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Trapped ions are among the leading platforms for quantum technologies, particularly in the field of quantum computing. Detecting states of trapped ions is essential for ensuring high-fidelity readouts of quantum states. In this work, we develop and benchmark a set of methods for ion quantum state detection using images obtained by a highly sensitive camera. By transforming the images from the camera and applying conventional and quantum machine learning methods, including convolution, support vector machine (classical and quantum), and quantum annealing, we demonstrate a possibility to detect the positions and quantum states of ytterbium ions in a Paul trap. Quantum state detection is performed with an electron shelving technique: depending on the quantum state of the ion its fluorescence under the influence of a 369.5 nm laser beam is either suppressed or not. We estimate fidelities for conventional and quantum detection techniques. In particular, conventional algorithms for detecting $^{171}$Yb$^{+}$, such as the support vector machine and photon statistics-based method,as well as our quantum annealing-based approach, have achieved perfect fidelity, which is beneficial compared to standard techniques. This result may pave the way for ultrahigh-fidelity detection of trapped ions via conventional and quantum machine learning techniques.

Qubit systems based on trapped ultracold ions win one of the leading positions in the quantum computing field, demonstrating quantum algorithms with the highest complexity to date. Surface Paul traps for ion confinement open the opportunity to scale quantum processors to hundreds of qubits and enable high-connectivity manipulations on ions. To fabricate such a system with certain characteristics, the special design of a surface electrode structure is required. The depth of the trapping potential, the stability parameter, the secular frequency and the distance between an ion and the trap surface should be optimized for better performance. Here we present the optimized design of a relatively simple surface trap that allows several important high-fidelity primitives: tight ion confinement, laser cooling, and wide optical access. The suggested trap design also allows to perform an important basic operation, namely, splitting an ion chain into two parts.

An efficient implementation of the Toffoli gate is of conceptual importance for running various quantum algorithms, including Grover's search and Shor's integer factorization. However, direct realizations of the Toffoli gate require either a prohibitive growth of the number of two-qubit gates or using ancilla qubits, whereas both of these resources are limited in the current generation of noisy intermediate-scale quantum devices. Here we experimentally demonstrate a scalable improvement of the realization of the Toffoli gate using $^{171}$Yb$^{+}$ trapped-ion-based dual-type optic-microwave qutrits ($d=3$) for the cases of three-, four-qubit and five-qubit versions of the Toffoli gate. With the use of the Molmer-Sorensen gate as a basic two-particle operation, we compare the standard qubit decomposition with the qutrit approach, where upper levels are used as ancillas. The presented decomposition requires only global control of the ancilla levels, which simplifies experimental implementation of the proposed approach. We present an estimation of the scalable improvement of our approach in the case of multi-qubit gates. As we expect, by combining this approach with the leveraging qudits ($d\geq4$) as a set of qubits, our approach may lead to a more efficient realization of various quantum algorithms. With qutrit-based decomposition in Grover's search with three ions, we experimentally demonstrate the 10\% increase in the average algorithm performance., Comment: 8+4 pages, 4+5 figures

Here we present the results of benchmarking of a quantum processor based on trapped $^{171}$Yb$^{+}$ ions by performing basic quantum machine learning algorithms. Specifically, we carry out a supervised binary classification of small-scale digits images, which are intentionally chosen so that they can be classified with 100% accuracy, using a quantum-enhanced Support Vector Machine algorithm with up to four qubits. In our work, we specifically consider different types of quantum encodings of the dataset and different levels of transpilation optimizations for the corresponding quantum circuits. For each quantum encoding, we obtain a classifier that is of 100% accuracy on both training and test sets, which demonstrates that the quantum processor can correctly solve the basic classification task considered. As we expect, with the increase of the capabilities quantum processors, they can become a useful tool for machine learning., Comment: 8 pages, 1 figure

