MUSS-TI: Multi-Level Shuttle Scheduling for QCCD

• MUSS-TI is a multi-level shuttle scheduling compiler designed for optimizing ion shuttling in large-scale trapped-ion quantum computers.
• It employs a zone-aware mapping using storage, operation, and optical zones—modeled after memory hierarchies—to minimize shuttle overhead and latency.
• Evaluations show shuttle operation reductions of 41–73% across different system scales, leading to improved execution time and enhanced quantum gate fidelity.

Searching arXiv for the exact MUSS-TI paper and closely related EML-QCCD/QCCD compilation context. MUSS-TI is a multi-level shuttle scheduling compiler tailored to large-scale trapped-ion systems that interconnect Quantum Charge-Coupled Device (QCCD) units via photonic entanglement modules. It is designed for entanglement module linked Quantum Charge-Coupled Device (EML-QCCD) architectures, where multiple QCCD modules are connected by fibers and each module contains storage zones, operation zones, and optical or entanglement zones. Its primary goal is to reduce shuttling overhead, a dominant source of latency and fidelity loss in shuttling-based trapped-ion architectures, by making scheduling explicitly zone-aware and by adopting strategies inspired by multi-level memory scheduling in classical computing. In the reported evaluation, 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 (Wu et al., 30 Sep 2025).

1. Architectural setting and problem formulation

EML-QCCD organizes a trapped-ion device as multiple QCCD modules connected through photonic interconnects. Within each module, storage zones function as parking areas with minimal optics, operation zones provide fully connected local interaction areas for high-fidelity Mølmer–Sørensen (MS) two-qubit gates, and optical or entanglement zones host photonic interfaces for remote entanglement and also support local two-qubit gates among ions co-resident in the optical zone. This separation concentrates high-precision photon interfaces in a few specialized zones while avoiding long-range physical shuttling across a large monolithic grid (Wu et al., 30 Sep 2025).

MUSS-TI treats these zones through a memory-hierarchy analogy. Storage zones are mapped to “Level 0,” operation zones to “Level 1,” and optical zones to “Level 2.” Gates are scheduled so operands are brought into the highest-functionality zone required for execution, and when zones are full the compiler evicts the least recently used ion and demotes it to a lower-level zone. This turns shuttle scheduling into a cross-zone, cross-module orchestration problem rather than a purely local routing task (Wu et al., 30 Sep 2025).

Level	Zone type	Role
Level 0	Storage zone	Parking ions when not immediately needed
Level 1	Operation zone	High-fidelity intra-module MS two-qubit gates
Level 2	Optical zone	Local gates and remote entanglement across modules

The scheduling problem can be described using a circuit DAG whose nodes are two-qubit gates and whose edges encode precedence. Zone exclusivity, capacity limits, ion-location consistency, and the distinction between local MS gates and remote entanglement gates impose the central feasibility constraints. A formalization given in the summary expresses the objective as minimizing shuttle count and total execution time while maximizing overall fidelity, but the implemented heuristic lexicographically prioritizes shuttle reduction and time (Wu et al., 30 Sep 2025).

2. Transport primitives, timing model, and fidelity model

MUSS-TI operates with four primitive shuttle actions inside a device: split, move, swap, and merge. These are the elementary transport operations required to separate ion chains, translate them, reorder ions to expose chain edges, and recombine chains. The simulations use fixed timing and heating parameters for these operations, together with gate times and fidelities for single-qubit, local two-qubit, and remote fiber-entanglement operations (Wu et al., 30 Sep 2025).

Operation	Time model	Fidelity or heating model
Split	80 μs	Heating increment modeled via $\bar{n} = 1$
Move	2 μm/μs	Heating increment $\bar{n} = 0.1$
Swap	40 μs	Heating increment $\bar{n} = 0.3$
Merge	80 μs	Heating increment $\bar{n} = 1$
Single-qubit gate	5 μs	Fidelity 0.9999
Local MS gate	40 μs	Fidelity $1 - \epsilon N^2$, with $\epsilon = 1/25600$
Fiber entangle	200 μs	Fidelity 0.99

The shuttle-induced fidelity degradation is modeled as

$F = e^{-t/T_1} - k\bar{n},$

with $T_1 = 600\times 10^6 \,\mu\text{s}$ and $k = 0.001$. Zone background fidelity is then applied multiplicatively:

$F'_g = B_i F_g.$

This model captures both coherence-limited decay through execution time and shuttle-limited loss through accumulated heating. A central implication is that reducing shuttles improves both latency and the fidelity of subsequent operations, since heating accumulates across transport sequences (Wu et al., 30 Sep 2025).

