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

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Vibrational decoherence in ion-trap quantum computers

Anupam Garg

Published Jul 6, 1998• 0 citations
Publisher

Abstract

Decoherence is studied in an attractive proposal for an actual implementation of a quantum computer based on trapped ions.Emphasis is placed on the decoherence arising from the vibrational motion of the ions, which is compared with that due to spontaneous emission from excited states of the ions. The calculations is made tractable by exploiting the vast difference in time scales between the vibrational excitations and the intra-ionic electronic excitations. Since the latter are several orders of magnitude faster, an adiabatic approximation is used to integrate them out and find the inclusive probability for the electronic state of the ions to evolve as it would in the absence of vibrational coupling, and the ions to evolve into any state whatsoever. The decoherence time is found at zero temperature and for any number of ions N in the computer. Comparison is made with the spontaneous emission decoherence, and the implications for how trap voltages and other parameters should be scaled with N are discussed.

DOI
10.1117/12.312644

Related papers

Vibrational Decoherence in Ion Trap Quantum Computers

Anupam Garg

The ion trap quantum computer proposed by Cirac and Zoller [Phys. Rev. Lett. 74, 4091 (1995)] is analyzed for decoherence due to vibrations of the ions. An adiabatic approximation exploiting the vast difference between the frequencies of the optical intraionic transition and the vibrational modes is used to find the decoherence time at any temperature T. The scaling of this decoherence time with the number of ions is discussed, and compared with that due to spontaneous emission.

arXiv:quant-ph/9710053•Fortschritte der Physik•Nov 1, 1998•4 citations

Decoherence in Ion Trap Quantum Computers

Anupam Garg

The intrinsic decoherence from vibrational coupling of the ions in the Cirac-Zoller quantum computer [Phys. Rev. Lett. 74, 4091 (1995)] is considered. Starting from a state in which the vibrational modes are at a temperature $T$, and each ion is in a superposition of an excited and a ground state, an adiabatic approximation is used to find the inclusive probability $P(t)$ for the ions to evolve as they would without the vibrations, and for the vibrational modes to evolve into any final state. An analytic form is found for $P(t)$ at $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$, and the decoherence time is found for all $T$. The decoherence is found to be quite small, even for 1000 ions.

Physical Review Letters•Jul 29, 1996•58 citations

Universal quantum computation with trapped ions in thermal motion by adiabatic passage

Xun‐Li Feng, Chunfeng Wu, C. H. Lai +1 more

We propose a universal quantum computation scheme for trapped ions in thermal motion via the technique of adiabatic passage, which incorporates the advantages of both the adiabatic passage and the model of trapped ions in thermal motion. Our scheme is immune from the decoherence due to spontaneous emission from excited states as the system in our scheme evolves along a dark state. In our scheme the vibrational degrees of freedom are not required to be cooled to their ground states because they are only virtually excited. It is shown that the fidelity of the resultant gate operation is still high even when the magnitude of the effective Rabi frequency moderately deviates from the desired value.

Physical Review A•Jun 26, 2008•4 citations

Decoherence in ion traps

Sara Schneider, Gerard J Milburn

Summary form only given.To model the decoherence in ion traps resulting from laser intensity and phase fluctuations, we assume that the stochastic processes involved are white noise processes, which enables us to give a simple master equation description of this source of decoherence. We discuss the effects those fluctuations have on gate operations in ion-trap quantum computation and briefly address possible detection and error correction mechanisms. The master equation is then averaged over the noise and is sufficient to describe the results of experiments that probe the oscillations in the electronic populations as energy is exchanged between the internal and electronic motion. We get solutions for the probability of the ion to be in the ground state for both intensity and phase fluctuations. Our results predict that the decoherence rate resulting from intensity fluctuations will depend on the vibrational quantum number in different ways depending on which vibrational excitation sideband is used. So the dependence of the decoherence rate for the second red sideband depends quadratically on the vibrational energy state |n> the ion is prepared in, whereas for the first sideband, this effect is linear in n. Due to this result, the second red (or any higher-order) sideband is a better choice for testing the dependence of decoherence on the excitation in the vibrational state experimentally than just the first-order sideband. Because those fluctuations in the exciting laser pulse are not the only source of decoherence, we briefly discuss fluctuations in the trap potential itself. These fluctuations lead to a wobbling trap center point, and we discuss the effects due to them.

