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arXiv:2210.09121 · Physical Review A

Realizing quantum gates with optically addressable Yb + 171 ion qudits

Mikhail A. Aksenov, Ilia V. Zalivako, Ilya A. Semerikov, A. S. Borisenko, Nikita V. Semenin, Pavel Sidorov, Aleksey K. Fedorov, Ksenia Yu. Khabarova, N. Kolachevsky

Published May 23, 2023• 45 citations
arXivHTMLPDF

Abstract

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 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 $^{171}\mathrm{Yb}^{+}$ ion qudits.

DOI
10.1103/physreva.107.052612

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We demonstrate a quantum processor based on a 3D linear Paul trap for 171Y b+ions. The trap design provides high secular frequencies and low heating rate in the radial plane, which together with individual addressing and readout optical systems, allows realization of operations on up to 8 ions in a string. In each of 8 ions, we use four quantum states coupled by the E2 optical transition for qudit encoding, which makes our processor equivalent to a 16 qubit system. We present the results of benchmarking single- and two-qubit operations and realizing basic quantum algorithms, including Bernstein-Vazirani algorithm, Grover search as well as H2and LiH molecular simulations.
Recent developments in qudit-based quantum computing, in particular with trapped ions, open interesting possibilities for scaling quantum processors without increasing the number of physical information carriers. Here, we propose a method for compiling quantum circuits in the case, where qubits are embedded into qudits of experimentally relevant dimensionalities, d=3,...,8d=3,...,8d=3,...,8, for the trapped-ion platform. In particular, we demonstrate how single-qubit, two-qubit, and multiqubit gates can be realized using single-qudit operations and the $\text{M}\o{}\text{lmer-S}\o{}\text{rensen}$ (MS) gate as a basic two-particle operation. We expect that our findings are directly applicable to the current generation of trapped-ion-based qudit processors.
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.
Abstract Scalable quantum information processing with limited physical resources is a key challenge in the pursuit of practical quantum advantage. Here, we introduce an approach that encodes two qubits per ion, enabling an n -ion–2 n -qubit quantum processor by harnessing four internal levels of trapped ions. As a proof of principle, we demonstrate a universal 1-ion–2-qubit processor using the valence electron spin and nuclear spin of a single 171 Yb + ion, achieving gate fidelities exceeding 98% for both single- and two-qubit operations via quantum process tomography. Furthermore, we implement Grover’s algorithm with a success rate surpassing 99%, showing the system’s computational capability. Through robust optimal quantum control, we enhance gate robustness against amplitude and frequency fluctuations, critical for large-scale operation. We present scalable architectures leveraging both laser-free and laser-based entangling gates, revealing that intra-atomic electron–nuclear spin interactions can reduce the complexity of inter-atomic operations. By substituting inter-atomic gates with high-fidelity intra-atomic ones, our scheme significantly improves circuit performance. This work establishes a pathway to exponentially expand the Hilbert space of quantum processors, and represents an important advance toward scalable, high-capacity quantum computing.
Abstract The development of a universal fault-tolerant quantum computer that can solve efficiently various difficult computational problems is an outstanding challenge for science and technology. In this work, we propose a technique for an efficient implementation of quantum algorithms with multilevel quantum systems (qudits). Our method uses a transpilation of a circuit in the standard qubit form, which depends on the characteristics of a qudit-based processor, such as the number of available qudits and the number of accessible levels. This approach provides a qubit-to-qudit mapping and comparison to a standard realization of quantum algorithms highlighting potential advantages of qudits. We provide an explicit scheme of transpiling qubit circuits into sequences of single-qudit and two-qudit gates taken from a particular universal set. We then illustrate our method by considering an example of an efficient implementation of a 6-qubit quantum algorithm with qudits. In this particular example, we demonstrate how using qudits allows a decreasing amount of two-body interactions in the qubit circuit implementation. We expect that our findings are of relevance for ongoing experiments with noisy intermediate-scale quantum devices that operate with information carriers allowing qudit encodings, such as trapped ions and neutral atoms, as well as optical and solid-state systems.