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

arXiv:1205.1717 · Physical Review A

Proposal for a scalable universal bosonic simulator using individually trapped ions

Hoi-Kwan Lau, Daniel F. V. James

Published Jun 28, 2012• 52 citations
arXivHTMLPDF

Abstract

We describe a possible architecture to implement a universal bosonic simulator using trapped ions. Single ions are confined in individual traps, and their motional states represent the bosonic modes. Single-mode linear operators, nonlinear phase shifts, and linear beam splitters can be realized by precisely controlling the trapping potentials. All the processes in a bosonic simulation, except the initialization and the readout, can be conducted beyond the Lamb-Dicke regime. Aspects of our proposal can also be applied to split adiabatically a pair of ions in a single trap.

DOI
10.1103/physreva.85.062329

Related papers

Trapped-Ion Quantum Simulator: Experimental Application to Nonlinear Interferometers

Dietrich G. Leibfried, Brian DeMarco, V. Meyer +8 more

We show how an experimentally realized set of operations on a single trapped ion is sufficient to simulate a wide class of Hamiltonians of a spin-1/2 particle in an external potential. This system is also able to simulate other physical dynamics. As a demonstration, we simulate the action of two nth order nonlinear optical beam splitters comprising an interferometer sensitive to phase shift in one of the interferometer beam paths. The sensitivity in determining these phase shifts increases linearly with n, and the simulation demonstrates that the use of nonlinear beam splitters (n=2,3) enhances this sensitivity compared to the standard quantum limit imposed by a linear beam splitter (n=1).

arXiv:quant-ph/0209028•Physical Review Letters•Nov 21, 2002•133 citations

Coherently manipulating cold ions in separated traps by their vibrational couplings

Miao Zhang, L. F. Wei

Recent experiments [K. R. Brown et al., Nature (London) 471, 196 (2011); M. Harlander et al., Nature (London) 471, 200 (2011)] have demonstrated the coherent manipulations on the external vibrations of two ions, confined individually in the separated traps. Using these recently developed techniques, we propose here an approach to realize the coherent operations, e.g., the universal quantum gates, between the separated ion-trap qubits encoded by two internal atomic states of the ions. Our proposal operates beyond the usual Lamb-Dicke limits and could be applied to the scalable ion traps coupled by their vibrations.

arXiv:1103.5670•Physical Review A•Jun 16, 2011•2 citations

Motional-mode analysis of trapped ions

Henning Kalis, Frederick Hakelberg, Matthias Wittemer +3 more

We present two methods for characterization of motional-mode configurations that are generally applicable to the weak- and strong-binding limit of single or multiple trapped atomic ions. Our methods are essential to realize control of the individual as well as the common motional degrees of freedom. In particular, when implementing scalable radio-frequency trap architectures with decreasing ion-electrode distances, local curvatures of electric potentials need to be measured and adjusted precisely, e.g., to tune phonon tunneling and control effective spin-spin interaction. We demonstrate both methods using single $^{25}\text{Mg}^{+}$ ions that are individually confined $40\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{m}$ above a surface-electrode trap array and prepared close to the ground state of motion in three dimensions.

arXiv:1605.01272•Physical Review A•Aug 1, 2016•13 citations

Arrays of individually controlled ions suitable for two-dimensional quantum simulations

Manuel Mielenz, Henning Kalis, Matthias Wittemer +8 more

A precisely controlled quantum system may reveal a fundamental understanding of another, less accessible system of interest. A universal quantum computer is currently out of reach, but an analogue quantum simulator that makes relevant observables, interactions and states of a quantum model accessible could permit insight into complex dynamics. Several platforms have been suggested and proof-of-principle experiments have been conducted. Here, we operate two-dimensional arrays of three trapped ions in individually controlled harmonic wells forming equilateral triangles with side lengths 40 and 80 μm. In our approach, which is scalable to arbitrary two-dimensional lattices, we demonstrate individual control of the electronic and motional degrees of freedom, preparation of a fiducial initial state with ion motion close to the ground state, as well as a tuning of couplings between ions within experimental sequences. Our work paves the way towards a quantum simulator of two-dimensional systems designed at will.

Nature Communications•Jun 13, 2016•152 citations

Universal quantum computation with two-level trapped ions

Andrew M. Childs, Isaac L. Chuang

Although the initial proposal for ion trap quantum computation made use of an auxiliary internal level to perform logic between ions, this resource is not necessary in principle. Instead, one may perform such operations directly using sideband laser pulses, operating with an arbitrary (sufficiently small) Lamb-Dicke parameter. We explore the potential of this technique, showing how to perform logical operations between the internal state of an ion and the collective motional state and giving explicit constructions for a controlled-NOT gate between ions.

