MUSS-TI: Multi-Level Shuttle Scheduling

• The paper introduces MUSS-TI, a compiler framework that hierarchically schedules qubit movement in heterogeneous zones to reduce shuttle operations.
• It employs dependency DAGs, locality-aware replacement, and SWAP heuristics to optimally map qubits within storage, operation, and optical zones.
• Empirical evaluations report 41–73% shuttle count reduction and improved execution times, especially for communication-intensive circuits.

Searching arXiv for the specified paper and closely related work to ground the article in current literature. Multi-Level Shuttle Scheduling (MUSS-TI) is a compiler and scheduling framework for large-scale entanglement-module-linked trapped-ion systems that targets the reduction of shuttling overhead in entanglement module linked Quantum Charge-Coupled Device (EML-QCCD) architectures. In this setting, multiple QCCD units are interconnected through entanglement module, and each unit contains heterogeneous zones with distinct roles: storage zones, operation zones, and optical or entanglement zones. MUSS-TI treats ion movement across these zones as a hierarchy-management problem analogous to multi-level memory scheduling in classical systems: qubits are kept as close as possible to where they will be used, moved only when necessary, and displaced via locality-aware replacement when scarce higher-functionality zones are full. The framework is specialized to the asymmetry of EML-QCCD rather than to homogeneous QCCD layouts, and its central reported outcome is a substantial reduction in shuttle operations across small, medium, and large benchmark classes (Wu et al., 30 Sep 2025).

1. Architectural context and compilation target

MUSS-TI is defined for EML-QCCD, a modular trapped-ion design in which multiple QCCD modules are connected by optical fibers through entanglement modules (Wu et al., 30 Sep 2025). Each QCCD is partitioned into three functionally distinct zone types. Storage zones hold idle qubits. Operation zones support local gate execution, especially high-quality two-qubit gates. Optical or entanglement zones support inter-QCCD communication via fiber-mediated entanglement and also allow internal two-qubit gates. This separation is a defining architectural assumption of MUSS-TI.

The compiler’s target problem is not generic qubit mapping but compilation under heterogeneous-zone constraints, finite zone capacities, gate dependencies, and both intra-module and inter-module communication modes. Intra-module communication is realized by shuttling ions among zones within a QCCD. Inter-module interaction can instead be realized photonicly between optical zones of different QCCDs. A two-qubit interaction therefore does not necessarily require physical co-location: the compiler may either move ions locally into a suitable zone or exploit optical zones for remote interaction across modules.

The hardware model used in the MUSS-TI study assigns explicit timings and fidelity surrogates to the primitive operations. A shuttle consists of split, move, and merge. The reported parameters are split: $80\,\mu s$, $\bar n = 1$; move: $2\,\mu m/\mu s$, $\bar n = 0.1$; swap: $40\,\mu s$, $\bar n = 0.3$; merge: $80\,\mu s$, $\bar n = 1$. Gate operations are modeled as 1-qubit gate: $5\,\mu s$, fidelity $0.9999$; 2-qubit gate: $\bar n = 1$0, fidelity $\bar n = 1$1; fiber entangle: $\bar n = 1$2, fidelity $\bar n = 1$3, where $\bar n = 1$4 is the number of qubits currently in the trap and $\bar n = 1$5. Shuttle fidelity is modeled as $\bar n = 1$6, with $\bar n = 1$7 and $\bar n = 1$8. If gate $\bar n = 1$9 executes in zone $2\,\mu m/\mu s$0, with zone background fidelity $2\,\mu m/\mu s$1, the effective fidelity is $2\,\mu m/\mu s$2 (Wu et al., 30 Sep 2025).

These assumptions position shuttling as both a latency source and a reliability hazard. That emphasis aligns with prior trapped-ion work showing that repeated shuttle operations increase quantum bit energy and degrade computation fidelity in shared multi-trap systems, with victim fidelity degradation reported in the range of approximately $2\,\mu m/\mu s$3X to $2\,\mu m/\mu s$4X under shuttle-exploiting attacks (Saki et al., 2021). MUSS-TI does not adopt that security framing, but the shared conclusion is that shuttle behavior must be elevated to a primary compilation concern rather than treated as a local routing afterthought.

2. Multi-level scheduling model

The phrase “multi-level shuttle scheduling” in MUSS-TI is explicit: the compiler draws an analogy to multi-level memory scheduling, with zone roles interpreted as a hierarchy (Wu et al., 30 Sep 2025). The reported levels are:

• Level 0: storage zone, analogous to external storage
• Level 1: operation zone, analogous to internal memory
• Level 2: optical zone, analogous to CPU

The scheduler tries to keep qubits in the highest useful level consistent with future use. If a qubit needed for a gate is not in the appropriate zone, it is promoted upward in the hierarchy. If the destination zone is full, another qubit is evicted to a lower level using a replacement policy. This makes shuttle decisions hierarchy-aware rather than purely gate-local.

