Topology-Aware Compilation Method

• Topology-aware compilation is a method that integrates physical device constraints into the compilation process to optimize resource allocation and execution fidelity.
• It leverages specialized partitioning strategies like PAC, CCMap, and GTQCP to manage connectivity and reduce overhead in quantum and network computing systems.
• By employing hardware-aware cost functions and heuristic optimizations, this approach achieves significant speedups, fidelity improvements, and scalable mapping for complex computing platforms.

A topology-aware compilation method is an approach in compiler design—most notably in quantum computing and networking—that integrates knowledge of hardware or network topology into algorithmic and mapping decisions. This enables efficient resource allocation, high-fidelity execution, and scalability by explicitly accounting for the constraints, connectivity, and physical properties of the underlying system. Topology-aware compilation contrasts with oblivious or "flat" compilers by leveraging physical structure (e.g., qubit arrays, chip interconnects, or SDN graphs) to guide partitioning, synthesis, and mapping steps.

1. Background and Motivation

Topology-aware compilation arises from the necessity to map abstract computational tasks onto hardware with nontrivial connectivity, dynamic reconfiguration possibilities, or localized resource constraints. In quantum computing, devices such as neutral atom arrays and modular chip architectures offer flexible layouts but introduce complex physical constraints—AOD crossing limits, limited coupler bandwidth, Rydberg interaction radii, and heterogeneous noise features. Similarly, in software-defined networking (SDN), program behavior may be specified over virtual topologies that must be concretized for physical switches.

Conventional compilers can suffer from performance bottlenecks, high error rates, or non-scalable partitioning by ignoring these constraints. Topology-aware methods strategically incorporate device-specific characteristics, improving compilation efficiency, execution fidelity, and scalability for large-scale hardware.

2. Topology-Aware Partitioning Strategies

Partitioning is a central technique for exposing parallelism and reducing algorithmic complexity by dividing computational graphs or circuits into well-chosen fragments compatible with hardware topology.

Quantum Neutral Atom Arrays:

The Physics-Aware Compilation (PAC) approach (Chen et al., 19 May 2025) for neutral atom arrays divides the hardware plane into independent regions using characteristics of AOD and SLM traps. Local partitions correspond to physically independent zones, each solving subcircuits in parallel. Inter-region dependencies are minimized and flagged for a global phase. This partitioning respects constraints such as the AOD crossing rule and Rydberg blockade. Mathematically, resolved qubits are placed in SLMs at local phase completion to avoid global qubit motion conflicts:

$$\forall i \in Q_{r1},\ \forall t,\ \text{if } t \text{ is the final stage},\ a_{i,t} = 0$$

Modular Quantum Chips:

In chip-to-chip coupler-connected systems, CCMap (Du et al., 14 May 2025) applies entanglement graph partitioning. Strongly interacting logical qubit groups are assigned to the same chip, reducing expensive inter-chip SWAPs. Community detection heuristics drive fragment placement, considering calibration-derived coupler errors in the cost metric.

Quantum Circuit Partitioning:

GTQCP (Clark et al., 3 Oct 2024) is a greedy topology-aware algorithm that partitions quantum circuits into subcircuits, using dependency graphs of qubits and gates. Candidate qubit groups are incrementally constructed to respect the maximum allowed width $k$, and partitions containing the most gates are reserved iteratively, resulting in near-optimal partitioning efficiency for NISQ platforms.

3. Algorithmic Principles and Decomposition

Topology-aware compilers exploit structural knowledge at multiple levels:

Physical Constraint Integration:

PAC directly encodes hardware motion and interaction limitations into the partitioning algorithm, enabling local solving without global constraint violations and reducing complexity by only considering active cross-region qubits in the global phase.

Cost-Driven Partitioning (CCMap):

A hardware-aware cost function includes terms for on-chip and inter-chip operations, temporal delays, and cumulative gate/coupler errors:

$$C_{\text{total}} = \alpha S_{\text{on}} + \beta S_{\text{inter}} + \gamma D + \delta \frac{\sum \epsilon}{\Gamma_{\text{avg}}}$$

where each term is directly calibrated to measured device characteristics.

Heuristic Complexity Management (GTQCP):

GTQCP traverses dependency DAGs greedily to enumerate candidate partitions, bounding worst-case complexity to $O(g n e^{k/e})$, an order-of-magnitude reduction over exhaustive methods ($O(g n^k)$ for ScanPartitioner).

Symbolic Automata and BDDs in Networking:

In NetKAT SDN compilation (Smolka et al., 2015), topology-aware pipelines use symbolic automata to track programs over network topologies, translating global state into per-switch local state, and employing forwarding decision diagrams for switch-specific table generation.

