1 more

We show how photon-photon spatial correlations in the light emitted by a system of $N$ ions in a linear trap, interacting with an incident $\\pi$ -pulse, can be used to implement a quantum search algorithm. We demonstrate that just two measurements are sufficient to identify a non-radiating isotope in the chain instead of performing N/2 classical queries.We show how photon-photon spatial correlations in the light emitted by a system of $N$ ions in a linear trap, interacting with an incident $\\pi$-pulse, can be used to implement a quantum search algorithm. We demonstrate that just two measurements are sufficient to identify a non-radiating isotope in the chain instead of performing N/2 classical queries.

Jan 22, 20040 citations

Limits to optical imaging of trapped ions

Erik W. Streed

Bulletin of the American Physical SocietyJun 4, 20140 citations

Quantum search in a nonclassical database of trapped ions

I. E. Linington, Peter A. Ivanov, Nikolay V. Vitanov

We propose an implementation of the Grover's search algorithm in a nonclassical database using a linear chain of trapped ions. The database comprises all collective states with two ionic excitations; hence the number of database entries scales quadratically with the number of ions $N$ . The system is initialized in an even superposition of all register states, i.e., in the symmetric Dicke state with $N$ ions sharing two excitations. The reflection-about-the-mean operator is produced merely by global addressing of the ion string by an off-resonant pulse with a suitable area, whereas the oracle operator is a control-phase gate. This simplification should allow a demonstration of quantum search in a database of hundreds of elements without needing to synthesize multiqubit quantum gates. The technique does not rely on coherent addition or subtraction of phonons, and hence the ion chain can be sympathetically cooled throughout the process.We propose an implementation of the Grover's search algorithm in a nonclassical database using a linear chain of trapped ions. The database comprises all collective states with two ionic excitations; hence the number of database entries scales quadratically with the number of ions $N$. The system is initialized in an even superposition of all register states, i.e., in the symmetric Dicke state with $N$ ions sharing two excitations. The reflection-about-the-mean operator is produced merely by global addressing of the ion string by an off-resonant pulse with a suitable area, whereas the oracle operator is a control-phase gate. This simplification should allow a demonstration of quantum search in a database of hundreds of elements without needing to synthesize multiqubit quantum gates. The technique does not rely on coherent addition or subtraction of phonons, and hence the ion chain can be sympathetically cooled throughout the process.

Physical Review AJan 26, 200914 citations

We show how photon-photon spatial correlations in the light emitted by a system of

N

ions in a linear trap, interacting with an incident

\\pi

-pulse, can be used to implement a quantum search algorithm. We demonstrate that just two measurements are sufficient to identify a non-radiating isotope in the chain instead of performing N/2 classical queries.

N

. The system is initialized in an even superposition of all register states, i.e., in the symmetric Dicke state with

N

ions sharing two excitations. The reflection-about-the-mean operator is produced merely by global addressing of the ion string by an off-resonant pulse with a suitable area, whereas the oracle operator is a control-phase gate. This simplification should allow a demonstration of quantum search in a database of hundreds of elements without needing to synthesize multiqubit quantum gates. The technique does not rely on coherent addition or subtraction of phonons, and hence the ion chain can be sympathetically cooled throughout the process.