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arXiv:0804.1261 · Physical Review A

Experimental quantum-information processing with C43a+ ions

Jan Benhelm, Gerhard Kirchmair, Christian F. Roos, R. Blatt

Published Jun 4, 2008• 90 citations
arXivHTMLPDF

Abstract

For quantum-information processing (QIP) with trapped ions, the isotope ${^{43}\text{C}\text{a}}^{+}$ offers the combined advantages of a quantum memory with long coherence time, a high-fidelity readout, and the possibility of performing two-qubit gates on a quadrupole transition with a narrow-band laser. Compared to other ions used for quantum computing, ${^{43}\text{C}\text{a}}^{+}$ has a relatively complicated level structure. We discuss how to meet the basic requirements for QIP and demonstrate ground-state cooling, robust state initialization, and efficient readout for the hyperfine qubit with a single ${^{43}\text{C}\text{a}}^{+}$ ion. A microwave field and a Raman light field are used to drive qubit transitions, and the coherence times for both fields are compared. Phase errors due to interferometric instabilities in the Raman field generation do not limit the experiments on a time scale of 100 ms. We find a quantum-information storage time of many seconds for the hyperfine qubit.

DOI
10.1103/physreva.77.062306

Related papers

Precision Spectroscopy and Quantum Information Processing with Trapped Calcium Ions

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Over the last decade quantum information processing (QIP) has exploded into a major field of physics, studied both experimentally and theoretically with a universal quantum computer as a long-term vision. Ions stored as strings in linear Paul traps are among the most promising systems for constructing a quantum device harnessing the computing power inherent in the laws of quantum physics. The two most important challenges in trapped ion quantum computing today are to realize and control systems with large numbers of ions, and to improve and integrate the operations which serve as basic building blocks, in particular universal gate operations. Quite surprisingly, even after many years of intense research with different atom species, it is still not evident which ion is best suited for QIP. This thesis describes the construction of a new experiment built to study a promising candidate qubit, namely the calcium isotope 43Ca+. 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Phase errors due to interferometric instabilities in the Raman field generation were not limiting the experiments on a time scale of at least 100ms. Even in the presence of magnetic field fluctuations we found a quantum information storage time exceeding one second. We implemented a Molmer-Sorensen type gate operation, entangling ions with a fidelity of 99.3(1)%. The gate was performed on a pair of qubits encoded in two trapped 40Ca+ ions using an amplitude-modulated laser beam interacting with both ions at the same time. A robust gate operation, mapping separable states onto maximally entangled states was achieved by adiabatically switching the laser-ion coupling on and off. The performance of a single gate and concatenations of up to 21 gate operations were analyzed. Concerning the fidelity, this result sets a world record for creating two-qubit entanglement on-demand irrespective of the physical realization considered. 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arXiv:quant-ph/0305129•May 22, 2003•52 citations

Long-lived metastable-qubit memory

Xiaoyang Shi, Jasmine Sinanan-Singh, Kyle DeBry +3 more

Coherent storage of quantum information is crucial to many quantum technologies. Long coherence times have been demonstrated in trapped-ion qubits, typically using the hyperfine levels within the ground state of a single ion. However, recent research suggests qubits encoded in metastable states could provide architectural benefits for quantum information processing, such as the possibility of effective dual-species operation in a single-species system and erasure-error conversion for fault-tolerant quantum computing. Here we demonstrate long-lived encoding of a quantum state in the metastable states of a trapped ion. By sympathetically cooling with another ion of the same species and constantly monitoring for erasure errors, we demonstrate a coherence time of 136(42) seconds with a qubit encoded in the metastable $5D_{5/2}$ state of a single $^{137}$Ba$^+$ ion. In agreement with a model based on empirical results from dynamical-decoupling-based noise spectroscopy, we find that dephasing of the metastable levels is the dominant source of error once erasure errors are removed.

