I. V. Zalivako

Channel spectrum benchmarking (CSB) provides a robust framework for characterizing quantum gate fidelities while remaining insensitive to state preparation and measurement (SPAM) errors. Yet, current CSB implementations encounter fundamental challenges when reconstructing noisy eigenvalues, particularly in the presence of spectral degeneracies and off-diagonal noise components in the target gate's eigenbasis. These issues become especially pronounced in the strong noise regime for gates with fidelities around $90\%$. To address these limitations, we introduce an extended CSB model together with a fidelity estimate interval (FEI) -- an interval-valued estimate of the target gate fidelity. Numerical simulation demonstrates that FEI remains sufficiently narrow, with its midpoint reliably approximating the true fidelity. We further validate the protocol on a trapped-ion quantum processor by benchmarking two implementations of the three-qubit Toffoli gate. The results reveal a clear advantage of the qutrit-based implementation over its qubit-based counterpart.

Multiqubit Greenberger-Horne-Zeilinger (GHZ) state preparation is demonstrated on two to eight qubits in the chain of ten $^{171}Yb^+$ ions in the linear Paul trap with a sequence of single-qubit and two-qubit operations and pulsed dynamical decupling. Fidelity of the 8-qubit GHZ state is estimated to be $58.9 \pm 0.6\%$. The expected enhanced sensitivity of the parity oscillations phase to the analyzing pulse phase is observed. This result is a step towards a multi-ion optical clock with ytterbium ions with frequency averaging following $1/N$ scaling law in contrast to the slower $1/\sqrt{N}$ scaling for an ensemble of independent particles in case when the decoherence is dominated by the spontaneous decay.

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 $^{171}$Yb$^{+}$ ion qudits in a linear trap. The rich level structure of $^{171}$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 Molmer-Sorensen operation with a two-ququart system, which is formally equivalent to a universal gate-based four-qubit processor. Our results paves a way towards further studies of more efficient implementations of quantum algorithms with trapped-ion-based processors and, specifically, exploring properties of $^{171}$Yb$^{+}$ ion qudits.