Vasilii N. Smirnov

Here we present the results of benchmarking a quantum processor based on trapped $^{171}$Yb$^{+}$ ions by performing basic quantum machine learning algorithms. Using a quantum-enhanced support vector machine algorithm with up to five qubits we perform a supervised binary classification on two types of datasets: small binary digit images and weighted graphs with a ring topology. For the first dataset, images are intentionally selected so that they could be classified with 100% accuracy. This allows us to specifically examine different types of quantum encodings of the digit dataset and study the impact of experimental noise. In the second dataset, graphs are divided into two categories based on the spectral structure of their Ising Hamiltonian models, which is related to the NP-hard problem. For this problem we consider an embedding of an exponentially large Hamiltonian spectrum into an entangled state of a linear number of qubits. For both problems, we study various levels of circuit optimization and found that, for all experiments conducted, we achieve classifiers with 100% accuracy on both training and testing datasets. This demonstrates that the quantum processor has the ability to correctly solve the basic classification task under consideration. As we expect, with the increase in the capabilities of quantum processors, they can be utilized for solving machine learning tasks.

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.