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arXiv:0810.1036 · Physical Review A

Memory coherence of a sympathetically cooled trapped-ion qubit

Jonathan Home, M. J. McDonnell, D. J. Szwer, B. C. Keitch, D. M. Lucas, Derek N. Stacey, Andrew M. Steane

Published May 22, 2009• 51 citations
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Abstract

We demonstrate sympathetic cooling of a ${^{43}\text{C}\text{a}}^{+}$ trapped-ion ``memory'' qubit by a ${^{40}\text{C}\text{a}}^{+}$ ``coolant'' ion sufficiently near the ground state of motion for fault-tolerant quantum logic, while maintaining coherence of the qubit. This is an essential ingredient in trapped-ion quantum computers. The isotope shifts are sufficient to suppress decoherence and phase shifts of the memory qubit due to the cooling light which illuminates both ions. We measure the qubit coherence during ten cycles of sideband cooling, finding a coherence loss of 3.3% per cooling cycle. The natural limit of the method is $O({10}^{\ensuremath{-}4})$ infidelity per cooling cycle.

DOI
10.1103/physreva.79.050305

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We demonstrate sympathetic cooling of a 43Ca+{^{43}\text{C}\text{a}}^{+}43Ca+ trapped-ion memory'' qubit by a ${^{40}\text{C}\text{a}}^{+}$ coolant'' ion sufficiently near the ground state of motion for fault-tolerant quantum logic, while maintaining coherence of the qubit. This is an essential ingredient in trapped-ion quantum computers. The isotope shifts are sufficient to suppress decoherence and phase shifts of the memory qubit due to the cooling light which illuminates both ions. We measure the qubit coherence during ten cycles of sideband cooling, finding a coherence loss of 3.3% per cooling cycle. The natural limit of the method is O(10\ensuremath−4)O({10}^{\ensuremath{-}4})O(10\ensuremath−4) infidelity per cooling cycle.
A quantum memory is an essential element for quantum computation, quantum network and quantum metrology. Previously, a single-qubit quantum memory with a coherence time of about an hour has been realized in a dual-species setup where a coolant ion provides sympathetic cooling for a memory ion of different species. However, the frequent random position hopping between the ions in the room-temperature trap limits the technique there only applicable to single-qubit storage. Here we report a multi-ion quantum memory in a cryogenic trap based on the dual-type scheme, and demonstrate a coherence time above two hours for a logical qubit encoded in the decoherence-free subspace, i.e. two-ion entangled states, after correcting the dominant leakage error. Our scheme alleviates the necessity of an ultra-stable frequency reference for the stored qubit, and has a preferable scalability owing to the same mass of the metastable-state memory ions and the ground-state coolant ion.
Sympathetic cooling of data qubits by coolant ions is an essential technique for trapped-ion quantum computing. Conventionally a second ion species is used, requiring additional lasers and complicating optical setups. We propose a scheme for sympathetic cooling using the same species and test it for 43^{43}43Ca+^++ ions. Pulsed sideband cooling and ion addressing are implemented via integrated microwave control, further simplifying optical requirements. We cool a two-ion gate mode close to its ground state (nˉ≈0.16\bar{n}\approx 0.16nˉ≈0.16) and benchmark an induced error on the data qubit of 1.7(4)×10−41.7(4)\times 10^{-4}1.7(4)×10−4 per cooling cycle.
Owing to their high controllability and connectivity, one-dimensional ion chains are attractive building blocks for near-term quantum computers. However, long ion chains are susceptible to motional heating caused by fluctuating external electric fields. To enable deep computations, this source of noise must be suppressed without inducing qubit decoherence or degrading qubit connectivity. We demonstrate steady-state mid-circuit sympathetic cooling of all computationally-relevant motional modes of a 23-ion chain consisting of \qubit qubit and \coolant coolant ions without using any qubit operations. In a room-temperature system, our cooling scheme preserves the mean phonon occupations of the long-wavelength axial and radial modes near their values following state preparation, while keeping the modes used to implement entangling gates near their ground states throughout a 56-ms circuit. Crucially, we show that our cooling sequence preserves qubit coherence, and evaluate its impact on single- and two-qubit gate operations. Additionally, we demonstrate a parallel qubit reset protocol leveraging the shared radial mode coupling between species. Our sympathetic cooling scheme represents a critical step toward reducing gate errors in individually-addressed long ion chains and establishes a versatile platform for simulating open quantum systems.
Sympathetic cooling is a technique often employed to mitigate motional heating in trapped-ion quantum computers. However, choosing system parameters such as number of coolants and cooling duty cycle for optimal gate performance requires evaluating trade-offs between motional errors and other slower errors such as qubit dephasing. The optimal parameters depend on cooling power, heating rate, and ion spacing in a particular system. In this study, we aim to analyze best practices for sympathetic cooling of long chains of trapped ions using analytical and computational methods. We use a case study to show that optimal cooling performance is achieved when coolants are placed at the center of the chain and provide a perturbative upper bound on the cooling limit of a mode given a particular set of cooling parameters. In addition, using computational tools, we analyze the trade-off between the number of coolant ions in a chain and the center-of-mass mode heating rate. We also show that cooling as often as possible when running a circuit is optimal when the qubit coherence time is otherwise long. These results provide a roadmap for how to choose sympathetic cooling parameters to maximize circuit performance in trapped-ion quantum computers using long chains of ions. Published by the American Physical Society 2024
High-fidelity quantum logic operations in trapped ions often require the ions' collective motion to be cooled to near the ground state. Since cooling the ions' motion typically involves dissipative processes such as spontaneous photon scattering, sympathetic cooling is used on select coolant ions between gate sequences to cool the ion chain without affecting the data qubits. Common implementations for coolant ions include different atomic species, different isotopes of the same species or individually addressable ions. Each of these approaches have challenges associated with them, which include increased hardware complexity, reduced efficiency of radial mode cooling and re-ordering events which add additional experimental overhead. We demonstrate a sympathetic cooling scheme leveraging internal metastable atomic levels accessible via a narrow quadrupole transition, utilizing the natural Zeeman shift and individually addressed Raman transitions, to achieve isolation of the non-coolant or ``data ions" from coolant ions. We demonstrate modest decoherence of the data ions due to cooling, while preserving the coherence requirements for high-fidelity gate operations.
A quantum memory is an essential element for quantum computation, quantum networks, and quantum metrology. Previously, a single-qubit quantum memory with a coherence time of about an hour has been realized in a dual-species setup where a coolant ion provides sympathetic cooling for a memory ion of a different species. However, the frequent random position hopping between the ions in the room-temperature trap limits the technique to be applicable only to single-qubit storage. Here, we report a multi-ion quantum memory in a cryogenic trap based on the dual-type scheme and demonstrate a coherence time above two hours for a qubit encoded in the decoherence-free subspace, i.e., two-ion entangled states, after correcting the dominant leakage error. Our scheme alleviates the necessity of an ultrastable frequency reference for the stored qubit, and it has a preferable scalability owing to the same mass of the metastable-state memory ions and the ground-state coolant ion.