The immediate consequence is zone-role awareness. Storage is cheap but cannot directly support all operations. Operation zones are intended for local high-quality gates. Optical zones are scarce but critical for remote communication. MUSS-TI therefore distinguishes between computation-heavy qubits, which should migrate toward operation zones, communication-heavy qubits, which may require optical-zone access, and idle qubits, which should be demoted to storage zones. The paper presents this as a departure from earlier QCCD schedulers that treated trap regions more homogeneously (Wu et al., 30 Sep 2025).

This hierarchy-centric view has a broader scheduling interpretation. The paper on “Multi-stage Flow Scheduling for LLM Serving” frames a related principle as “defer-and-promote”: slack-rich work should begin at low priority and be promoted only as urgency matures, implemented through a Reverse Multi-Level Queue (Sun et al., 18 Mar 2026). MUSS-TI does not import that mechanism directly. A plausible implication is that both frameworks treat scarce high-value resources as levels in a hierarchy and attempt to preserve them for work whose structural role justifies immediate service. In MUSS-TI, the scarce resources are higher-functionality zones rather than network priority queues.

3. Scheduling procedure and core heuristics

MUSS-TI operates on a dependency DAG constructed from the input quantum circuit, where each gate is a node and a directed edge $2\,\mu m/\mu s$5 indicates that $2\,\mu m/\mu s$6 depends on $2\,\mu m/\mu s$7 (Wu et al., 30 Sep 2025). Nodes with zero in-degree form the frontier, and frontier gates are the candidates for scheduling. Single-qubit gates are largely ignored during the key scheduling stages.

The compiler pipeline is described as: input circuit, dependency graph construction, initial mapping, iterative gate scheduling, qubit routing and zone selection, conflict handling or eviction, optional SWAP insertion, and output of an executable schedule with shuttles and gates. The DAG construction complexity is stated as $2\,\mu m/\mu s$8, where $2\,\mu m/\mu s$9 is the number of gates.

Gate selection proceeds in two stages. Among frontier gates, MUSS-TI first prioritizes gates already executable under the current physical placement. If no frontier gate is immediately executable, it uses a first-come, first-served policy. The reported complexity for gate selection is $\bar n = 0.1$0, where $\bar n = 0.1$1 is the number of qubits. This heuristic explicitly favors execution-ready work so as to avoid unnecessary qubit movement (Wu et al., 30 Sep 2025).

Once a gate is selected, the compiler performs qubit routing and target-zone selection. The chosen zone is prioritized by functional compatibility, availability, and proximity in level. The text does not define a formal distance metric, but it specifies that the preference is toward zones closest in “level” that can execute the gate. Reported complexity for this phase is $\bar n = 0.1$2, where $\bar n = 0.1$3 is the number of zones in one device.

When the chosen destination zone is full, MUSS-TI resolves the conflict through replacement. The replacement policy is LRU (Least Recently Used): the qubit that has not been used for the longest time is evicted. The evicted qubit is then moved down to the nearest lower suitable level; if that lower level is also full, the conflict handling recurses. The reported complexity of this step is $\bar n = 0.1$4, where $\bar n = 0.1$5 is the zone capacity. Combining the per-gate work gives $\bar n = 0.1$6, which the paper states as the overall worst-case complexity (Wu et al., 30 Sep 2025).

Two initial mapping options are provided. The trivial mapping places qubits in zone order from highest level to lowest. The SABRE-inspired alternative applies a two-fold search: build the forward DAG $\bar n = 0.1$7, start from trivial mapping $\bar n = 0.1$8, execute to get $\bar n = 0.1$9, use $40\,\mu s$0 as the initial mapping for reversed graph $40\,\mu s$1, execute $40\,\mu s$2, obtain $40\,\mu s$3, then use $40\,\mu s$4 as the improved initial mapping for forward execution. The notation $40\,\mu s$5, $40\,\mu s$6, $40\,\mu s$7, $40\,\mu s$8, and $40\,\mu s$9 is given explicitly in the paper (Wu et al., 30 Sep 2025).

4. SWAP insertion and locality management

A distinctive component of MUSS-TI is its inter-QCCD SWAP insertion heuristic (Wu et al., 30 Sep 2025). The purpose is not merely to satisfy hardware constraints, but to improve future locality after remote interactions. Following a remote gate between qubits $\bar n = 0.3$0 and $\bar n = 0.3$1 located on different QCCDs, the compiler may swap logical identities so that a qubit with near-future interactions on another QCCD is effectively relocated there.

