MUSS-TI: Multi-level Shuttle Scheduling for Large-Scale Entanglement Module Linked Trapped-Ion

TL;DR

This paper addresses the scalability bottleneck in trapped-ion quantum computing by introducing MUSS-TI, a multi-level shuttle scheduling compiler for entanglement module linked QCCD (EML-QCCD) devices. The method combines a DAG-based dependency representation, multi-level qubit routing, SWAP gate insertion with a look-ahead mechanism, and SABRE-inspired initial mapping to minimize shuttle moves and improve fidelity. Empirical results show substantial shuttle reductions across small to large circuits (up to ≈$73.38\%$), faster execution times, and improved fidelity, especially for communication-intensive workloads, with trade-offs in compilation time. The work advances practical large-scale modular trapped-ion platforms and highlights the benefits of zone-aware hardware design and co-optimized compilation for quantum scalability.

Abstract

Trapped-ion computing is a leading architecture in the pursuit of scalable and high fidelity quantum systems. Modular quantum architectures based on photonic interconnects offer a promising path for scaling trapped ion devices. In this design, multiple Quantum Charge Coupled Device (QCCD) units are interconnected through entanglement module. Each unit features a multi-zone layout that separates functionalities into distinct areas, enabling more efficient and flexible quantum operations. However, achieving efficient and scalable compilation of quantum circuits in such entanglement module linked Quantum Charge-Coupled Device (EML-QCCD) remains a primary challenge for practical quantum applications. In this work, we propose a scalable compiler tailored for large-scale trapped-ion architectures, with the goal of reducing the shuttling overhead inherent in EML-QCCD devices. MUSS-TI introduces a multi-level scheduling approach inspired by multi-level memory scheduling in classical computing. This method is designed to be aware of the distinct roles of different zones and to minimize the number of shuttling operations required in EML-QCCD systems. We demonstrate that EML-QCCD architectures are well-suited for executing large-scale applications. Our evaluation shows that MUSS-TI reduces shuttle operations by 41.74% for applications with 30-32 qubits, and by an average of 73.38% and 59.82% for applications with 117-128 qubits and 256-299 qubits, respectively.

Figures (13)

• Figure 1: Comparison of (a) Entanglement module linked and (b) QCCD grid architectures. Entanglement module linked trapped-ion device consists of multiple improved QCCD devices, which are connected by a fiber. Qubits in different traps can interact through the fiber to perform two-qubit gates.
• Figure 2: (a) The overview of entanglement module linked QCCD (EML-QCCD) devices. EML-QCCDs are interconnected via fibers, which enable communication between the qubits within different QCCDs. (b) The internal structure of EML-QCCD. Yellow traps are storage zones for qubits. Red traps form the operation zone, where qubits are fully connected and can undergo two-qubit gates. White traps represent the optical zone, connected via fibers to enable entanglement and two-qubit gate operations with qubits in other QCCDs' optical zones. Additionally, qubits within the optical zone can also perform two-qubit gates internally, similar to the operation zone. (c) Shuttle operation in QCCD. In the QCCD device, to meet the hardware limitations, shuttle operations are required to move qubits between traps. A complete shuttle operation consists of three steps: split, move, and merge.
• Figure 3: Illustration of the MUSS-TI framework.
• Figure 4: An example of MUSS-TI scheduling. Initially, we execute $g_0$ since it already meets the hardware requirement. Given that neither $g_1$ nor $g_2$ meets the requirements, we select $g_1$ on a first-come, first-served basis. Subsequently, we aim to pick a zone for $g_1$. Both zones at level 1 and level 2 are viable options; however, due to the shorter distance, $q_1$ is relocated to the level 2 zone where $q_0$ resides. Similarly, we select level 2 zone for $g_2$ and $q_3$ needs to be moved to the level 2 zone occupied by $q_2$. At this point, the level 2 zone has reached its capacity limit. Given that $q_0$ and $q_1$ have been recently utilized, we apply the LRU strategy to evict $q_4$ from the level 2 zone. In accordance with the Multi-level scheduling strategy, $q_4$ is then transferred to the level 1 zone. It is important to note that shuttling operations can only occur at the edges of the qubit chain. Therefore, to facilitate this movement, we employ SWAP gates to reconfigure the arrangement of the qubit chain.
• Figure 5: An example of SWAP gate insertion. By inserting a SWAP gate to transfer qubit $q_0$ to another trap, the number of shuttle operations can be effectively reduced. Moreover, the operational cost of two-qubit gates in the internal zone is significantly lower than that of fiber-entanglement operations in the optical zone.