We demonstrate a quantum processor based on a 3D linear Paul trap that uses $^{171}$Yb$^{+}$ ions with 8 individually controllable four-level qudits (ququarts), which is computationally equivalent to a 16-qubit quantum processor. The design of the developed ion trap provides high secular frequencies, low heating rate, which, together with individual addressing and readout optical systems, allows executing quantum algorithms. In each of the 8 ions, we use four electronic levels coupled by E2 optical transition at 435 nm for qudit encoding. We present the results of single- and two-qubit operations benchmarking and realizing basic quantum algorithms, including Bernstein-Vazirani and Grover's search algorithms as well as H$_2$ and LiH molecular simulations. Our results pave the way to scalable qudit-based quantum processors using trapped ions., Comment: 21 pages, 12 figures

Scalable quantum computers hold the promise to solve hard computational problems, such as prime factorization, combinatorial optimization, simulation of many-body physics, and quantum chemistry. While being key to understanding many real-world phenomena, simulation of non-conservative quantum dynamics presents a challenge for unitary quantum computation. In this work, we focus on simulating non-unitary parity-time symmetric systems, which exhibit a distinctive symmetry-breaking phase transition as well as other unique features that have no counterpart in closed systems. We show that a qutrit, a three-level quantum system, is capable of realizing this non-equilibrium phase transition. By using two physical platforms -- an array of trapped ions and a superconducting transmon -- and by controlling their three energy levels in a digital manner, we experimentally simulate the parity-time symmetry-breaking phase transition. Our results indicate the potential advantage of multi-level (qudit) processors in simulating physical effects, where additional accessible levels can play the role of a controlled environment., Comment: 20 pages, 10 figures

The use of multilevel quantum information carriers, also known as qudits, attracts a significant deal of interest as a way for further scalability of quantum computing devices. However, a nontrivial task is to experimentally achieve a gain in the efficiency of realizing quantum algorithms with qudits since higher qudit levels typically have relatively short coherence times compared to qubit states. Here we propose and experimentally demonstrate two approaches for the realization of continuous dynamical decoupling of magnetic-sensitive states with $m_F=\pm1$ for qudits encoded in optical transition of trapped $^{171}$Yb$^{+}$ ions. We achieve improvement in qudit levels coherence time by the order of magnitude (more than 9 ms) without any magnetic shielding, which reveals the potential advantage of the symmetry of the $^{171}$Yb$^{+}$ ion energy structure for counteracting the magnetic field noise. Our results are a step towards the realization of qudit-based algorithms using trapped ions., Comment: 12 pages, 5 figures

Trapped ions are one of the most promising platforms for quantum computing due to the longest qubit coherence times and the highest gate fidelities. However, scaling the number of ions (qubits) in a linear Coulomb crystal is the key difficulty on the way to multi-qubit systems. One of the promising pathways to scale the number of qubits is to implement the pulsed non-adiabatic gates based on the sequence of State Dependent Kicks (SDKs). We have analytically and numerically studied the influence of coherent effects in the SDK sequence and, correspondingly, have deduced the influence of the individual SDK error on the net gate fidelity. We have shown that the coherence effects significantly impact the fidelity of non-adiabatic gates and must be taken into the account. As practical examples, we have developed a numerical model for full simulation of coherence effects using a linear ion microtrap array and a 2D microtrap array. We have also studied the dependency of the gate fidelity on the laser power fluctuations., Comment: 10 pages, 7 figures

The paper describes the results achieved in the development of the compact transportable fully automated optical clock based on a single 171Yb+ ion in a radiofrequency (RF) quadrupole trap. The resulted measurements demonstrated the 4.9E-16 output RF signal relative instability on 1000 s integration time with 298.1 kg weight, 0.921 volume, and 2.766 kW input power consumption of the device. A transformation of the ultrastable optical signal into the RF range was performed via the optical frequency comb with a supercontinuum fiber laser generator. The transformation was conducted without loss of initial stability and accuracy characteristics of the signal., Comment: The paper has several serious issues in the 'Results and discussion' part, and should be withdrawn for time until the issues are fully corrected