Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

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

G. S. Agarwal, Gombojav O. Ariunbold, Joachim von Zanthier, HERBERT WALTHER

Published Jan 22, 2004• 0 citations
OpenAlex

Abstract

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.

Related papers

Nonclassical imaging for a quantum search of trapped ions

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

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/0401141•Physical Review A•Dec 27, 2004•8 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.

Physical Review A•Jan 26, 2009•14 citations

Search for correlation effects in linear chains of trapped Ca + ions

C. J. S. Donald, D. M Lucas, P. A Barton +5 more

We report a precise search for correlation effects in linear chains of 2 and 3 trapped Ca + ions. Unexplained correlations in photon emission times within a linear chain of trapped ions have been reported, which, if genuine, cast doubt on the potential of an ion trap to realize quantum information processing. We observe quantum jumps from the metastable 3 d 2 D 5/2 level for several hours, searching for correlations between the decay times of the different ions. We find no evidence for correlations: the number of quantum jumps with separations of less than 10 ms is consistent with statistics to within errors of 0.05%; the lifetime of the metastable level derived from the data is consistent with that derived from independent single-ion data at the level of the experimental errors (1%); and no rank correlations between the decay times were found with sensitivity to rank correlation coefficients at the level of | R | = 0.024.

arXiv:physics/0003085•Europhysics Letters (EPL)•Aug 15, 2000•16 citations

Scalable quantum search using trapped ions

Svetoslav S. Ivanov, Peter A. Ivanov, I. E. Linington +1 more

We propose a scalable implementation of Grover's quantum search algorithm in a trapped-ion quantum information processor. The system is initialized in an entangled Dicke state by using adiabatic techniques. The inversion-about-average and oracle operators take the form of single off-resonant laser pulses. This is made possible by utilizing the physical symmetries of the trapped-ion linear crystal. The physical realization of the algorithm represents a dramatic simplification: each logical iteration (oracle and inversion about average) requires only two physical interaction steps, in contrast to the large number of concatenated gates required by previous approaches. This not only facilitates the implementation but also increases the overall fidelity of the algorithm.

arXiv:1002.3246•Physical Review A•Apr 29, 2010•24 citations

Implementation of Grover’s quantum search algorithm in a scalable system

Kathy-Anne Brickman, P. C. Haljan, P. J. Lee +3 more

We report the implementation of Grover's quantum search algorithm in the scalable system of trapped atomic ion quantum bits. Any one of four possible states of a two-qubit memory is marked, and following a single query of the search space, the marked element is successfully recovered with an average probability of 60(2)%. This exceeds the performance of any possible classical search algorithm, which can only succeed with a maximum average probability of 50%.

arXiv:quant-ph/0510066•Physical Review A•Nov 30, 2005•186 citations

Simple implementation of a quantum search with trapped ions

Svetoslav S. Ivanov, Peter A. Ivanov, Nikolay V. Vitanov

We propose an ion-trap implementation of Grover's quantum search algorithm for an unstructured database of arbitrary length $N$. The experimental implementation is appealingly simple because the linear ion trap allows for a straightforward construction, in a single interaction step and without a multitude of Hadamard transforms, of the reflection operator, which is the engine of the Grover algorithm. Consequently, a dramatic reduction in the number of the required physical steps takes place, to just $O(\sqrt{N})$, the same as the number of mathematical steps. The proposed setup allows for demonstration of both the original (probabilistic) Grover search and its deterministic variation, and is remarkably robust to imperfections in the register initialization.

arXiv:0909.5401•Physical Review A•Sep 4, 2008•17 citations
We show how photon-photon spatial correlations in the light emitted by a system of NNN ions in a linear trap, interacting with an incident pi\\pipi-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 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 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 NNN. The system is initialized in an even superposition of all register states, i.e., in the symmetric Dicke state with NNN 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 report a precise search for correlation effects in linear chains of 2 and 3 trapped Ca + ions. Unexplained correlations in photon emission times within a linear chain of trapped ions have been reported, which, if genuine, cast doubt on the potential of an ion trap to realize quantum information processing. We observe quantum jumps from the metastable 3 d 2 D 5/2 level for several hours, searching for correlations between the decay times of the different ions. We find no evidence for correlations: the number of quantum jumps with separations of less than 10 ms is consistent with statistics to within errors of 0.05%; the lifetime of the metastable level derived from the data is consistent with that derived from independent single-ion data at the level of the experimental errors (1%); and no rank correlations between the decay times were found with sensitivity to rank correlation coefficients at the level of | R | = 0.024.
We propose a scalable implementation of Grover's quantum search algorithm in a trapped-ion quantum information processor. The system is initialized in an entangled Dicke state by using adiabatic techniques. The inversion-about-average and oracle operators take the form of single off-resonant laser pulses. This is made possible by utilizing the physical symmetries of the trapped-ion linear crystal. The physical realization of the algorithm represents a dramatic simplification: each logical iteration (oracle and inversion about average) requires only two physical interaction steps, in contrast to the large number of concatenated gates required by previous approaches. This not only facilitates the implementation but also increases the overall fidelity of the algorithm.
We propose an ion-trap implementation of Grover's quantum search algorithm for an unstructured database of arbitrary length NNN. The experimental implementation is appealingly simple because the linear ion trap allows for a straightforward construction, in a single interaction step and without a multitude of Hadamard transforms, of the reflection operator, which is the engine of the Grover algorithm. Consequently, a dramatic reduction in the number of the required physical steps takes place, to just O(N)O(\sqrt{N})O(N​), the same as the number of mathematical steps. The proposed setup allows for demonstration of both the original (probabilistic) Grover search and its deterministic variation, and is remarkably robust to imperfections in the register initialization.