Conference on Lasers and Electro-Optics•Nov 27, 2002•0 citations

Ion Trap Quantum Computer with Bichromatic Light

Anders Søndberg Sørensen, Klaus Mølmer

In the ion trap quantum computer, quantum bits are represented by the internal state of the trapped ions, and the collective vibrations of the ions are exploited for the coherent manipulation of the state of several bits. We have developed a method to perform gates on different ions by illuminating the ions with bichromatic light. Our gates are independent of the motional state of the ions and they may be applied to ions in any state or, e.g., thermal mixture of vibrational states. Moreover, our proposal allows the production of multiparticle entangled states even in situations without experimental access to the individual ions in the trap. Maximally entangled states of any number of ions are produced by simply illuminating all ions with the same beams of bichromatic light.

Fortschritte der Physik•Sep 1, 2000•6 citations

Decoherence, Measurement and Quantum Computing in Ion Traps

Sara Schneider

This thesis is concerned with various aspects of ion traps and their use as a quantum simulation and computation device. In its first part we investigate various sources of noise and decoherence in ion traps. As quantum information is very fragile, a detailed knowledge of noise and decoherence sources in a quantum computation device is essential. In the special case of an ion trap quantum computer we investigate the effects of intensity and phase noise in the laser, which is used to perform the gate operations. We then look at other sources of noise which are present without a laser being switched on. These are fluctuations in the trapping frequency caused by noise in the electric potentials applied to the trap and fluctuating electrical fields which will cause heating of the centre-of-mass vibrational state of the ions in the trap. For the case of fluctuating electrical fields we estimate the effect on a quantum gate operation. We then propose a scheme for performing quantum gates without having the ions cooled down to their motional ground state. The second part deals with various aspects of the use of ion traps as a device for quantum computation. We start with the use of ionic qubits as a measurement device for the centre-of-mass vibrational mode and investigate in detail the effect these measurements will have on the vibrational mode. If one wants to use quantum computation devices as systems to simulate quantum mechanics, it is of interest to know how to simulate say a k-level system with N qubits. We investigate the easiest case of this wider problem and look at how to simulate a three-level system (a so called trit) with two qubits in an ion trap quantum computer. We show how to get and measure a SU (3) geometric phase with this toy model. Finally we investigate how to simulate collective angular momentum models with a string of qubits in an ion trap. We assume that the ionic qubits are coupled to a thermal reservoir and derive a master equation for this case. We investigate the semiclassical limit of this master equation and, in the case for two qubits in the trap, determine the entanglement of the steady state. We also outline a way to find the steady state for the master equation using coherence vectors.

