S-SYNC Compiler for QCCD Architectures

• S-SYNC compiler is a circuit-level quantum compiler for QCCD architectures that co-optimizes shuttle and SWAP operations to improve fidelity and efficiency.
• It models the QCCD device as a weighted graph where in-trap SWAPs and shuttling incur time and heating costs, providing a clear framework for execution routing.
• Empirical benchmarks demonstrate significant reductions in shuttle operations and an increase in success rates, highlighting its practical benefits for scalable trapped-ion processors.

The S-SYNC compiler is a circuit-level quantum compiler designed for the Quantum Charge-Coupled Device (QCCD) architecture. QCCD systems employ arrays of segmented electrode traps to hold and manipulate chains of trapped-ion qubits, leveraging their long coherence times and high-fidelity quantum operations. In these architectures, the dominant sources of execution overhead and fidelity degradation stem from the necessity to shuttle qubits between traps and to insert SWAP operations, particularly when a required qubit is not at the end of a trap’s chain. S-SYNC introduces a co-optimization framework for simultaneously minimizing shuttle and SWAP operations, thereby improving quantum circuit success rate and execution efficiency (Zhu et al., 2 May 2025).

1. QCCD Device Structure and Operational Bottlenecks

A QCCD device consists of an array of traps, each trap holds a small (typically linear) chain of ions representing qubits. Traps are interconnected by shuttle regions made up of segmented electrodes; the movement between traps involves splitting ions from their chain, moving them via the shuttling electrodes, and merging them into the target chain. Arbitrary two-qubit gates are feasible within a single trap (e.g., via Molmer–Sørensen interactions), but cross-trap operations require shuttling. Each shuttle operation increases thermal motion (characterized by phonon occupation $\bar n$), lengthens total runtime, and reduces two-qubit gate fidelity; such heating effects are cumulative across many shuttling steps.

In addition, when the qubit to be shuttled is not on the edge of the chain, it must be moved there through a sequence of SWAP gates, which further increase circuit depth and decrease overall fidelity. Thus, minimizing both shuttling and SWAP operations is essential for scalable and high-fidelity QCCD quantum computing.

2. Formal Co-Optimization Problem

S-SYNC models the QCCD device as a static, weighted graph $G = (V, E, W)$:

• $V = Q \cup S$, the union of qubit nodes $Q$ and space nodes $S$ (representing empty sites).
• An edge $(u, v) \in E$ connects two positions that can be interchanged, either via an in-trap SWAP if both are qubits or via a shuttle operation if one position is empty.
• Each edge is weighted: $W(u, v)$ is proportional to the incurred time and heating cost. For $W(u,v) \leq \tau_{\text{swap}}$, it represents an in-trap SWAP; for $W(u,v) > \tau_{\text{swap}}$, it represents a shuttle.

A quantum circuit is represented by a dependency DAG $\mathcal{G}$, with its frontier $\mathcal{G}.\mathrm{frontier}$ comprising two-qubit gates ready for execution. A gate $g$ on qubits $(q_1, q_2)$ can execute when $(\pi(q_1), \pi(q_2)) \in E$ and $W(\pi(q_1), \pi(q_2)) \leq \tau_{\max}$, where $\pi$ maps logical qubits to physical device locations.

The S-SYNC co-optimization objective is:

$$\min \left( \sum_{\text{generic swaps } s} W(s) + \lambda \cdot \#\text{SWAP\_gates} \right)$$

subject to all gates in $\mathcal{G}$ becoming executable. Here, each "generic swap" is an allowed edge interchange, and $\lambda$ is a penalty parameter balancing the trade-off between shuttling and SWAP insertion.

3. S-SYNC Scheduling Heuristics and Algorithms

Preprocessing

1. Input quantum circuit is transformed into a dependency DAG $\mathcal{G}$.
2. The QCCD graph $G=(V,E,W)$ is constructed from the physical layout, with space-nodes and operational weights assigned according to device and shuttling parameters.

Generic-Swap Scheduling

The compiler proceeds iteratively:

1. While $\mathcal{G}.\mathrm{frontier}$ is non-empty:
   • For each frontier gate $g$, if $g$ is executable under the current mapping $\pi$, execute and update the DAG.
   • Else, add $g$ to a wait-list.
2. If no gate executes in the iteration:
   • Identify the candidate set $S$ of valid swap edges.

