The use of multilevel information carriers, also known as qudits, is a promising path for exploring scalability of quantum computing devices. Here we present a proof-of-principle realization of a quantum processor register that uses optically addressed ${}^{171}\mathrm{Yb}^{+}$ ion qudits in a linear trap. The rich level structure of ${}^{171}\mathrm{Yb}^{+}$ ions allows using the Zeeman sublevels of the quadrupole clock transition at 435.5 nm for efficient and robust qudit encoding. We demonstrate the realization of the universal set of gates consisting of single-qudit rotations and a two-qudit Mølmer-Sørensen operation with a two-ququart system, which is formally equivalent to a universal gate-based four-qubit processor. Our results paves a way toward further studies of more efficient implementations of quantum algorithms with trapped-ion-based processors and, specifically, exploring properties of ${}^{171}\mathrm{Yb}^{+}$ ion qudits.

We demonstrate a quantum processor based on a 3D linear Paul trap that uses ${}^{171}\mathrm{Yb}^{+}$ ions with eight individually controllable four-level qudits (ququarts), which is computationally equivalent to a sixteen-qubit quantum processor. The design of the developed ion trap provides high secular frequencies and a low heating rate, which, together with individual addressing and readout optical systems, allows executing quantum algorithms. In each of the eight 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 the Bernstein–Vazirani and Grover’s search algorithms as well as H₂ and LiH molecular simulations. Our results pave the way to scalable qudit-based quantum processors using trapped ions.

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 implementation of the Toffoli gate either entails a prohibitive increase in the number of two-qubit gates or requires 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 N-qubit Toffoli gate improvement using ^{171}Yb^{+} trapped-ion-based optical-metastable-ground encoded qutrits for the cases of up to N=10. With the use of the Mølmer-Sørensen gate as a basic entangling operation, we compare the standard qubit decomposition with the qutrit approach, where upper levels are used as ancillae. The presented decomposition requires only global control of the ancilla levels, which simplifies experimental implementation of the proposed approach. Using the example of a three-qubit Grover's search, we also demonstrate an increase in the algorithm's accuracy by monitoring the leakage from the qubit subspace during a qutrit-based Toffoli gate implementation.

A scheme based on a laser cooling system has been proposed to detect the state of an optical qubit in the ¹⁷¹Yb⁺ ion. Analytical expressions have been derived for the readout fidelity including the dark photon counts and background. The parameters of the experiment have been numerically optimized to minimize the readout infidelity. The upper bound on the fidelity associated with a transient process at the beginning of the measurement procedure has been determined as 99.4%. The characteristic parameters of detection ensuring a sufficient proximity to the upper bound have been found.

The optimization of the parameters of laser cooling and the investigation of the heating rate in ion traps require the measurement of the temperature of ion chains for which the Lamb–Dicke regime is satisfied. A novel method based on the investigation of the dynamics of Rabi oscillations at a narrow electron transition in an individual ion of the chain has been suggested for such measurement. An analytical expression for the population of the upper state as a function of the excitation time is derived taking into account the thermal distribution of phonons over the vibrational modes of a chain with an arbitrary number of ions. The method is tested experimentally for the chain of five $$^{{171}}{\text{Y}}{{{\text{b}}}^{ + }}$$ ions using the quadrupole transition at 435 nm, as well as for a single ion. The heating rate measured for the axial vibrational mode in the implemented trap is 8 × 10³ phonons/s.