arXiv:2408.00975•Aug 2, 2024•0 citations
For quantum-information processing (QIP) with trapped ions, the isotope 43Ca+{^{43}\text{C}\text{a}}^{+}43Ca+ offers the combined advantages of a quantum memory with long coherence time, a high-fidelity readout, and the possibility of performing two-qubit gates on a quadrupole transition with a narrow-band laser. Compared to other ions used for quantum computing, 43Ca+{^{43}\text{C}\text{a}}^{+}43Ca+ has a relatively complicated level structure. We discuss how to meet the basic requirements for QIP and demonstrate ground-state cooling, robust state initialization, and efficient readout for the hyperfine qubit with a single 43Ca+{^{43}\text{C}\text{a}}^{+}43Ca+ ion. A microwave field and a Raman light field are used to drive qubit transitions, and the coherence times for both fields are compared. Phase errors due to interferometric instabilities in the Raman field generation do not limit the experiments on a time scale of 100 ms. We find a quantum-information storage time of many seconds for the hyperfine qubit.
Over the last decade quantum information processing (QIP) has exploded into a major field of physics, studied both experimentally and theoretically with a universal quantum computer as a long-term vision. Ions stored as strings in linear Paul traps are among the most promising systems for constructing a quantum device harnessing the computing power inherent in the laws of quantum physics. The two most important challenges in trapped ion quantum computing today are to realize and control systems with large numbers of ions, and to improve and integrate the operations which serve as basic building blocks, in particular universal gate operations. Quite surprisingly, even after many years of intense research with different atom species, it is still not evident which ion is best suited for QIP. This thesis describes the construction of a new experiment built to study a promising candidate qubit, namely the calcium isotope 43Ca+. Due to its nuclear spin of I = 7/2, the isotope 43Ca+ exhibits a relatively complicated level structure, compared to other ions used so far for QIP. This work develops various strategies to successfully control such a complex level scheme. Initially we investigated the hyperfine structure of the 4s S1/2 ↔ 3d D5/2 quadrupole transition at a wavelength of 729 nm by laser spectroscopy using a single trapped 43Ca+ ion. We determined the hyperfine structure constants of the metastable level as AD5/2 = −3.893 12(3)MHz and BD5/2 = −4.239(1)MHz. The isotope shift of this transition with respect to 40Ca+ was measured to be ∆ iso /(2π) = 4 134 711 720(390)Hz. Armed with this knowledge, we were able to demonstrate ground-state cooling, robust state initialization and efficient readout of a qubit encoded in the ground-state hyperfine structure of a 43Ca+ ion. A microwave and a Raman light field were used to drive qubit transitions, and the coherence times for both fields were compared. Phase errors due to interferometric instabilities in the Raman field generation were not limiting the experiments on a time scale of at least 100ms. Even in the presence of magnetic field fluctuations we found a quantum information storage time exceeding one second. We implemented a Molmer-Sorensen type gate operation, entangling ions with a fidelity of 99.3(1)%. The gate was performed on a pair of qubits encoded in two trapped 40Ca+ ions using an amplitude-modulated laser beam interacting with both ions at the same time. A robust gate operation, mapping separable states onto maximally entangled states was achieved by adiabatically switching the laser-ion coupling on and off. The performance of a single gate and concatenations of up to 21 gate operations were analyzed. Concerning the fidelity, this result sets a world record for creating two-qubit entanglement on-demand irrespective of the physical realization considered. Zusammenfassung Die Quanteninformationsverarbeitung (QIV) als experimentelles und theoretisches Teilgebiet der Physik mit dem universellen Quantencomputer als Fernziel entwickelte sich innerhalb der letzten Dekade geradezu explosionsartig. Fur die technische Realisierung einer Maschine zur Ausnutzung der den Gesetzen der Quantenmechanik eigenen Rechenkraft gibt es eine Vielzahl an Moglichkeiten. Ionen, die sich in linearen Paul-Fallen wie auf einer Perlenschnur aufreihen, haben sich dabei mittlerweile als sehr vielversprechenden Ansatz etabliert. Die beiden grosten Herausforderungen der Ionenfallen-Experimente zur QIV bestehen gegenwartig in der Skalierung zu einer Vielzahl kontrollierter Quantenbits und in der Verbesserung und Integration der bereits demonstrierten Grundbausteine, insbesondere universeller Gatteroperationen. Uberraschenderweise ist auch nach vielen Jahren intensiver Forschung unklar, welche Ionen-Sorte zu diesem Zweck am besten geeignet ist. Die vorliegende Arbeit beschreibt den Aufbau eines neuen Experiments zur Untersuchung