The heuristic is driven by a look-ahead weight table $\bar n = 0.3$2, where $\bar n = 0.3$3 is the number of gates within the first $\bar n = 0.3$4 DAG layers involving qubit $\bar n = 0.3$5 and qubits located on QCCD $\bar n = 0.3$6. The paper sets $\bar n = 0.3$7. After a remote gate involving $\bar n = 0.3$8 and $\bar n = 0.3$9, the compiler checks whether $80\,\mu s$0, meaning $80\,\mu s$1 has no near-future use on its current QCCD $80\,\mu s$2, and whether there exists another QCCD $80\,\mu s$3 such that $80\,\mu s$4, together with a qubit $80\,\mu s$5 on $80\,\mu s$6 satisfying $80\,\mu s$7. If so, the compiler inserts a SWAP between $80\,\mu s$8 and $80\,\mu s$9. The same logic is applied symmetrically to $\bar n = 1$0. The threshold is required to satisfy $\bar n = 1$1, because a SWAP typically costs three MS gates, and the experiments set $\bar n = 1$2. The complexity of deciding SWAP insertion is reported as $\bar n = 1$3 (Wu et al., 30 Sep 2025).

The paper notes that larger $\bar n = 1$4 is not always better. Too much look-ahead may reveal that a qubit is still needed locally, which can suppress beneficial SWAPs. In the ablation study, SWAP insertion alone gives only small gains under trivial placement, SABRE gives larger gains, and SABRE plus SWAP insertion gives the best fidelity (Wu et al., 30 Sep 2025). This indicates that initial placement and forward-looking relocation are complementary rather than interchangeable.

This locality-management perspective is consistent with the paper’s stated analogy to cache and memory hierarchy. It also echoes, at a conceptual level, the design lesson from multi-program trapped-ion systems that initial placement and dynamic shuttle policy must be coordinated because placement decisions shape future shuttle demand, shuttle direction, and reliability outcomes (Saki et al., 2021). MUSS-TI operationalizes that coordination in a compiler for modular EML-QCCD rather than in a shared multi-program QCCD setting.

5. Evaluation methodology and empirical behavior

The evaluation compares MUSS-TI against three baselines: QCCDsim / Murali et al. (ISCA 2020), Dai et al. 2024 “Advanced Shuttle Strategies for Parallel QCCD Architectures,” and MQT / Schoenberger et al.’s scalable QCCD shuttling compiler (Wu et al., 30 Sep 2025). Benchmarks are drawn from prior QCCD work and QASMBench and include Adder_32, BV_32, GHZ_32, QAOA_32, QFT_32, and SQRT_30. The benchmark sizes span $\bar n = 1$5 to $\bar n = 1$6 qubits and $\bar n = 1$7 to $\bar n = 1$8 two-qubit gates.

The experiments group workloads into three scales: small, covering 30–32 qubits; medium, covering 117–128 qubits; and large, covering 256–299 qubits. Architecture sizes are scaled accordingly: small experiments use $\bar n = 1$9 and $5\,\mu s$0 QCCD grids, medium uses a $5\,\mu s$1 grid, and large uses a $5\,\mu s$2 grid. For small-scale comparison, trap capacity is 12 on $5\,\mu s$3 and 8 on $5\,\mu s$4. For larger simulations, trap capacity is often set to 16, with one optical zone, one operation zone, and two storage zones per QCCD. The number of QCCDs grows dynamically with application size, and a new $5\,\mu s$5 QCCD grid is added when total qubit count exceeds a multiple of 32 (Wu et al., 30 Sep 2025).

The metrics are shuttle count, execution time, and fidelity. Fidelity is computed as the product of individual operation fidelities under the model described earlier. The headline reductions in shuttle count are reported as $5\,\mu s$6 for applications with 30–32 qubits, $5\,\mu s$7 on average for applications with 117–128 qubits, and $5\,\mu s$8 on average for applications with 256–299 qubits (Wu et al., 30 Sep 2025). Reported average execution-time reductions are $5\,\mu s$9 for small, $0.9999$0 for medium, and $0.9999$1 for large workloads.

The detailed small-scale table shows large benchmark-specific differences. On a $0.9999$2 grid, Adder_32 is reduced from $0.9999$3 shuttle counts across the three baselines to $0.9999$4 under MUSS-TI; BV_32 from $0.9999$5 to $0.9999$6; GHZ_32 from $0.9999$7 to $0.9999$8; QAOA_32 from $0.9999$9 to $\bar n = 1$00; QFT_32 from $\bar n = 1$01 to $\bar n = 1$02; and SQRT_30 from $\bar n = 1$03 to $\bar n = 1$04. On a $\bar n = 1$05 grid, Adder_32 is reduced from $\bar n = 1$06 to $\bar n = 1$07; BV_32 from $\bar n = 1$08 to $\bar n = 1$09; GHZ_32 from $\bar n = 1$10 to $\bar n = 1$11; QAOA_32 from $\bar n = 1$12 to $\bar n = 1$13; QFT_32 from $\bar n = 1$14 to $\bar n = 1$15; and SQRT_30 from $\bar n = 1$16 to $\bar n = 1$17. The paper also notes a case where Adder_32 on $\bar n = 1$18 improves from $\bar n = 1$19 and $\bar n = 1$20 fidelity to $\bar n = 1$21 and $\bar n = 1$22 fidelity (Wu et al., 30 Sep 2025).

