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Construction of a ytterbium and lutetium ion trap and quantum control for multi-partite entanglement

Arjun D. Rao

Published Jan 1, 2024• 0 citations
OpenAlex

Abstract

The technology of linear ion traps are constantly innovating with increasingly varying atomic species being trapped in more scalable systems. In some iterations, multiple species can be confined, offering advanced computing capabilities such as sympathetic cooling. As the ion chains grow in size, the ion operations must scale with it, permitting universal quantum computation in larger qubit arrays. In this thesis, the design, construction and preliminary characterisation of a dual-species trapped-ion system is described. Additionally, an investigation into how entangling gates operate in these systems is performed. Laser setups at 355nm drive the spin-motion coupling in ytterbium ions to produce entanglement at high fidelities in longer chains. First, entangling gates are implemented in the ytterbium trapwith improvements to the control software. Primitive Mølmer-Sørensen gates are introducedand phase modulated gates using Q-CTRL’s graph based optimiser are implemented. Second, entanglement is computationally investigated in multipartite systems. Comparisons aredrawn between quantum control techniques such as laser modulation and Rabi rate imbalances are investigated.

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The technology of linear ion traps are constantly innovating with increasingly varying atomic species being trapped in more scalable systems. In some iterations, multiple species can be confined, offering advanced computing capabilities such as sympathetic cooling. As the ion chains grow in size, the ion operations must scale with it, permitting universal quantum computation in larger qubit arrays. In this thesis, the design, construction and preliminary characterisation of a dual-species trapped-ion system is described. Additionally, an investigation into how entangling gates operate in these systems is performed. Laser setups at 355nm drive the spin-motion coupling in ytterbium ions to produce entanglement at high fidelities in longer chains. First, entangling gates are implemented in the ytterbium trapwith improvements to the control software. Primitive Mølmer-Sørensen gates are introducedand phase modulated gates using Q-CTRL’s graph based optimiser are implemented. Second, entanglement is computationally investigated in multipartite systems. Comparisons aredrawn between quantum control techniques such as laser modulation and Rabi rate imbalances are investigated.
Quantum computing promises solutions to some of the world's most important problems that classical computers have failed to address. The trapped-ion-based quantum computing platform has a lot of advantages for doing so: ions are perfectly identical and near-perfectly isolated, feature long coherent times, and allow high-fidelity individual laser-controlled operations. One of the greatest remaining obstacles in trapped-ion-based quantum computing is the issue of scalability. The approach that we take to address this issue is a modular architecture: separate ion traps, each with a manageable number of ions, are interconnected via photonic links. To avoid photon-generated crosstalk between qubits and utilize advantages of different kinds of ions for each role, we use two distinct species - ¹⁷¹Yb⁺ as memory qubits and ¹³⁸Ba⁺ as communication qubits. The qubits based on ¹⁷¹Yb⁺ are defined within the hyperfine "clock" states characterized by a very long coherence time while ¹³⁸Ba⁺ ions feature visible-range wavelength emission lines. Current optical and fiber technologies are more efficient in this range than at shorter wavelengths. We present a theoretical description and experimental demonstration of the key elements of a quantum network based on the mixed-species paradigm. The first one is entanglement between an atomic qubit and the polarization degree of freedom of a pure single photon. We observe a value of the second-order correlation function g⁽²⁾(0) = (8.1 ± 2.3)⨉10⁻⁵ without background subtraction, which is consistent with the lowest reported value in any system. Next, we show mixed-species entangling gates with two ions using the Mølmer-Sørensen and Cirac-Zoller protocols. Finally, we theoretically generalize mixed-species entangling gates to long ion chains and characterize the roles of normal modes there. In addition, we explore sympathetic cooling efficiency in such mixed-species crystals. Besides these developments, we demonstrate new techniques for manipulating states within the D₃⸝₂-manifold of zero-nuclear-spin ions - a part of a protected qubit scheme promising seconds-long coherence times proposed by Aharon et al. in 2013. As a next step, we provide a detailed description of the protocols for three- and four-node networks with mixed species, along with a novel design for the third trap with in-vacuum optics to optimize light collection.
Quantum computing represents an exciting frontier in the realm of information processing; it is a promising technology that may provide future advances in a wide range of fields, from quantum chemistry to optimization problems. This thesis discusses experimental results for several quantum algorithms performed on a programmable quantum computer consisting of a linear chain of five or seven trapped 171Yb+ atomic clock ions with long coherence times and high gate fidelities. We execute modular one- and two-qubit computation gates through Raman transitions driven by a beat note between counter-propagating beams from a pulsed laser. The system's individual addressing capability provides arbitrary single-qubit rotations as well as all possible two-qubit entangling gates, which are implemented using a pulse-segmentation scheme. The quantum computer can be programmed from a high-level interface to execute arbitrary quantum circuits, and comes with a toolbox of many important composite gates and quantum subroutines. We present experimental results for a complete three-qubit Grover