des Calciumisotops 43Ca+ als attraktiven Kandidaten. Aufgrund des Kernspins von I = 7/2 hat das Isotop 43Ca+, verglichen mit Atomsorten, die bisher fur die QIV verwandt wurden, ein komplizierteres Energieniveauschema. Diese Arbeit diskutiert die daraus resultierenden Moglichkeiten und beschreibt deren experimentelle Realisierung, so dass diese Komplexitat erfolgreich genutzt werden kann. Zunachst wurde die Hyperfein-Struktur des 4s S1/2 ↔ 3d D5/2 Quadrupol-Ubergangs bei einer Wellenlange von 729 nm mittels Laserspektroskopie an einem einzelnen 43Ca+Ion untersucht. Die Hyperfein-Konstanten des metastabilen Energieniveaus wurden zu AD5/2 = −3.893 12(3)MHz, BD5/2 = −4.239(1)MHz bestimmt. Als Nebenprodukt ergab sich die Isotopieverschiebung auf diesem Ubergang bezogen auf 40Ca+ zu ∆ iso /(2π) = 4 134 711 720(390)Hz. Mit diesem Wissen gelang es einzelne 43Ca+-Ionen nahe an den Bewegungsgrundzustand einer Mode zu kuhlen, sowie 43Ca+-Hyperfein-Qubits mit hoher Gute zu initialisieren und auszulesen. Die Koharenzzeiten dieses Hyperfein-Qubits wurden mit einem Mikrowellenfeld und einem Raman-Lichtfeld gemessen. Trotz der Anwesenheit magnetischer Storfelder konnte Quanteninformation uber eine Sekunde gespeichert werden. Auserdem ergaben Messungen, dass die interferometrischen Stabilitatsanforderungen der Raman-Lichtfelder, auf einer Zeitskala von 100ms keine Limitierung darstellen. Die Arbeit schliest mit der Beschreibung einer Molmer-Sorensen Gatteroperation, die verschrankte Zustande mit einer Gute von 99.3(1)% erzeugte. Dieser Gattertyp wurde erstmals auf einem optischen Qubit mittels eines amplitudenmodulierten Lasers realisiert, der an zwei 40Ca+-Ionen gleichermasen koppelte. Eine robuste Gatteroperation, die separable in verschrankte Zustande uberfuhrt, wurde durch adiabatisches Anund Ausschalten dieses Lasers erreicht. Zur Bestimmung moglicher Fehlerquellen wurden bis zu 21 aneinandergereihte Gatteroperationen analysiert. Bezuglich der erreichten Gute stellt das Ergebnis die momentan beste deterministische Zwei-Qubit-Verschrankungsoperation aller bekannter Systeme dar.
We report on experiments with strings of laser-cooled Ca+ ions for quantum information processing. An experiment using the isotope 43Ca+ was set up from scratch. We devised techniques for loading and laser-cooling 43Ca+ ion strings, initializing the ions in the hyperfine clock states and reading out the quantum state with high efficiency. Coherence times of the qubits are about 1 s. The single-qubit gates were implemented using microwave and Raman excitation, and coupling to the motional state was demonstrated. Very recently, a pair of 43Ca+ ions were entangled for the first time. In a second line of experiments, we demonstrated simple quantum algorithms with few 40Ca+ ions as well as the implementation of a high-fidelity gate operation entangling a pair of ions with a fidelity of 99.3(1)%. Among the milestone experiments are the demonstration and quantum process tomography of a Cirac-Zoller gate with mean fidelity of about 93%, the demonstration of entanglement in a decoherence-free sub space lasting for 20s, the demonstration of deterministic quantum teleportation, a Toffoli gate, deterministic entanglement swapping a partial measurement of a GHZ state preserving entanglement in the remaining qubits, creation and analysis of an 8-ion W-state, the application of entangled ions for precision spectroscopy.
This thesis describes theoretical and experimental work whose main aim is the development of techniques for using trapped 43Ca⁺ ions for quantum information processing. I present a rate equations model of 43Ca⁺, and compare it with experimental data. The model is then used to investigate and optimise an electron-shelving readout method from a ground-level hyperfine qubit. The process is robust against common experimental imperfections. A shelving fidelity of up to 99.97% is theoretically possible, taking 100 μs. The laser pulse sequence can be greatly simplified for only a small reduction in the fidelity. The simplified method is tested experimentally with fidelities up to 99.8%. The shelving procedure could be applied to other commonly-used species of ion qubit. An entangling two-qubit quantum controlled-phase gate was attempted between a 40Ca⁺ and a 43Ca⁺ ion. The experiment did not succeed due to frequent decrystallisation of the ion pair, and strong motional decoherence. The source of the problems was never identified despite significant experimental effort, and the decision was made to suspend the experiments and continue them in an improved ion trap which is under construction. A sequence of pi-pulses, inspired by the Hahn spin-echo, was derived that is capable of greatly reducing dephasing of any qubit. If the qubit precession frequency varies with time as an nth-order polynomial, an (n+1) pulse sequence is theoretically capable of perfectly cancelling the resulting phase error. The sequence is used on a 43Ca+ magnetic-field-sensitive hyperfine qubit, with 20 pulses increasing the coherence time by a factor of 75 compared to an experiment without any spin-echo. In our ambient noise environment the well-known Carr-Purcell-Meiboom-Gill dynamic-decoupling method was found to be comparably effective.
