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.

Mid-circuit measurement of individual qubits is a necessary element in the implementation of quantum error correction protocols and allows for the reduction of resource requirements for the execution of a number of quantum algorithms. In this paper, we present a protocol for mid-circuit measurement of qubits implemented at an optical transition $$^{2}{{S}_{{1/2}}}(F = 0,{{m}_{F}} = 0){{ \to }^{2}}{{D}_{{3/2}}}(F = 2,{{m}_{F}} = 0)$$ in ions ¹⁷¹ Yb ⁺ . The proposed protocol enables selective measurement of a subset of qubits (target qubits) without destroying the state of the rest (spectator qubits). The method involves the use of an auxiliary state $$^{2}{{D}_{{3/2}}}(F = 1)$$ , as well as a spin echo technique to maintain the coherence of the spectator qubits during the operation. The average reliability of the target qubit measurement operation of 98.2(1)% was experimentally demonstrated, while maintaining the amplitude of Ramsey oscillations on the spectator qubit at least 95.2(6)%. The proposed method does not require the movement of ions or the complication of the addressing system, due to which it can be implemented in a chain of ions of one type and easily integrated into existing quantum processors based on ¹⁷¹ Yb ⁺ . The capabilities of the developed protocol are demonstrated by an experimental implementation of CNOT gate teleportation.

In this work, we report a high-precision experimental determination of the ratio $g_{F,D}/g_{F,S}=0.998060\left(5\right)$ between the Landé g-factors for states ${}_{}{}^{2}S_{1/2}^{}(F=1)$ and ${}_{}{}^{2}D_{3/2}^{}(F=1)$ in ¹⁷¹Yb⁺. Together with the recently calculated g-factor of the ${}_{}{}^{2}S_{1/2}^{}$ state $g\left(S_{1/2}\right)=2.002615\left(70\right)$, this yields a value of $g\left(D_{3/2}\right)=0.79917\left(3\right)$ for ${}_{}{}^{2}D_{3/2}^{}$ with a precision more than an order of magnitude higher than that of previous measurements. The experiment was performed by microwave spectroscopy of hyperfine transitions in the ${}_{}{}^{2}S_{1/2}^{}$ and ${}_{}{}^{2}D_{3/2}^{}$ manifolds of trapped ions confined in a linear Paul trap. We also obtain the hyperfine splitting $W_{D_{3/2}}=857,178,077\left(3\right)$ Hz, agreeing with previous measurements. Precise knowledge of the ${}_{}{}^{2}D_{3/2}^{}$ state Landé g-factor is essential for evaluating systematic shifts in ¹⁷¹Yb⁺ optical clocks and for tests of fundamental theories using such frequency standards.