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Computational Capabilities of the Trapped-Ion Quantum Computer

L. Schmid, Eisinger, Jurek, Daniel Schoenberger, Christian D. Marciniak, Janine Hilder, Ulrich Poschinger, Robert Wille, Ferdinand Schmidt‐Kaler

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Trapped-ion quantum computer hardware is scaling to larger qubit numbers, but the computational capabilities of these devices remain largely unknown. From an abstract computer-science perspective, we address this problem in a two-step approach: First, we categorize levels of qubit connectivity for a processor based on ion-shuttling and individual ion addressing. Second, we apply computer-science techniques to develop optimized compilers that map arbitrary algorithms to sequences of ion-register reconfiguration and gate operations. We present compilers for 1D and 2D architectures, optimizing cost functions such as the qubit reconfiguration effort.

DOI
10.18420/se2026-ws_21

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Trapped-ion quantum computer hardware is scaling to larger qubit numbers, but the computational capabilities of these devices remain largely unknown. From an abstract computer-science perspective, we address this problem in a two-step approach: First, we categorize levels of qubit connectivity for a processor based on ion-shuttling and individual ion addressing. Second, we apply computer-science techniques to develop optimized compilers that map arbitrary algorithms to sequences of ion-register reconfiguration and gate operations. We present compilers for 1D and 2D architectures, optimizing cost functions such as the qubit reconfiguration effort.
Shuttling-based trapped-ion quantum computers (QCCD) rank among the most mature hardware platforms. Existing and envisaged devices exhibit architectural differences in terms of register layout and connectivity. Platform-specific compilers are required to translate quantum circuits into resource-optimized hardware-level command chains. Hardware platforms and compiler software stacks are mostly developed independently of one another by different research communities. This work aims to bridge these communities by abstracting QCCD architectures and native operations, enabling computer scientists to address compilation problems using generic methods without requiring a deep background in the physical operating principles of the platform. The resulting design space is organized into a small set of architectural archetypes, each posing its own compilation problem. We then select and apply compilation methods to one- and two-dimensional QCCD architectures, finding that the routing overhead scales approximately cubically with the number of qubits for the one-dimensional architecture and approximately quadratically for the two-dimensional one. Extending this to compilation with a quantum error-correction layer reveals additional differences and similarities between the physical and logical levels. We conclude that co-design is a requirement rather than an option, and this work provides the vocabulary, archetypes, and compilation abstraction it needs.
Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to implement a particular algorithm or execute a limited number of computational paths. Here, we demonstrate a five-qubit trapped-ion quantum computer that can be programmed in software to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates. We compile algorithms into a fully-connected set of gate operations that are native to the hardware and have a mean fidelity of 98 %. Reconfiguring these gate sequences provides the flexibility to implement a variety of algorithms without altering the hardware. As examples, we implement the Deutsch-Jozsa (DJ) and Bernstein-Vazirani (BV) algorithms with average success rates of 95 % and 90 %, respectively. We also perform a coherent quantum Fourier transform (QFT) on five trappedion qubits for phase estimation and period finding with average fidelities of 62 % and 84 %, respectively. This small quantum computer can be scaled to larger numbers of qubits within a single register, and can be further expanded by connecting several such modules through ion shuttling or photonic quantum channels.
The increasing capabilities of quantum computing hardware and the challenge of realizing deep quantum circuits require fully automated and efficient tools for compiling quantum circuits. To express arbitrary circuits in a sequence of native gates specific to the quantum computer architecture, it is necessary to make algorithms portable across the landscape of quantum hardware providers. In this work, we present a compiler capable of transforming and optimizing a quantum circuit targeting a shuttling-based trapped-ion quantum processor. It consists of custom algorithms set on top of the quantum circuit framework Pytket. The performance was evaluated for a wide range of quantum circuits and the results show that the gate counts can be reduced by factors up to 5.1 compared to standard Pytket and up to 2.2 compared to standard Qiskit compilation.
Quantum computers can solve certain problems more efficiently compared to conventional classical methods. In the endeavor to build a quantum computer, several competing platforms have emerged that can implement certain quantum algorithms using a few qubits. However, the demonstrations so far have been done usually by tailoring the hardware to meet the requirements of a particular algorithm implemented for a limited number of instances. Although such proof of principal implementations are important to verify the working of algorithms on a physical system, they further need to have the potential to serve as a general purpose quantum computer allowing the flexibility required for running multiple algorithms and be scaled up to host more qubits. Here we demonstrate a small programmable quantum computer based on five trapped atomic ions each of which serves as a qubit. By optically resolving each ion we can individually address them in order to perform a complete set of single-qubit and fully connected two-qubit quantum gates and alsoperform efficient individual qubit measurements. We implement a computation architecture that accepts an algorithm from a user interface in the form of a standard logic gate sequence and decomposes it into fundamental quantum operations that are native to the hardware using a set of compilation instructions that are defined within the software. These operations are then effected through a pattern of laser pulses that perform coherent rotations on targeted qubits in the chain. The architecture implemented in the experiment therefore gives us unprecedented flexibility in the programming of any quantum algorithm while staying blind to the underlying hardware. As a demonstration we implement the Deutsch-Jozsa and Bernstein-Vazirani algorithms on the five-qubit processor and achieve average success rates of 95 and 90 percent, respectively. We also implement a five-qubit coherent quantum Fourier transform and examine its performance in the period finding and phase estimation protocol. We find fidelities of 84 and 62 percent, respectively. While maintaining the same computation architecture the system can be scaled to more ions using resources that scale favorably (O(N^2)) with the number of qubits N.
Abstract The field of quantum computing has grown from concept to demonstration devices over the past 20 years. Universal quantum computing offers efficiency in approaching problems of scientific and commercial interest, such as factoring large numbers, searching databases, simulating intractable models from quantum physics, and optimizing complex cost functions. Here, we present an 11-qubit fully-connected, programmable quantum computer in a trapped ion system composed of 13 171 Yb + ions. We demonstrate average single-qubit gate fidelities of 99.5 %\%% % , average two-qubit-gate fidelities of 97.5 %\%% % , and SPAM errors of 0.7 %\%% % . To illustrate the capabilities of this universal platform and provide a basis for comparison with similarly-sized devices, we compile the Bernstein-Vazirani and Hidden Shift algorithms into our native gates and execute them on the hardware with average success rates of 78 %\%% % and 35 %\%% % , respectively. These algorithms serve as excellent benchmarks for any type of quantum hardware, and show that our system outperforms all other currently available hardware.
An algorithm for the generation of shuttling sequences is necessary for the operation of a linear segmented ion-trap quantum computer. The present work provides an implementation of an algorithm that produces sequences proved to be optimal for circuits with a quantum Fourier transform-like structure. Such optimality was proved in previous work of our group. We first present an approach for qubit mapping, i.e. determining the initial ordering of the ions, termed the common ion order, and develop a heuristic algorithm for its implementation. We explain how this heuristic is integrated in the shuttling sequence generation algorithm described in the previous work. The results show the increased performance of the heuristic in terms of reducing the number of required shuttling operations. The number of ion displacements required exhibits a polynomial increase in terms of the number of qubits, such that these operations become the main contribution to the overall resource cost. Furthermore, we show that multiple zones for gate interactions can reduce the amount of qubit register reordering.