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arXiv:1708.02634 · Physical Review A

Generation of high-fidelity quantum control methods for multilevel systems

J. Randall, A. M. Lawrence, S. C. Webster, Sebastian Weidt, Nikolay V. Vitanov, W. K. Hensinger

Published Oct 8, 2018• 39 citations
arXivHTMLPDF

Abstract

In recent decades there has been a rapid development of methods to experimentally control individual quantum systems. A broad range of quantum control methods has been developed for two-level systems; however, the complexity of multilevel quantum systems make the development of analogous control methods extremely challenging. Here we exploit the equivalence between multilevel systems with SU(2) symmetry and spin-1/2 systems to develop a technique for generating new robust, high-fidelity, multilevel control methods. As a demonstration of this technique, we develop adiabatic and composite multilevel quantum control methods and experimentally realize these methods using a $^{171}\mathrm{Yb}^{+}$ ion system. We measure the average infidelity of the process in both cases to be around ${10}^{\ensuremath{-}4}$, demonstrating that this technique can be used to develop high-fidelity multilevel quantum control methods and can, for example, be applied to a wide range of quantum computing protocols, including implementations below the fault-tolerant threshold in trapped ions.

DOI
10.1103/physreva.98.043414

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Qubits encoded within internal energy levels of atoms and ions have been used to demonstrate high-performance primitives of quantum computing for small numbers of qubits. Yet, the path to achieving sufficient size and fidelity for useful fault-tolerant quantum computation remains daunting. In this dissertation, I present several techniques I developed as steps along this path. These results include high-fidelity, low-loss detection for alkali atoms in optical tweezers, crosstalk-mitigated parallel one-qubit gates, robust entangling gates on trapped ions, and leakage-to-erasure conversion for non-destructive detection of atom loss errors. Through this collection of techniques, I have sought to make full use of the underlying atomic physics to alleviate technical burden in scaling up to large systems while maintaining or improving on qubit control fidelity. I emphasize that all these results are achieved with low technical overhead, allowing for direct implementation in systems at scale.
Abstract A major obstacle in the way of practical quantum computing is achieving scalable and robust high-fidelity entangling gates. To this end, quantum control has become an essential tool, as it can make the entangling interaction resilient to sources of noise. Nevertheless, it may be difficult to identify an appropriate quantum control technique for a particular need given the breadth of work pertaining to robust entanglement. To this end, we attempt to consolidate the literature by providing a non-exhaustive summary and critical analysis. The quantum control methods are separated into two categories: schemes which extend the robustness to (i) spin or (ii) motional decoherence. We choose to focus on extensions of the σ x ⊗ σ x Mølmer–Sørensen interaction using microwaves and a static magnetic field gradient. Nevertheless, some of the techniques discussed here can be relevant to other trapped ion architectures or physical qubit implementations. Finally, we experimentally realize a proof-of-concept interaction with simultaneous robustness to spin and motional decoherence by combining several quantum control methods presented in this manuscript.
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This PhD thesis reports on the development of a wide variety of theoretical and experimental capabilities in the field of quantum information processing using trapped ions. The presentation is organized in two distinct parts. The first part presents a series of published articles containing theoretical results, and their experimental validation, advancing a range of tools and techniques in error-resilient quantum control and robust verification procedures. One of the fundamental challenges in realizing a general purpose quantum computer is the management of error in fragile quantum systems. A familiar aspect of this challenge is decoherence, a process by which the system looses its stored quantum information, rendering it useless for subsequent computation. This collection of works focuses on reducing sources of quantum decoherence and precisely quantifying residual errors in real quantum systems dominated by realistic temporally-correlated noise processes, of central importance in any future architecture for quantum computing. The second part focuses on the design, construction and characterization of a complex experimental system capable of supporting a broad calls of quantum simulation experiments with hundreds of spin qubits using 9Be+ ions in a Penning trap. The trap design is optimized to suppress non-harmonic trapping potentials while providing wide optical access for engineering enhanced spin-motion coupling across large ion crystals. A superconducting magnet, equipped with a fully closed-cycle dual LN2/LHe recondensor, provides the magnetic field for trapping and produces the 55-GHz Zeeman-split qubit states suitable for microwave control. A custom UV laser system for driving the relevant transitions in neutral and ionized beryllium, as well as UV-compatible fibers and in-bore optomechanics for delivering microwave and laser beams to the trap, is presented. The thesis concludes with a brief outlook towards future theoretical and experimental studies, and extensions of the experimental setup
Here, we focus on using composite pulses to realize high-robustness and high-fidelity coherent control in three-level quantum systems. We design the dynamic parameters (Rabi frequency and detuning) for three-level Hamiltonians for high-fidelity quantum state control using five well-known coherent control techniques including a composite adiabatic passage (CAP). Furthermore, we compare their performance against the Rabi frequency and systematic errors, and accordingly show that the CAP is the most robust against them. It features a broad range of high efficiencies above 99.9%. Thus, it provides an accurate approach for manipulating the evolution of quantum states in three-level quantum systems.