Remote inter-module coupling is treated as a deterministic gate with fixed latency and fidelity. The summary explicitly notes that the evaluation does not include a probabilistic link-generation model, retries, or entanglement queues. This modeling choice removes one source of scheduling uncertainty and isolates the effects of zone-aware ion movement and placement (Wu et al., 30 Sep 2025).

3. Multi-level scheduling algorithm

The compiler first transforms the circuit into a dependency graph and maintains the ready frontier of zero in-degree gates. Gate selection prioritizes operations that are immediately executable under the current placement; otherwise it uses first-come, first-served selection. When a selected gate is not executable, MUSS-TI chooses a feasible target zone that is nearest in level, preferring optical zones for cross-module entanglement and operation zones for local MS gates, then routes operands there using split, move, merge, and, when necessary, swap operations to expose ions at chain edges (Wu et al., 30 Sep 2025).

Conflict resolution is handled by an LRU replacement policy. If the target zone is full, the least recently used ion is evicted and demoted from optical to operation or storage, or from operation to storage. The summary characterizes this as exploiting locality, with recent use serving as a proxy for near-future demand. The overall complexity is

$\bar{n} = 0.1$0

where $\bar{n} = 0.1$1 is the number of gates, $\bar{n} = 0.1$2 the qubit count, $\bar{n} = 0.1$3 the number of zones per device, and $\bar{n} = 0.1$4 the zone capacity (Wu et al., 30 Sep 2025).

A distinctive component is inter-module SWAP insertion. After a two-qubit gate between qubits in different modules, the compiler checks a lookahead table $\bar{n} = 0.1$5 counting the number of gates within the next $\bar{n} = 0.1$6 layers that involve ion $\bar{n} = 0.1$7 and some qubit currently mapped to module $\bar{n} = 0.1$8. MUSS-TI uses lookahead depth $\bar{n} = 0.1$9 and threshold $\bar{n} = 0.3$0. If a qubit has no anticipated reuse in its current module but high anticipated reuse elsewhere, a SWAP may be inserted to move it to the more advantageous module. Because a SWAP is typically decomposed into 3 MS gates, the summary notes that $\bar{n} = 0.3$1 is sensible and that the implementation uses $\bar{n} = 0.3$2 (Wu et al., 30 Sep 2025).

Initial mapping combines a trivial placement with a SABRE-style two-fold search. The compiler first executes the DAG under the trivial mapping to obtain a final placement, then executes the reversed DAG from that placement to derive a new initial mapping for the forward compilation. The summary interprets this as prefetching or staging “hot” qubits into working zones. This suggests that MUSS-TI is not merely a runtime scheduler; it also performs placement conditioning so that the subsequent shuttle schedule begins from a more locality-aware state (Wu et al., 30 Sep 2025).

4. Evaluation methodology and quantitative performance

The evaluation uses circuits drawn from prior trapped-ion compilation benchmarks and QASMBench, spanning small-scale applications with 30–32 qubits, medium-scale applications with 117–128 qubits, and large-scale applications with 256–299 qubits. Two-qubit gate counts range from 31 to 4376. Baselines are QCCDsim, “Advanced Shuttle Strategies for Parallel QCCD,” and the Munich Quantum Toolkit shuttling compiler (Wu et al., 30 Sep 2025).

The EML-QCCD setting used for MUSS-TI assigns each module one optical zone, one operation zone, and two storage zones; trap capacity is 16 unless varied, module capacity is capped at 32 qubits, and the number of modules scales with circuit size by adding a new $\bar{n} = 0.3$3 QCCD grid per 32 qubits. Small, medium, and large baseline grids are reported as $\bar{n} = 0.3$4, $\bar{n} = 0.3$5, and $\bar{n} = 0.3$6 QCCD layouts, respectively (Wu et al., 30 Sep 2025).