•Jan 1, 2000•0 citations
Decoherence is studied in an attractive proposal for an actual implementation of a quantum computer based on trapped ions.Emphasis is placed on the decoherence arising from the vibrational motion of the ions, which is compared with that due to spontaneous emission from excited states of the ions. The calculations is made tractable by exploiting the vast difference in time scales between the vibrational excitations and the intra-ionic electronic excitations. Since the latter are several orders of magnitude faster, an adiabatic approximation is used to integrate them out and find the inclusive probability for the electronic state of the ions to evolve as it would in the absence of vibrational coupling, and the ions to evolve into any state whatsoever. The decoherence time is found at zero temperature and for any number of ions N in the computer. Comparison is made with the spontaneous emission decoherence, and the implications for how trap voltages and other parameters should be scaled with N are discussed.
The intrinsic decoherence from vibrational coupling of the ions in the Cirac-Zoller quantum computer [Phys. Rev. Lett. 74, 4091 (1995)] is considered. Starting from a state in which the vibrational modes are at a temperature TTT, and each ion is in a superposition of an excited and a ground state, an adiabatic approximation is used to find the inclusive probability P(t)P(t)P(t) for the ions to evolve as they would without the vibrations, and for the vibrational modes to evolve into any final state. An analytic form is found for P(t)P(t)P(t) at T=0T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0T=0, and the decoherence time is found for all TTT. The decoherence is found to be quite small, even for 1000 ions.
We propose a universal quantum computation scheme for trapped ions in thermal motion via the technique of adiabatic passage, which incorporates the advantages of both the adiabatic passage and the model of trapped ions in thermal motion. Our scheme is immune from the decoherence due to spontaneous emission from excited states as the system in our scheme evolves along a dark state. In our scheme the vibrational degrees of freedom are not required to be cooled to their ground states because they are only virtually excited. It is shown that the fidelity of the resultant gate operation is still high even when the magnitude of the effective Rabi frequency moderately deviates from the desired value.
Summary form only given.To model the decoherence in ion traps resulting from laser intensity and phase fluctuations, we assume that the stochastic processes involved are white noise processes, which enables us to give a simple master equation description of this source of decoherence. We discuss the effects those fluctuations have on gate operations in ion-trap quantum computation and briefly address possible detection and error correction mechanisms. The master equation is then averaged over the noise and is sufficient to describe the results of experiments that probe the oscillations in the electronic populations as energy is exchanged between the internal and electronic motion. We get solutions for the probability of the ion to be in the ground state for both intensity and phase fluctuations. Our results predict that the decoherence rate resulting from intensity fluctuations will depend on the vibrational quantum number in different ways depending on which vibrational excitation sideband is used. So the dependence of the decoherence rate for the second red sideband depends quadratically on the vibrational energy state |n> the ion is prepared in, whereas for the first sideband, this effect is linear in n. Due to this result, the second red (or any higher-order) sideband is a better choice for testing the dependence of decoherence on the excitation in the vibrational state experimentally than just the first-order sideband. Because those fluctuations in the exciting laser pulse are not the only source of decoherence, we briefly discuss fluctuations in the trap potential itself. These fluctuations lead to a wobbling trap center point, and we discuss the effects due to them.
In the ion trap quantum computer, quantum bits are represented by the internal state of the trapped ions, and the collective vibrations of the ions are exploited for the coherent manipulation of the state of several bits. We have developed a method to perform gates on different ions by illuminating the ions with bichromatic light. Our gates are independent of the motional state of the ions and they may be applied to ions in any state or, e.g., thermal mixture of vibrational states. Moreover, our proposal allows the production of multiparticle entangled states even in situations without experimental access to the individual ions in the trap. Maximally entangled states of any number of ions are produced by simply illuminating all ions with the same beams of bichromatic light.
This thesis is concerned with various aspects of ion traps and their use as a quantum simulation and computation device. In its first part we investigate various sources of noise and decoherence in ion traps. As quantum information is very fragile, a detailed knowledge of noise and decoherence sources in a quantum computation device is essential. In the special case of an ion trap quantum computer we investigate the effects of intensity and phase noise in the laser, which is used to perform the gate operations. We then look at other sources of noise which are present without a laser being switched on. These are fluctuations in the trapping frequency caused by noise in the electric potentials applied to the trap and fluctuating electrical fields which will cause heating of the centre-of-mass vibrational state of the ions in the trap. For the case of fluctuating electrical fields we estimate the effect on a quantum gate operation. We then propose a scheme for performing quantum gates without having the ions cooled down to their motional ground state. The second part deals with various aspects of the use of ion traps as a device for quantum computation. We start with the use of ionic qubits as a measurement device for the centre-of-mass vibrational mode and investigate in detail the effect these measurements will have on the vibrational mode. If one wants to use quantum computation devices as systems to simulate quantum mechanics, it is of interest to know how to simulate say a k-level system with N qubits. We investigate the easiest case of this wider problem and look at how to simulate a three-level system (a so called trit) with two qubits in an ion trap quantum computer. We show how to get and measure a SU (3) geometric phase with this toy model. Finally we investigate how to simulate collective angular momentum models with a string of qubits in an ion trap. We assume that the ionic qubits are coupled to a thermal reservoir and derive a master equation for this case. We investigate the semiclassical limit of this master equation and, in the case for two qubits in the trap, determine the entanglement of the steady state. We also outline a way to find the steady state for the master equation using coherence vectors.