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Physical Review Applied

Fast Molmer-Sørensen gates in trapped-ion quantum processors with compensated carrier transition

Evgeny V. Anikin, Andrey Chuchalin, N. V. Morozov, Olga Lakhmanskaya, Kirill Lakhmanskiy

Published Jul 1, 2025• 1 citation
Publisher
DOI
10.1103/kbwc-t19c

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Carrier transition is one of the major factors hindering the high-speed implementation of the Mølmer-Sørensen gates in trapped-ion quantum processors. We present an approach to design laser pulse shapes for the Mølmer-Sørensen gate in ion chains which accounts for the effect of carrier transition on qubit-phonon dynamics. We show that the fast-oscillating carrier term effectively modifies the spin-dependent forces acting on ions, and this can be compensated by a simple nonlinear transformation of a laser pulse. Using numerical simulations for short ion chains and perturbation theory for longer chains up to 202020 ions, we demonstrate that our approach allows to reach the infidelity below 10−410^{-4}10−4 while keeping the gate duration of the order of tens of microseconds.
High-fidelity two-qubit entangling gates are essential for the realization of useful quantum algorithms on quantum processors. The Mølmer-Sørensen (MS) gate has become a common choice for trapped-ion quantum computing due to its resilience to ion temperature and its demonstrated record fidelities. However, the spectral impurity of the driving laser field impacts gate performance, with phase noise influencing the qubit dynamics through mechanisms operating on different timescales. In this work, we present a comprehensive theoretical analysis of laser phase noise in the MS gate, identifying two spectral ranges which influence the gate fidelity the most: "fast" noise at frequencies near the motional mode spectrum, and "slow" noise at frequencies on the order of the inverse gate time. We derive the noise Hamiltonians for two common laser beam geometries and obtain analytical expressions for the average gate error in terms of the laser noise power spectral density and gate parameters. For slowly varying noise spectra, we provide simplified error estimates. In addition, we validate our findings against previously published numerical simulations.
Qudits, or multi-level quantum information carriers, present a promising path for scaling quantum computers. However, their use introduces increased complexity in quantum logic, necessitating careful control of relative phases between different qudit levels. In trapped-ion systems, entangling operations accumulate phases on specific levels that are no longer global, unlike in qubit architectures. Furthermore, the structure of multi-level gates becomes increasingly intricate with higher-dimensional Hilbert spaces. This work explores the theory of these additional local and nonlocal phases, accumulated in Mølmer--Sørensen and Light-shift gates. We propose methods to actively compensate for these phases, enhance gate robustness against parameter fluctuations, and simplify native gates for more efficient circuit decomposition. Our results pave the way toward the practical and scalable implementation of qudit-based quantum processors.
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 171Yb+^{171}\mathrm{Yb}^{+}171Yb+ ion qudits in a linear trap. The rich level structure of 171Yb+^{171}\mathrm{Yb}^{+}171Yb+ 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 M\o{}lmer-S\o{}rensen 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 171Yb+^{171}\mathrm{Yb}^{+}171Yb+ ion qudits.