4. Synthesis and Mapping with Topology Awareness

Topology-Aware Unitary Synthesis:

TopAS (Weiden et al., 2022) partitions wide quantum circuits before mapping, matching each fragment’s logical connectivity to sparse physical device subtopologies via a similarity kernel:

$$\operatorname{similarity}(v_p, v_L) = \frac{v_p \cdot v_L}{\|v_p\|\|v_L\|}$$

This process minimizes SWAP overhead and enables heavy reductions in circuit depth and gate count compared to classical and post-mapping compilers.

Interaction Graph Analysis:

Full-stack hardware-aware compilers (Bandic et al., 2022) utilize algorithm-driven placement, such as assigning highly interactive logical qubits to adjacent hardware qubits, thus prepping the mapping step for fewer SWAP insertions and lower overall error.

Sequence Parallelism in Deep Learning:

TASP (Wang et al., 30 Sep 2025) for long-context LLMs applies Hamiltonian decomposition of complete device graphs to create multiple orthogonal ring datapaths, fully utilizing AlltoAll topologies in GPU clusters. Primitive decomposition aligns communication patterns with hardware, yielding up to $3.58\times$ speedup over prior ring-based methods.

5. Performance Benchmarks and Scalability

Topology-aware compilation methods consistently demonstrate dramatic improvements in scaling and practical execution metrics:

• PAC achieves up to $78.5\times$ speedup over DPQA on $16\times16$ atom arrays, with performance advantage increasing at $64\times64$ scale; circuit quality remains comparable, with average depth differences $<1$ layer (Chen et al., 19 May 2025).
• CCMap offers up to 21.9% fidelity improvement and 58.6% compilation cost reduction by minimizing inter-chip operations and leveraging calibration data (Du et al., 14 May 2025).
• GTQCP provides 96% runtime improvement over ScanPartitioner and 18% over QuickPartitioner, with 38% partition reduction (Clark et al., 3 Oct 2024).
• TopAS achieves up to 62% reduction in CNOT count and up to 38% depth reduction over traditional compilers when targeting Google mesh and IBM Falcon topologies (Weiden et al., 2022).
• TASP yields up to $4.7\times$ communication time reduction and near-linear scaling on multi-node clusters by exploiting hardware graph decompositions (Wang et al., 30 Sep 2025).
• NetKAT compiler generates flow tables for large networks in $\sim2$ seconds (vs $10+$ minutes for prior compilers), with compact rule sets due to topology-aware symbolic automata and FDDs (Smolka et al., 2015).

6. Applications and Implications

Topology-aware compilation has become essential for a range of modern computing platforms:

• Quantum Computing:
  • Massive atom arrays, modular superconducting chips, and NISQ platforms all benefit from compilation frameworks that explicitly encode and exploit their connectivity and device characteristics. Compilers such as PAC, CCMap, TopAS, and GTQCP have enabled scalable execution, high fidelity, and parallel resource utilization, directly addressing the challenges of hardware heterogeneity and large problem sizes.
• SDN and Networking:
  • Compilers for languages like NetKAT leverage abstractions over virtual and global topologies, yielding tractable and efficient hardware table generation for large-scale networks.
• Deep Learning/LLMs:
  • Sequence parallelism mechanisms such as TASP maximize accelerator interconnect bandwidth via graph-theoretic topology decomposition, boosting training and inference for large models.

The convergence of hardware–software co-design, calibration-driven cost metrics, and graph-based partitioning underscores the critical role of topology-aware compilation in future systems.

7. Limitations and Future Directions

Despite substantial advancements, some limitations remain:

• Greedy heuristics (GTQCP) may in rare cases miss globally optimal partitions; theoretical bounds for complexity are yet to be fully characterized (Clark et al., 3 Oct 2024).
• Most quantum partitioning algorithms rely on accurate interaction graphs and calibration data; dynamic reconfiguration or time-varying noise may still pose challenges (as suggested by CCMap and PAC findings).
• TopAS and similar synthesis tools are constrained by partition size ($k$); global optimization remains exponential for larger blocks (Weiden et al., 2022).
• Sequence parallelism solutions like TASP are most beneficial for communication-bound workloads; computation-heavy models see limited gains (Wang et al., 30 Sep 2025).

A plausible implication is that the continued evolution of topology-aware compilation will rely on tighter integration of device diagnostics, runtime calibration, and adaptive algorithms, further broadening scalability, robustness, and fidelity across computing domains.