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arXiv:quant-ph/0702175

On the Transport of Atomic Ions in Linear and Multidimensional Ion Trap Arrays

David Hucul, Mark Yeo, W. K. Hensinger, James Rabchuk, Steven Olmschenk, Christopher R. Monroe

Published Feb 16, 2007• 2 citations
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Abstract

Trapped atomic ions have become one of the most promising architectures for a quantum computer, and current effort is now devoted to the transport of trapped ions through complex segmented ion trap structures in order to scale up to much larger numbers of trapped ion qubits. This paper covers several important issues relevant to ion transport in any type of complex multidimensional rf (Paul) ion trap array. We develop a general theoretical framework for the application of time-dependent electric fields to shuttle laser-cooled ions along any desired trajectory, and describe a method for determining the effect of arbitrary shuttling schedules on the quantum state of trapped ion motion. In addition to the general case of linear shuttling over short distances, we introduce issues particular to the shuttling through multidimensional junctions, which are required for the arbitrary control of the positions of large arrays of trapped ions. This includes the transport of ions around a corner, through a cross or T junction, and the swapping of positions of multiple ions in a laser-cooled crystal. Where possible, we make connections to recent experimental results in a multidimensional T junction trap, where arbitrary 2-dimensional transport was realized.

DOI
10.48550/arxiv.quant-ph/0702175

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Trapped atomic ions have become one of the most promising architectures for a quantum computer, and current effort is now devoted to the transport of trapped ions through complex segmented ion trap structures in order to scale up to much larger numbers of trapped ion qubits. This paper covers several important issues relevant to ion transport in any type of complex multidimensional rf (Paul) ion trap array. We develop a general theoretical framework for the application of time-dependent electric fields to shuttle laser-cooled ions along any desired trajectory, and describe a method for determining the effect of arbitrary shuttling schedules on the quantum state of trapped ion motion. In addition to the general case of linear shuttling over short distances, we introduce issues particular to the shuttling through multidimensional junctions, which are required for the arbitrary control of the positions of large arrays of trapped ions. This includes the transport of ions around a corner, through a cross or T junction, and the swapping of positions of multiple ions in a laser-cooled crystal. Where possible, we make connections to recent experimental results in a multidimensional T junction trap, where arbitrary 2-dimensional transport was realized.
Trapped atomic ions have become one of the most promising architectures for a quantum computer, and current effort is now devoted to the transport of trapped ions through complex segmented ion trap structures in order to scale up to much larger numbers of trapped ion qubits. This paper covers several important issues relevant to ion transport in any type of complex multidimensional rf (Paul) ion trap array. We develop a general theoretical framework for the application of time-dependent electric fields to shuttle laser-cooled ions along any desired trajectory, and describe a method for determining the effect of arbitrary shuttling schedules on the quantum state of trapped ion motion. In addition to the general case of linear shuttling over short distances, we introduce issues particular to the shuttling through multidimensional junctions, which are required for the arbitrary control of the positions of large arrays of trapped ions. This includes the transport of ions around a corner, through a cross or T junction, and the swapping of positions of multiple ions in a laser-cooled crystal. Where possible, we make connections to recent experimental results in a multidimensional T junction trap, where arbitrary 2-dimensional transport was realized.
Trapped atomic ions have become one of the most promising architectures for a quantum computer, and current effort is now devoted to the transport of trapped ions through complex segmented ion trap structures in order to scale up to much larger numbers of trapped ion qubits. This paper covers several important issues relevant to ion transport in any type of complex multidimensional rf (Paul) ion trap array. We develop a general theoretical framework for the application of time-dependent electric fields to shuttle laser-cooled ions along any desired trajectory, and describe a method for determining the effect of arbitrary shuttling schedules on the quantum state of trapped ion motion. In addition to the general case of linear shuttling over short distances, we introduce issues particular to the shuttling through multidimensional junctions, which are required for the arbitrary control of the positions of large arrays of trapped ions. This includes the transport of ions around a corner, through a cross or T junction, and the swapping of positions of multiple ions in a laser-cooled crystal. Where possible, we make connection to recent experimental results in a multidimensional T junction trap, where arbitrary 2-dimensional transport was realized.
We demonstrate a two-dimensional 11-zone ion trap array, where individual laser-cooled atomic ions are stored, separated, shuttled, and swapped. The trap geometry consists of two linear rf-ion trap sections that are joined at a 90° angle to form a T-shaped structure. We shuttle a single ion around the corners of the T-junction and swap the positions of two crystallized ions using voltage sequences designed to accommodate the nontrivial electrical potential near the junction. Full two-dimensional control of multiple ions demonstrated in this system may be crucial for the realization of scalable ion trap quantum computation and the implementation of quantum networks.
We demonstrate a two-dimensional 11-zone ion trap array, where individual laser-cooled atomic ions are stored, separated, shuttled, and swapped. The trap geometry consists of two linear rf-ion trap sections that are joined at a 90° angle to form a T-shaped structure. We shuttle a single ion around the corners of the T-junction and swap the positions of two crystallized ions using voltage sequences designed to accommodate the nontrivial electrical potential near the junction. Full two-dimensional control of multiple ions demonstrated in this system may be crucial for the realization of scalable ion trap quantum computation and the implementation of quantum networks.
We have demonstrated transport of 9{}^{9}9Be+{}^{+}+ions through a two-dimensional Paul-trap array that incorporates an X junction, while maintaining the ions near the motional ground state of the confining potential well. We expand on the first report of the experiment in Blakestad et al. [Phys. Rev. Lett. 102, 153002 (2009)], including a detailed discussion of how the transport potentials were calculated. Two main mechanisms that caused motional excitation during transport are explained, along with the methods used to mitigate such excitation. We reduced the motional excitation below the results in the above reference by a factor of approximately 50. The effect of a mu-metal shield on qubit coherence is also reported. Finally, we examined a method for exchanging energy between multiple motional modes on the few-quanta level, which could be useful for cooling motional modes without directly accessing the modes with lasers. These results establish how trapped ions can be transported in a large-scale quantum processor with high fidelity.
Shuttle-based trapped ion quantum processors typically employ a one-dimensional (1D) linear architecture to transport ion-qubits between one ore more laser interaction zones where the quantum gates are implemented, along with several qubit register storage segments. The two-dimensional (2D) quantum CCD architecture employs also T- or X-junctions for an improved scaling and efficiency. Here, we explore the shuttling layer in the compilation of quantum algorithm typical building blocks in such architecture. To weight the effort of linear shuttle and junction shuttle, we introduce individual cost functions for each operation. This allows comparing the total cost for quantum circuit building blocks such as the QFT, Carry, Adder, Shift, and Comparator circuits. We study their scaling properties with increased qubit numbers. At equivalent transport cost for junction and linear shuttling, we show that 2D architectures outperform the 1D linear trap with the ratio improving as the number of ions increases. Finally, we discuss the use of cells, such that the entire processor is constructed from a 2D array of such interconnected cells. The work aims to optimize quantum processor architectures, implementing a co-design that fits to the specific task and scaling up in a shuttle-efficient way.