arXiv:quant-ph/0008065•Physical Review A•Dec 11, 2000•79 citations

Scalable Ion Trap Architecture for Universal Quantum Computation by Collisions

Liang, Pengfei, Lingzhen Guo

We propose a scalable ion trap architecture for universal quantum computation, which is composed of an array of ion traps with one ion confined in each trap. The neighboring traps are designed capable of merging into one single trap. The universal two-qubit $\sqrt{SWAP}$ gate is realized by direct collision of two neighboring ions in the merged trap, which induces an effective spin-spin interaction between two ions. We find that the collision-induced spin-spin interaction decreases with the third power of two ions' trapping distance. Even with a $200\ μm$ trapping distance between atomic ions in Paul traps, it is still possible to realize a two-qubit gate operation with speed in $0.1\ kHz$ regime. The speed can be further increased up into $0.1\ MHz$ regime using electrons with $10\ mm$ trapping distance in Penning traps.

arXiv:1801.02593•Jan 8, 2018•2 citations
We describe a possible architecture to implement a universal bosonic simulator using trapped ions. Single ions are confined in individual traps, and their motional states represent the bosonic modes. Single-mode linear operators, nonlinear phase shifts, and linear beam splitters can be realized by precisely controlling the trapping potentials. All the processes in a bosonic simulation, except the initialization and the readout, can be conducted beyond the Lamb-Dicke regime. Aspects of our proposal can also be applied to split adiabatically a pair of ions in a single trap.
We show how an experimentally realized set of operations on a single trapped ion is sufficient to simulate a wide class of Hamiltonians of a spin-1/2 particle in an external potential. This system is also able to simulate other physical dynamics. As a demonstration, we simulate the action of two nth order nonlinear optical beam splitters comprising an interferometer sensitive to phase shift in one of the interferometer beam paths. The sensitivity in determining these phase shifts increases linearly with n, and the simulation demonstrates that the use of nonlinear beam splitters (n=2,3) enhances this sensitivity compared to the standard quantum limit imposed by a linear beam splitter (n=1).
Recent experiments [K. R. Brown et al., Nature (London) 471, 196 (2011); M. Harlander et al., Nature (London) 471, 200 (2011)] have demonstrated the coherent manipulations on the external vibrations of two ions, confined individually in the separated traps. Using these recently developed techniques, we propose here an approach to realize the coherent operations, e.g., the universal quantum gates, between the separated ion-trap qubits encoded by two internal atomic states of the ions. Our proposal operates beyond the usual Lamb-Dicke limits and could be applied to the scalable ion traps coupled by their vibrations.
We present two methods for characterization of motional-mode configurations that are generally applicable to the weak- and strong-binding limit of single or multiple trapped atomic ions. Our methods are essential to realize control of the individual as well as the common motional degrees of freedom. In particular, when implementing scalable radio-frequency trap architectures with decreasing ion-electrode distances, local curvatures of electric potentials need to be measured and adjusted precisely, e.g., to tune phonon tunneling and control effective spin-spin interaction. We demonstrate both methods using single 25Mg+^{25}\text{Mg}^{+}25Mg+ ions that are individually confined $40\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{m}$ above a surface-electrode trap array and prepared close to the ground state of motion in three dimensions.
A precisely controlled quantum system may reveal a fundamental understanding of another, less accessible system of interest. A universal quantum computer is currently out of reach, but an analogue quantum simulator that makes relevant observables, interactions and states of a quantum model accessible could permit insight into complex dynamics. Several platforms have been suggested and proof-of-principle experiments have been conducted. Here, we operate two-dimensional arrays of three trapped ions in individually controlled harmonic wells forming equilateral triangles with side lengths 40 and 80 μm. In our approach, which is scalable to arbitrary two-dimensional lattices, we demonstrate individual control of the electronic and motional degrees of freedom, preparation of a fiducial initial state with ion motion close to the ground state, as well as a tuning of couplings between ions within experimental sequences. Our work paves the way towards a quantum simulator of two-dimensional systems designed at will.
Although the initial proposal for ion trap quantum computation made use of an auxiliary internal level to perform logic between ions, this resource is not necessary in principle. Instead, one may perform such operations directly using sideband laser pulses, operating with an arbitrary (sufficiently small) Lamb-Dicke parameter. We explore the potential of this technique, showing how to perform logical operations between the internal state of an ion and the collective motional state and giving explicit constructions for a controlled-NOT gate between ions.
We propose a scalable ion trap architecture for universal quantum computation, which is composed of an array of ion traps with one ion confined in each trap. The neighboring traps are designed capable of merging into one single trap. The universal two-qubit SWAP\sqrt{SWAP}SWAP​ gate is realized by direct collision of two neighboring ions in the merged trap, which induces an effective spin-spin interaction between two ions. We find that the collision-induced spin-spin interaction decreases with the third power of two ions' trapping distance. Even with a 200 μm200\ μm200 μm trapping distance between atomic ions in Paul traps, it is still possible to realize a two-qubit gate operation with speed in 0.1 kHz0.1\ kHz0.1 kHz regime. The speed can be further increased up into 0.1 MHz0.1\ MHz0.1 MHz regime using electrons with 10 mm10\ mm10 mm trapping distance in Penning traps.