The reported gains are strongest for communication-intensive applications, with SQRT exceeding $\bar n = 1$23 improvement in some settings, whereas communication-light or nearest-neighbor-like circuits such as QAOA show smaller improvements. The look-ahead sensitivity study reports that larger $\bar n = 1$24 can help when communication distances are long, but nearest-neighbor circuits are almost insensitive to $\bar n = 1$25. The trap-capacity study identifies a non-monotonic fidelity relationship: too small a trap capacity increases shuttling, whereas too large a trap worsens two-qubit gate fidelity because larger ion chains reduce $\bar n = 1$26. The best fidelity is often achieved around 14 to 18 qubits per trap, slightly below the 15–25 range cited for near-term QCCD in prior work (Wu et al., 30 Sep 2025).

6. Relation to adjacent scheduling literatures and limitations

MUSS-TI is best understood as a hardware-specialized compiler for modular trapped-ion systems with heterogeneous zones and photonic interconnects rather than as a general-purpose shuttle scheduler (Wu et al., 30 Sep 2025). Its central abstraction is a zone hierarchy, not a general vehicle-routing or flow-shop abstraction. Even so, several adjacent scheduling literatures illuminate its structure.

The paper on “Joint Machine-Transporter Scheduling for Multistage Jobs with Adjustable Computation Time” studies a joint machine-transporter scheduling problem for multistage jobs in which transporters are assigned to one job until completion, time is discretized, and candidate schedules are solved in a sliding time window by ILP (Khateri et al., 2023). That work is not directly transferable to MUSS-TI because it assumes a dedicated transporter per job and does not model the detailed trapped-ion movement network. Nevertheless, it provides a useful analogue for viewing shuttle-mediated execution as a multistage precedence-constrained scheduling problem with resource capacities. This suggests that MUSS-TI occupies a similar design space at the compiler level, but with zone functionality and ion-chain physics replacing generic machine and transporter resources.

The 2026 HLP paper uses “shuttle buses” in a different sense: elongated rotated surface-code patches that mediate sparse long-range logical interactions only once every $\bar n = 1$27 level-0 rounds (Chen et al., 21 Jun 2026). That work is not about ion shuttling inside QCCD. However, it contributes a genuinely multi-level scheduling viewpoint in which local frequent activity and sparse higher-level interactions are separated in time. A plausible implication is that both MUSS-TI and HLP treat expensive communication mechanisms as scarce higher-level resources whose use must be structured around architectural asymmetry.

The transit literature on integrated timetabling, vehicle scheduling, and dynamic capacity allocation under demand uncertainty introduces another meaning of multi-level scheduling, coordinating timetable, formation sizing, unit circulation, recourse, and rolling-horizon replanning (Xia et al., 2024). MUSS-TI does not include stochastic demand, rolling horizons, or scenario-based recourse. Still, the common theme is that the true conserved resource is not a monolithic vehicle or module, but a set of heterogeneous subresources whose deployment must be jointly optimized.

The limitations of MUSS-TI are explicit. The main design assumes one optical or entanglement zone per QCCD in most experiments, although a later study finds that two entanglement zones usually improve fidelity by distributing communication load and reducing local heating. The method is heuristic rather than optimal: gate selection, routing, eviction, and SWAP insertion are local and greedy. The fidelity model is simplified, based on multiplicative proxies $\bar n = 1$28, $\bar n = 1$29, and $\bar n = 1$30, rather than a full physical simulation. Results depend on the architectural assumptions of distinct storage, operation, and optical zones, fixed fiber-entanglement latency and fidelity, and the specialization of high-functionality zones to operation and optical roles. The strongest gains appear in communication-heavy circuits, while communication-light circuits benefit less (Wu et al., 30 Sep 2025).

Taken together, these characteristics define MUSS-TI as a zone-role-aware, modular-architecture-aware compilation strategy for EML-QCCD. Its primary contribution is not merely a heuristic reduction in shuttle count, but the reframing of trapped-ion qubit movement as a hierarchy-management problem in which functionality, capacity, locality, and future communication patterns determine when and where shuttling should occur (Wu et al., 30 Sep 2025).