Quantum information processing with trapped ions

Wineland, David J.; Barrett, M. D.; Britton, J.; Chiaverini, John; DeMarco, Brian; Itano, Wayne M.; Jelenković, Branislav; Langer, C.; Leibfried, D.; Meyer, V.; Rosenband, T.; Schätz, T.

doi:10.1098/rsta.2003.1205

Cited by 152 publications

(118 citation statements)

References 48 publications

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“…We choose the polarizations of the beams such that the different couplings due to the ac-Stark shifts by beams (b) or (c) and the associated forces are related by F ↓ = −3/2 F ↑ [20,22]. They point along the trap axis z but in opposite directions.…”

Section: Simulating the Spin-spin Interactionmentioning

confidence: 99%

The “arch” of simulating quantum spin systems with trapped ions

et al. 2009

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We cannot translate quantum behavior arising with superposition states or entanglement efficiently into the classical language of conventional computers (Feynman et al. in Int. J. Theor. Phys. 21:467, 1982). A universal quantum computer could describe and help to understand complex quantum systems. But it is envisioned to become functional only within the next decade(s). A shortcut was proposed via simulating the quantum behavior of interest in another quantum system, where all relevant parameters and interactions can be controlled and observables of interest detected sufficiently well. For example simulating quantum spin systems within an architecture of trapped ions (Porras and Cirac in Phys. Rev. Lett. 92:207901, 2004). Here we specify how we simulate the spin and all necessary interactions and how we calibrate their amplitudes. For example via a two-ion phase-gate operation on two axial motional modes simultaneously at a fidelity exceeding 95%. We explain the complete mode of operation of a quantum simulator on the basis of our simple model case-the proof of principle experiment of simulating the transition of a quantum magnet from paramagnetic into entangled ferromagnetic order (Friedenauer et al. in Nat. Phys. 4:757, 2008) and emphasize some of the similarities and differences with a quantum computer.

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Section: Simulating the Spin-spin Interactionmentioning

confidence: 99%

The “arch” of simulating quantum spin systems with trapped ions

et al. 2009

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“…is realized by a state dependent optical dipole force [6,20,21]. For this, two Raman laser beams at frequencies ω 1 and ω 2 , both detuned (2π · 80 GHz) blue from the 2 S 1/2 → 2 P 3/2 electric dipole transition (λ ≈ 280 nm) induce an AC-Stark shift of the electronic states.…”

mentioning

confidence: 99%

“…2. After finishing a walk sequence, we detect the coin state by (electronic-) state-dependent fluorescence measurements [21]. A closed cycling transition on 2 S 1/2 → 2 P 3/2 driven by a laser beam on resonance provides a fluorescence rate of 200 kHz for state |T and negligible fluorescence for state |H (off-resonant by ω 0 ).…”

mentioning

confidence: 99%

Quantum Walk of a Trapped Ion in Phase Space

Schmitz¹,

Matjeschk²,

Schneider³

et al. 2009

Phys. Rev. Lett.

473

448

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We implement the proof of principle for the quantum walk of one ion in a linear ion trap. With a single-step fidelity exceeding 0.99, we perform three steps of an asymmetric walk on the line. We clearly reveal the differences to its classical counterpart if we allow the walker/ion to take all classical paths simultaneously. Quantum interferences enforce asymmetric, non-classical distributions in the highly entangled degrees of freedom (of coin and position states). We theoretically study and experimentally observe the limitation in the number of steps of our approach, that is imposed by motional squeezing. We propose an altered protocol based on methods of impulsive steps to overcome these restrictions, in principal allowing to scale the quantum walk to several hundreds of steps.PACS numbers: 03.67. Ac, 05.40Fb, 0504Jc A quantum walk[1] is the deterministic quantum mechanical extension of a classical random walk. A simple classical version requires two basic operations: Tossing the coin (coin-operation), allowing for two possible and random outcomes. Dependent on this outcome, the walker performs a step to the right or left (stepoperation). In the quantum mechanical extension the operations allow for coherent superpositions of entangled coin and position states. After several iterations the probability to be in a certain position is determined by quantum mechanical interference of the walker state that leads to fundamentally different characteristics of the walk [2].The motivation for studying quantum walks is twofold. On the one hand, many classical algorithms include random walks. Examples can be found in biology, psychology, economics and physics, for example Einstein's simple model for Brownian motion [3]. The extension of the walk to quantum mechanics might allow for substantial speedup of related quantum versions [2], as in prominent algorithms suggested by Shor[4] and Grover [5] due to other quantum-subroutines. On the other hand, the quantum walk could lead to new insights into entanglement and decoherence in mesoscopic systems [6]. These topics might be explored by increasing the amount of walkers -even before any algorithm might benefit from the quantum random walk.Quantum walks have been thoroughly investigated theoretically and first attempts at implementation have been performed with a very limited amount of steps due to a lack of operation fidelity or fundamental restrictions within the protocol. Some aspects have been realized on the longitudinal modes of a linear optical resonator [7] and in a nuclear magnetic resonance experiment [8]. An implementation based on neutral atoms in a spin-dependent optical lattice[9, 10, 11] has resulted in an experiment recently. Other proposals considered an array of microtraps illuminated by a set of microlenses [12] and Bose-Einstein condensates [13]. Travaglione and Milburn[14] proposed a scheme for trapped ions to transfer the high operational fidelities [6] obtained in quantum information processing (QIP) into To implement the deterministic "tossing of t...

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“…Since the parameters specified above, the second-order Stark shift E (2) α of state |α due to the frequency comb can be computed for an arbitrary polarization (taking = 1) [26,28]:…”

Section: Fourth-order Stark Shift Theorymentioning

confidence: 99%

Engineering large Stark shifts for control of individual clock state qubits

et al. 2016

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In quantum information science, the external control of qubits must be balanced with the extreme isolation of the qubits from the environment. Atomic qubit systems typically mitigate this balance through the use of gated laser fields that can create superpositions and entanglement between qubits. Here we propose the use of high-order optical Stark shifts from optical fields to manipulate the splitting of atomic qubits that are insensitive to other types of fields. We demonstrate a fourthorder AC Stark shift in a trapped atomic ion system that does not require extra laser power beyond that needed for other control fields. We individually address a chain of tightly-spaced trapped ions and show how these controlled shifts can produce an arbitrary product state of ten ions as well as generate site-specific magnetic field terms in a simulated spin Hamiltonian.

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Quantum information processing with trapped ions

Cited by 152 publications

References 48 publications

The “arch” of simulating quantum spin systems with trapped ions

The “arch” of simulating quantum spin systems with trapped ions

Quantum Walk of a Trapped Ion in Phase Space

Engineering large Stark shifts for control of individual clock state qubits

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