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arXiv:2112.10655 · Physical Review A

Controlling long ion strings for quantum simulation and precision measurements

Florian Kranzl, Manoj K. Joshi, Christine Maier, Tiff Brydges, Johannes Franke, R. Blatt, Christian F. Roos

Published May 18, 2022• 32 citations
arXivHTMLPDF

Abstract

In order to better characterize the performance of trapped ion systems and ease the experimental difficulties of addressing individual ions, the authors apply carefully-timed pulse sequences to ion chains up to 51 ions long. These techniques allow them to generate entanglement between all neighboring ion pairs and to quantify and mitigate sources of decoherence in the chains.

DOI
10.1103/physreva.105.052426

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In order to better characterize the performance of trapped ion systems and ease the experimental difficulties of addressing individual ions, the authors apply carefully-timed pulse sequences to ion chains up to 51 ions long. These techniques allow them to generate entanglement between all neighboring ion pairs and to quantify and mitigate sources of decoherence in the chains.
We show that trapped ions can be used to simulate a highly symmetrical Hamiltonian with eigenstates naturally protected against local sources of decoherence. This Hamiltonian involves long-range coupling between particles and provides a more efficient protection than nearest neighbor models discussed in previous works. Our results open the perspective of experimentally realizing, in controlled atomic systems, complex entangled states with decoherence times up to 9 orders of magnitude longer than isolated quantum systems.
Trapped atomic ion systems are currently the most advanced platform for quantum information processing. Their long coherence times, pristine state initialization and detection, and precisely controllable and versatile interactions make them excellent quantum systems for experiments in quantum computation and quantum simulation. One of the more promising schemes for quantum computing consists of performing single and multi-qubit quantum gates on qubits in a linear ion crystal. Some of the key challenges of scaling such a system are the individual addressing of arbitrary subsets of ions and controlling the growing complexity of motional mode interactions as the number of qubits increases or when the gates are performed faster. Traditional entangling quantum gates between ion qubits use laser pulses to couple the qubit states to the collective motion of the crystal, thereby generating a spin-spin interaction that can produce entanglement between selected qubits. The intrinsic limitations on the performance of gates using this method can be alleviated by applying optimally shaped pulses instead of pulses with constant amplitude. This thesis explains the theory behind this pulse shaping scheme and how it is implemented on a chain of Yb ions held in a linear radiofrequency `Paul' trap. Several experiments demonstrate the technique in chains of two, three, and five ions using various types of pulse shapes. A tightly focused individual addressing beam allows us to apply the entangling gates to a target pair of ions, and technical issues related to such tight focusing are discussed. Other advantages to the pulse shaping scheme include a robustness against detuning errors and the possibility of suppressing undesirable coupling due to optical spillover on neighboring ions. Combined with ion shuttling, we harness these features to perform sequential gates to different qubit pairs in order to create genuine tripartite entangled states and demonstrate the programmable quantum information processing capability of our system.
Very long, one-dimensional ion chains are the basis for many applications, in particular in quantum information processing, and reliable diagnostics are needed to quantify them. To that purpose, we have experimentally tested Dubin's model for very long ion chains [Phys. Rev. E 55, 4017 (1997)] which describes the equilibrium state of a one-dimensional correlated system. For chains larger than 100 ions, this diagnostic allows us to determine the number of trapped ions with a precision of 8% in a 95% confidence interval, without counting individual ions. This measurement is based on the experimental determination of the ion-ion distance of the innermost particles and of the trapping potential along the ion chain direction. The agreement of the model with experiments allows one to determine the degree of local homogeneity of the ion crystal in the center of the chain.
Abstract High-fidelity operation of quantum computers requires precise knowledge of the physical system through characterization. For motion-mediated entanglement generation in trapped ions, it is crucial to have precise knowledge of the motional-mode parameters such as the mode frequencies and the Lamb–Dicke parameters. Unfortunately, the state-of-the-art mode-characterization schemes do not easily render the mode parameters in a sufficiently accurate and efficient fashion for large-scale devices, due to the unwanted excitation of adjacent modes in the frequency space when targeting a single mode, an effect known as the cross-mode coupling. Here, we develop an alternative scheme that leverages the degrees of freedom in pulse design for the characterization experiment such that the effects of the cross-mode coupling is actively silenced. Further, we devise stabilization methods to accurately characterize the Lamb–Dicke parameters even when the mode frequencies are not precisely known due to experimental drifts or characterization inaccuracies. We extensively benchmark our scheme in simulations of a three-ion chain and discuss the parameter regimes in which the shaped pulses significantly outperform the traditional square pulses.