- The paper proposes a routing-aware placement method that integrates movement constraints into the initial placement stage to minimize rearrangement steps.
- It employs an A* search algorithm with a specialized cost function and heuristic to efficiently navigate the large placement space.
- Evaluation shows an average 17% reduction in rearrangement steps, significantly decreasing computation time and improving fidelity.
This paper introduces a novel approach called routing-aware placement for zoned neutral atom-based quantum computing architectures. It addresses a key inefficiency in existing quantum compilers for this hardware: the separation of the placement and routing stages. Current methods prioritize minimizing atom travel distance during placement, often leading to sub-optimal routing that requires many sequential rearrangement steps and increases computation time due to decoherence.
The core problem stems from the specific constraints of atom movement in zoned architectures (Figure 1). Atoms are moved using AODs, and multiple movements can happen in parallel within a "rearrangement step" if they satisfy non-crossing, preservation (same row/column), and ghost-spot constraints. If movements conflict, they must be serialized into multiple steps. Existing placement algorithms, unaware of these constraints, might create a placement that is physically close but requires many steps to reach, as illustrated in Figure 2.
The proposed routing-aware placement method integrates awareness of these rearrangement constraints directly into the placement stage of the compiler workflow (Figure 3). The goal is to find placements for each layer of two-qubit gates (and intermediate states) that minimize the number of rearrangement steps and the maximum distance within each parallel step, thereby reducing the total rearrangement time. This is crucial because atom state decoheres over time, and reducing rearrangement time helps maintain high fidelity.
Implementing this involves searching a vast space of possible atom placements. The paper utilizes the A* search algorithm (Figure 4) to navigate this space efficiently. The search operates on nodes representing partial placements, extending them atom-by-atom or gate-by-gate until a full placement is determined.
The effectiveness of A* depends heavily on its cost function and heuristic. The paper defines a cost function (Equation 2) that combines:
- A proxy for actual routing cost: This is based on grouping compatible movements in the current partial placement and summing the square roots of the maximum distance in each group (Equation 1). The square root reflects the physical relationship between distance and movement time.
- A look-ahead cost: This estimates future movement costs for atoms involved in subsequent gates. For reused atoms, it considers the cost of moving their future interaction partner. This look-ahead helps identify placements that might be good locally but problematic globally, and also evaluates the cost/benefit of reusing atoms in the entanglement zone (Figure 5).
The A* heuristic (Equation 5) guides the search faster towards promising placements. It comprises three parts:
- Admissible part (Equation 3): A lower bound on the remaining cost, assuming future movements can be added to existing groups optimally.
- Accelerating part: This estimates the likelihood of future conflicts based on the structure of the current partial placement. It favors placements that maintain spatial patterns (like gaps) from the previous layer, which are easier to extend without violating constraints (Figure 4). This is quantified using the standard deviation of differences between source and target locations in discrete coordinates, adjusted by scaling factors (Figure 5).
- Look-ahead part: An average of the look-ahead costs of all unplaced atoms/gates to incorporate future costs into the heuristic guidance.
For efficient implementation and rapid cost/heuristic calculation during the A* search, a dedicated data structure is used (Figure 6). For each group of compatible movements, the row and column mappings from source to target locations are stored in separate binary search trees. Checking if a new movement is compatible with an existing group involves quick lookups and comparisons within these trees based on discrete coordinates (Example 4, Example 5). Pruning strategies, such as limiting the search to a window of nearby target traps, are also employed to further reduce the search space explored.
The proposed method was implemented in C++ as part of the open-source Munich Quantum Toolkit (MQT) map component. It was evaluated against a re-implemented state-of-the-art routing-agnostic placement approach using benchmark circuits from QASMBench and MQT Bench (Table 1).
The evaluation shows a trade-off: the more sophisticated routing-aware placement takes longer for the placement stage itself compared to the simpler routing-agnostic method. However, this increased placement time is moderate and acceptable, even for larger circuits. Crucially, the subsequent routing stage is significantly more efficient because the placement is designed with routing constraints in mind. The number of rearrangement steps is reduced by an average of 17% (and up to 59% in the best case), and the total rearrangement time during the quantum computation is reduced by an average of 17% (and up to 49% in the best case). This reduction in rearrangement time directly translates to potentially higher computation fidelity on neutral atom hardware.
In summary, the paper presents the first practical routing-aware placement method for zoned neutral atom architectures. By considering movement constraints and future gate requirements during placement, it produces layouts that, while potentially taking longer to compute during compilation, result in significantly fewer, faster rearrangement steps during quantum execution, improving overall performance and fidelity. The open-source implementation allows practitioners to integrate this capability into their compilation workflows for this promising hardware platform.