Quantum information processing combines information theory with laws of quantum mechanics to provide an interesting new study that promises significant technological advances in the field of computation. The quest for a physical quantum information processor not only tests the limits of quantum mechanics but also motivates the development of new control techniques for quantum systems. This thesis documents the implementation of the necessary components of a quantum computer in a new atomic ion species, while demonstrating an entangling procedure that is uniquely insensitive to certain types of phase noise. Quantum bits are stored in the ground state hyperfine levels of individual trapped cadmium ions, and the collective vibration of the ions in the trap potential form a quantum databus through which information can be transferred. Quantum state measurements and initialization processes are accomplished through optical pumping, and quantum logic operations are performed through interactions with applied electromagnetic fields. The spin-dependent force, which is the underlying principle of many entanglement schemes for trapped ions, is investigated in detail in a series of Schrodinger cat experiments that generates entangled wavepackets well separated in the momentum-position phase space (alpha = 6). Phase control of the interaction in the gate scheme proposed by Molmer and Sorensen results in phase coherence between single-qubit rotations and a robust two-qubit entangling logic gate that can operate on magnetic-field insensitive clock qubits at finite temperature. The coherence time of the clock qubit (∼ 1s) is long compared to the gate time (∼ 100mus). Finally, quantum state tomography is performed on two ions, featuring a set of universal quantum logic gates that is sufficient for any quantum computation, with an entangling gate fidelity of 0.83. The combination of the tools developed here is sufficient to perform universal quantum computation. With the advent of scalable, multi-zone ion trap structures, the concept of a quantum computation device may become reality in the not so distant future.
Experiments with individual trapped ions are ideally suited to investigate fundamental issues of quantum mechanics such as the measurement process. At the same time electrodynamically trapped ions have been used with great success to demonstrate quantum logic operations and are a candidate for scalable quantum computing. In this article a brief introduction is given to the basic steps that constitute a quantum measurement; in particular, measurements on single quantum systems are considered. Then experiments with single Yb+ are reviewed demonstrating the quantum Zeno paradox, as well as an experiment where an adaptive algorithm for quantum state estimation of qubits was implemented. In the last section of this article -- devoted to experiments and new ideas related to quantum information processing (QIP) with trapped ions -- the realization of various quantum channels using a hyperfine qubit of Yb+ is briefly discussed. Then a concept for QIP with trapped ions is reviewed where rf or microwave radiation is used instead of laser light for coherent manipulation of a collection of ions. In a suitably modified trap the ions form an artificial ion "molecule" to which the techniques developed in nuclear magnetic resonance and electron spin resonance experiments can be directly applied. Finally, coherent excitation of optical electric quadrupole transitions in Yb+ and Ba+ is reported. In addition, robust Raman cooling of a pair of Ba+ ions is reviewed.
Coherent storage of quantum information is crucial to many quantum technologies. Long coherence times have been demonstrated in trapped-ion qubits, typically using the hyperfine levels within the ground state of a single ion. However, recent research suggests qubits encoded in metastable states could provide architectural benefits for quantum information processing, such as the possibility of effective dual-species operation in a single-species system and erasure-error conversion for fault-tolerant quantum computing. Here we demonstrate long-lived encoding of a quantum state in the metastable states of a trapped ion. By sympathetically cooling with another ion of the same species and constantly monitoring for erasure errors, we demonstrate a coherence time of 136(42) seconds with a qubit encoded in the metastable 5D5/25D_{5/2}5D5/2​ state of a single 137^{137}137Ba+^++ ion. In agreement with a model based on empirical results from dynamical-decoupling-based noise spectroscopy, we find that dephasing of the metastable levels is the dominant source of error once erasure errors are removed.