   • For each candidate $s \in S$:

     • Calculate the cost using:

     $$H(s) = \min_{g \in \mathrm{wait}} [\mathrm{decay}(g) \cdot \mathrm{score}_\pi(g)] + W(s)$$

- Apply the swap $s^* = \arg\min_s H(s)$ yielding the lowest heuristic cost.

Heuristic Cost Definitions

For a gate $g$ on $(q_1, q_2)$:

$$\mathrm{score}_\pi(g) = \min_{\text{path}} \left( \sum_{(u,v)\,\text{path}} W(u,v) + \mathrm{Pen}(g) \right)$$

where $\mathrm{Pen}(g)$ penalizes configurations with no remaining space-nodes in traps, thus avoiding deadlocks.

The decay factor is defined with:

$$\mathrm{decay}(g) = \begin{cases} 1+\delta, & \text{if } g \text{ involved a recent swap}\ 1, & \text{otherwise} \end{cases}$$

Initial Mapping Strategies

S-SYNC employs a two-level initial mapping:

1. First level: Assign logical qubits to traps by one of:
   • Even-divided mapping
   • Gathering mapping (cluster, reserve spaces)
   • STA mapping (spatio-temporal adjacency)
2. Second level: Order qubits inside each trap using the metric:

   $l(q_i) = -\alpha E(q_i) + \beta I(q_i)$

where $E(q_i)$ is the projected count of look-ahead gates involving $q_i$ interacting outside its trap, and $I(q_i)$ is the count for inside-trap interactions. Qubits likely to leave the trap are arranged at chain edges (“mountain-shaped” queue).

4. Quantitative Results

Benchmarks were conducted against two prior QCCD compilers ([32], [33]). Seven quantum applications (Adder, QAOA, ALT ansatz, BV, QFT$_{24}$, QFT$_{64}$, Heisenberg$_{48}$) and six device topologies (L-4, L-6, G-2×2, G-2×3, G-3×3, S-4) were tested.

• Shuttle operations reduced by 3.69× on average.
• SWAP gates reduced to 0.6× the baseline count.
• Application success rate (fidelity) improved by 1.73×.

For the G-2×3 topology (FM gate model):

	Baseline [32]	Baseline [33]	S-SYNC
# Shuttles	4120	3985	1081 (–74%)
# SWAPs	514	472	176 (–66%)
Success rate	17.8%	18.3%	30.8% (+73%)

Empirical plots (Figures 1–3 (Zhu et al., 2 May 2025)) demonstrate S-SYNC’s reductions in shuttle and SWAP counts and consistent improvement in application success rate relative to previous methods.

5. Architectural Topology and Initial Mapping Trade-Offs

Topology selection and initial qubit mapping have direct effects on compiler outputs:

• Topology Impact: Grid arrangements (G-2×3, G-3×3) allow well-balanced low shuttle counts and high success rates. Linear topologies (L-6) necessitate frequent cross-trap moves, increasing costs; ring topologies (S-4) lessen long-distance shuttling but at the expense of trapped capacity and gate speed.
• Trap Capacity: Optimal performance is observed with 10–15 ions per trap; exceeding this range escalates gate times and degrades fidelity.
• Mapping Trade-Offs:
  • Gathering mapping minimizes shuttles but lengthens in-trap gate times, which can reduce success rate.
  • Even-divided mapping alleviates gate-time blow-up but results in increased shuttling.
  • STA mapping intermediates by co-locating logical qubits with frequent interactions.

Figure 1 (in (Zhu et al., 2 May 2025)) elucidates that optimal mapping is contingent upon the underlying noise/gate-time model.

6. Context and Significance

S-SYNC’s contribution is its "generic swap" scheduling formalism paired with multi-level initial mapping, which addresses unique characteristics of QCCD hardware. By explicitly balancing shuttle and SWAP costs in its objective, and by integrating trap layout, operation weights, and application circuit structure into scheduling decisions, S-SYNC advances both practical quantum circuit compilation and informs architectural design considerations for large-scale trapped-ion processors. This framework provides actionable insights for managing cross-trap interaction overheads and for selecting physical layouts and mapping strategies that optimize performance in QCCD-based quantum computation (Zhu et al., 2 May 2025).