Scale	Shuttle reduction	Execution-time improvement
30–32 qubits	41.74% average	58.9% average
117–128 qubits	73.38% average	64.9% average
256–299 qubits	59.82% average	60.3% average

The reported fidelity improvements track shuttle and time reductions. Simple communication patterns such as BV, GHZ, and QAOA show comparable fidelity across architectures, whereas more complex circuits benefit substantially from reduced shuttling-induced heating. For QFT at medium and large scales, fidelity is below floating-point precision for all methods and is therefore omitted. Communication-heavy circuits such as SQRT show more than 90% shuttle reductions (Wu et al., 30 Sep 2025).

These results support the paper’s central claim that EML-QCCD architectures are well-suited for large-scale applications when the scheduler is explicitly aware of zone functionality and future communication structure. A plausible implication is that the advantage comes not only from having photonic links available, but from reducing the frequency with which ions must be staged into optical zones at all (Wu et al., 30 Sep 2025).

5. Ablations, sensitivity analyses, and design trade-offs

Ablation studies isolate the roles of scheduling, SWAP insertion, and initial mapping. Trivial scheduling alone is weakest. SWAP insertion alone gives limited benefit under trivial mapping because few qubit pairs qualify for safe swaps. SABRE mapping alone improves fidelity through better initial placement. SABRE plus SWAP insertion gives the highest fidelity, indicating complementary benefits between initial locality optimization and future-aware inter-module relocation (Wu et al., 30 Sep 2025).

Trap-capacity analysis on the 117–128 qubit workloads reveals a non-monotone behavior. Small capacities increase shuttling and therefore heating, while large capacities increase the ion count $\bar{n} = 0.3$7 seen by two-qubit gates and degrade local-gate fidelity through

$\bar{n} = 0.3$8

The reported sweet spot for EML-QCCD is 14–18 ions per trap, slightly below the 15–25 range suggested for near-term monolithic QCCD. Multiple optical or entanglement zones further improve fidelity by distributing entangling load and mitigating heat accumulation in a single zone, especially at the 256–299 qubit scale (Wu et al., 30 Sep 2025).

Lookahead depth $\bar{n} = 0.3$9 is application-dependent. Larger $\bar{n} = 1$0 helps for long-distance communication, but excessive lookahead can suppress beneficial swaps by revealing near-term local reuse. Compilation time scales approximately as $\bar{n} = 1$1, with occasional spikes attributed to expanded search spaces after locally optimal scheduling choices. This suggests that MUSS-TI exposes a standard compiler trade-off: higher-quality scheduling decisions increase compile-time search effort, but the growth remains linear in qubit and gate counts rather than exponential in the reported experiments (Wu et al., 30 Sep 2025).

6. Assumptions, limitations, and open directions

MUSS-TI is based on several simplifying assumptions. Remote entanglement is modeled as a deterministic gate with fixed time and fidelity, rather than as a stochastic process with link-attempt probabilities, queues, or retries. Single-qubit gates are ignored for scheduling optimization. Measurement, reset, and feedforward are not explicitly modeled. The shuttle-fidelity expression $\bar{n} = 1$2 is a simplified aggregate model, and the paper notes that actual fidelity effects are device- and sequence-specific. The heuristic choices, including LRU eviction and first-come-first-served tie-breaking, provide strong empirical performance but no optimality guarantee (Wu et al., 30 Sep 2025).

These limitations matter because they delimit the current scope of the compiler. In particular, the deterministic treatment of fiber entanglement means that the scheduler is not yet a full control stack for photonic-network uncertainty. Likewise, the omission of measurement and reset means that the present framework targets transport and two-qubit execution rather than fault-tolerant or adaptive workflows (Wu et al., 30 Sep 2025).

The identified future directions are correspondingly hardware-aware. The paper highlights integration of quantum error correction tailored to EML-QCCD, modeling stochastic photonic link generation with $\bar{n} = 1$3, $\bar{n} = 1$4, and queueing, and extending MUSS-TI to jointly optimize pulse-level control and measurement or reset scheduling. More broadly, the results suggest that EML-QCCD compilation is best treated as a co-design problem linking scheduler policy, trap capacity, number of optical zones, and workload structure rather than as a routing problem in isolation (Wu et al., 30 Sep 2025).