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arXiv:quant-ph/0609228 · Physical Review Letters

Process Tomography of Ion Trap Quantum Gates

Mark Riebe, Kihwan Kim, Philipp Schindler, Thomas Monz, Piet O. Schmidt, Th. Körber, W. Hänsel, Hartmut Häffner, Christian F. Roos, R. Blatt

Published Dec 1, 2006• 195 citations
arXivHTMLPDF

Abstract

A crucial building block for quantum information processing with trapped ions is a controlled-NOT quantum gate. In this Letter, two different sequences of laser pulses implementing such a gate operation are analyzed using quantum process tomography. Fidelities of up to 92.6(6)% are achieved for single-gate operations and up to 83.4(8)% for two concatenated gate operations. By process tomography we assess the performance of the gates for different experimental realizations and demonstrate the advantage of amplitude-shaped laser pulses over simple square pulses. We also investigate whether the performance of concatenated gates can be inferred from the analysis of the single gates.

DOI
10.1103/physrevlett.97.220407

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A crucial building block for quantum information processing with trapped ions is a controlled-NOT quantum gate. In this Letter, two different sequences of laser pulses implementing such a gate operation are analyzed using quantum process tomography. Fidelities of up to 92.6(6)% are achieved for single-gate operations and up to 83.4(8)% for two concatenated gate operations. By process tomography we assess the performance of the gates for different experimental realizations and demonstrate the advantage of amplitude-shaped laser pulses over simple square pulses. We also investigate whether the performance of concatenated gates can be inferred from the analysis of the single gates.
Abstract We present a framework for quantum process tomography of two-ion interactions that leverages modulations of the trapping potential and composite pulses from a global laser beam to achieve individual-ion addressing. Tomographic analysis of identity and delay processes reveals dominant error contributions from laser decoherence and slow qubit frequency drift during the tomography experiment. We use this framework on two co-trapped 40 Ca + ions to analyze both an optimized and an overpowered Mølmer–Sørensen gate and to compare the results of this analysis to a less informative Bell-state tomography measurement and to predictions based on a simplified noise model. These results show that the technique is effective for the characterization of two-ion quantum processes and for the extraction of meaningful information about the errors present in the system. The experimental convenience of this method will allow for more widespread use of process tomography for characterizing entangling gates in trapped-ion systems.
Highly-localized light-matter interactions are necessary for scaling trapped-ion architectures. In hyperfine qubits, counterpropagating beams generate entangling gates by coupling with motion, but this effect is undesirable during single-qubit operations. For that reason, single-qubit gates are traditionally implemented with copropagating beams, and the coexistence of two beam geometries adds hardware and computational overhead. In an effort towards collective performance improvement with minimal overhead, we design and implement pulse-amplitude and dephasing robust dynamically corrected gates using Space Curve Quantum Control (SCQC) and compare them against the constant-amplitude gate implementation. We perform gate set tomography on a four-qubit trapped-ion register, and we discover more than 50% error reduction when robust pulses are used. We find that counterpropagating robust gates often outperform their copropagating counterparts and reach error rates as low as (3.59±1.25)⋅10−3(3.59 \pm 1.25)\cdot 10^{-3}(3.59±1.25)⋅10−3, using diamond distance as a metric. This value establishes a laser-driven-gate error reference and is merely an order of magnitude higher than the best reported microwave\textit{microwave}microwave gate on a single\textit{single}single ion. Additional experiments reveal that robust pulses can effectively suppress non-Markovian errors that grow during runtime. Our work challenges the widely accepted belief that copropagating gates should be preferred for their weak motional coupling and invites the adoption of high-performance robust pulses that suppress multiple noise sources of the trapped-ion error budget.
Quantum information processing is performed with single trapped Ca(+) ions, stored in a linear Paul trap and laser-cooled to the ground state of their harmonic quantum motion. Composite laser-pulse sequences were used to implement SWAP gate, phase gate and controlled-NOT gate operations. Stark shifts on the quantum-bit transitions were precisely measured and compensated. For a demonstration of quantum information processing, a Deutsch-Jozsa algorithm has been implemented using two quantum bits encoded on a single ion.
We demonstrate single-qubit operations by transporting a beryllium ion with a controlled velocity through a stationary laser beam. We use these to perform coherent sequences of quantum operations, and to perform parallel quantum logic gates on two ions in different processing zones of a multiplexed ion trap chip using a single recycled laser beam. For the latter, we demonstrate individually addressed single-qubit gates by local control of the speed of each ion. The fidelities we observe are consistent with operations performed using standard methods involving static ions and pulsed laser fields. This work therefore provides a path to scalable ion trap quantum computing with reduced requirements on the optical control complexity.
Many efforts are currently underway to build a device capable of large scale quantum information processing (QIP). Whereas QIP has been demonstrated for a few qubits in several systems, many technical difficulties must be overcome in order to construct a large-scale device. In one proposal for large-scale QIP, trapped ions are manipulated by precisely controlled light pulses and moved through and stored in multizone trap arrays. The technical overhead necessary to precisely control both the ion geometrical configurations and the laser interactions is demanding. Here we propose methods that significantly reduce the overhead on laser-beam control for performing single- and multiple-qubit operations on trapped ions. We show how a universal set of operations can be implemented by controlled transport of ions through stationary laser beams. At the same time, each laser beam can be used to perform many operations in parallel, potentially reducing the total laser power necessary to carry out QIP tasks. The overall setup necessary for implementing transport gates is simpler than for gates executed on stationary ions. We also suggest a transport-based two-qubit gate scheme utilizing microfabricated permanent magnets that can be executed without laser light.
In ion traps, entangling gate operations can be realized by a bichromatic pair of laser beams that collectively interact with the ions. In this paper, a new method of modelling the laser–ion interaction is introduced that turns out to be superior to standard techniques for the description of gate operations on optical qubits. The treatment allows for a comparison of the performance of gates based on σ z ⊗σ z and σ ϕ ⊗σ ϕ interactions on optical transitions where the bichromatic laser field can be realized by an amplitude-modulated laser resonant with the qubit transition. Shaping the amplitude of the bichromatic laser pulse is shown to make the gates more robust against experimental imperfections.