quantum search algorithm, a hallmark application of a quantum computer with a well-known speedup over classical searches of an unsorted database, and report better-than-classical performance. The algorithm is performed for all 8 possible single-result oracles and all 28 possible two-result oracles. All quantum solutions are shown to outperform their classical counterparts. Performing parallel operations will be a powerful capability as deeper circuits on larger, more complex quantum computers present new challenges. Here, we perform a pair of 2-qubit gates simultaneously in a single chain of trapped ions. We employ a pre-calculated pulse shaping scheme that modulates the phase and amplitude of the Raman transitions to drive programmable high-fidelity 2-qubit entangling gates in parallel by coupling to the collective modes of motion of the ion chain. Ensuring the operation yields only spin-spin interactions between the desired pairs, with neither residual spin-motion entanglement nor crosstalk spin-spin entanglement, is a nonlinear constraint problem, and pulse solutions are found using optimization techniques. As an application, we demonstrate the quantum full adder using a depth-4 circuit requiring the use of parallel 2-qubit operations.
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.
The high-fidelity multi-ion entangled states and quantum gates are the basis for trapped-ion quantum computing. Among the developed quantum gate schemes, Mølmer-Sørensen gate is a relatively mature experimental technique to realize multi-ion entanglement and quantum logic gates. In recent years, there have also been schemes to realize ultrafast quantum entanglement and quantum logic gates that operate outside the Lamb-Dicke regime by designing ultrafast laser pulse sequences. In such a many-body quantum system, these entanglement gates couple the spin states between ions by driving either the phonon energy level or the motional state of the ion chain. To improve the fidelity of quantum gates, the modulated laser pulses or the appropriately designed pulse sequences are applied to decouple the multi-mode motional states. In this review, we summarize and analyze the essential aspects of realizing these entanglement gates from both theoretical and experimental points of view. We also reveal that the basic physical process of realizing quantum gates is to utilize nonlinear interactions in non-equilibrium processes through driving the motional states of an ion chain with laser fields.
Scaling up controlled quantum systems to involve large numbers of qubits remains one of the outstanding challenges of quantum information science. One path toward scalability is the use of a modular architecture where adjacent qubits may be entangled with applied electromagnetic fields, and remote qubits may be entangled using photon interference. Trapped atomic ion qubits are one of the most promising platforms for scaling up quantum systems by combining long coherence times with high fidelity entangling operations between proximate and remote qubits. In this thesis, I present experimental progress on combining entanglement between remote atomic ions separated by 1 meter with near-eld entanglement between atomic ions in the same ion trap. I describe the experimental improvements to increase the remote entanglement rate by orders of magnitude to nearly 5 per second. This is the first experimental demonstration where the remote entanglement rate exceeds the decoherence rate of the entangled qubits. The flexibility of creating remote entanglement through photon interference is demonstrated by using the interference of distinguishable photons without sacrificing remote entanglement rate or fidelity. Next I describe the use of master clock in combination with a frequency comb to lock the phases of all laser-induced interactions between remote ion traps while removing optical phase stability requirements. The combination of both types of entanglement gates to create a small quantum network are described. Finally, I present ways to mitigate cross talk between photonic and memory qubits by using different trapped ion species. I show preliminary work on performing state detection of nuclear spin 0 ions by using entanglement between atomic ion spin and photon polarization. These control techniques may be important for building a large-scale modular quantum system.
Trapped atomic ions are among leading platforms in quantum information processing with their long coherence times and high fidelity quantum operations. Scaling up to larger numbers of qubits is a remaining major challenge. A network of trapped ion modules offers a promising solution by keeping a manageable number of qubits within a module while photonic interfaces connect separate modules together to increase the number of controlled memory qubits. Since the generation of entanglement between qubits in different modules is probabilistic, an excessive number of connection trials might result in decoherence on the memory qubits through absorption of stray photons. This crosstalk issue could be circumvented by introducing a different atomic species as photonic qubits. Compared to a system that only utilizes single species of atoms, there are also additional advantages in a multi-species apparatus where attractive features of each atom can be employed for certain tasks. In this thesis, I present experimental demonstrations of necessary ingredients of a multi-species module for quantum networking. In these experiments, barium ions are intended to be used as photonic communication qubits with visible photon emission lines that are more convenient for current fiber optics and detector technologies while ytterbium ions are used for storing and processing quantum information where long coherence times available in hyperfine clock states make them suitable memory qubits. The key experiments include demonstration of atom-photon entanglement using the barium qubit and utilizing the Coulomb interaction between ytterbium and barium with spin-dependent forces for transfer of information from communication to memory qubits.