Guided Circuit Mapping (GCM)

• Guided Circuit Mapping (GCM) is a collection of methods that use explicit guidance signals to bias circuit-to-implementation decisions, targeting metrics like delay, area, balancing overhead, and fidelity.
• Techniques range from learned delay predictors and reinforcement learning to synthesis-based cost tables and symmetry exploitation, and are applied across classical standard-cell mapping to quantum and neutral-atom architectures.
• Empirical evaluations show significant improvements, such as a 19.9% reduction in delay with GPA and up to 2.7× reduction in balancing overhead with PBMap, highlighting GCM's impact on mitigating search-space complexity.

Guided Circuit Mapping (GCM) denotes a class of mapping and compilation methods in which circuit-to-implementation decisions are steered by an explicit guidance signal rather than by unguided local rewrites alone. In the literature, the signal may be a learned delay predictor for candidate cuts, a path-balancing cost, an architecture-distance heuristic, a fidelity proxy, a symmetry orbit, a precomputed permutation-aware synthesis table, or a learned proposal distribution for local rewrites (Jiang et al., 14 Jan 2026, Pasandi et al., 2018, Reumann et al., 1 Jul 2026, Zhu et al., 2021, Yu et al., 2023, Liu et al., 2023, Rosenhahn et al., 14 Oct 2025). The term does not appear as a single canonical formalism across all domains; instead, the common pattern is objective shaping, search-space restriction, or policy biasing so that local mapping decisions better reflect downstream delay, area, balancing overhead, fidelity, or movement cost.

1. Scope and conceptual structure

Across the cited work, GCM spans several distinct but structurally related settings: standard-cell technology mapping, SFQ path-balancing technology mapping, superconducting-qubit placement and routing, neutral-atom movement scheduling, and post-compilation remapping or local rewrite optimization. What unifies them is not a shared substrate, but a shared methodology: each system defines a mapping state, a constrained action space, and a guidance signal that ranks or filters otherwise combinatorial choices.

Setting	Guidance signal	Representative work
Standard-cell mapping	Delay prediction, library pruning	GPA (Jiang et al., 14 Jan 2026), MapTune (Liu et al., 2024)
SFQ mapping	Path-balancing DFF cost	PBMap (Pasandi et al., 2018)
Superconducting quantum mapping	A* distance heuristics, permutation-aware synthesis, fidelity proxies, symmetry	MLIR A* (Reumann et al., 1 Jul 2026), PAS+PAM (Liu et al., 2023), multi-agent cooperation (Zhu et al., 2021), symmetry remapping (Yu et al., 2023)
Neutral-atom mapping	Transfer lower bounds, distance/PTO objectives	NAQC movement mapping (Gentil et al., 18 Jun 2026)
Guided local optimization	Neural attention over reducible regions	Neural guided sampling (Rosenhahn et al., 14 Oct 2025)

A recurrent distinction in this literature is between guidance internal to the mapper and guidance wrapped around the mapper. PBMap and GPA alter cut evaluation directly during technology mapping, whereas MapTune guides the composition of the effective library presented to an existing mapper (Pasandi et al., 2018, Jiang et al., 14 Jan 2026, Liu et al., 2024). In quantum compilation, some systems guide SWAP selection or routing directly, while others guide remapping among equivalent embeddings or guide only local rewrite opportunities after placement and routing (Reumann et al., 1 Jul 2026, Yu et al., 2023, Rosenhahn et al., 14 Oct 2025).

2. Formal problem structure and representations

The formal structure of GCM depends on the representation chosen for the source circuit and target architecture. In delay-oriented standard-cell technology mapping, the input is a technology-independent Boolean network, primarily an AIG, and the mapper enumerates candidate cuts, matches them to library implementations, and uses dynamic programming to choose a cover. The central weakness identified in that setting is that conventional cut selection relies on abstract pin-based delay models that are insufficiently predictive of true post-mapping timing (Jiang et al., 14 Jan 2026).

In superconducting quantum mapping, the canonical state is a layout

$$\pi_s:\{q_0,\ldots,q_{n-1}\}\rightarrow\{Q_0,\ldots,Q_{m-1}\},$$

with executability determined by the coupling graph. The MLIR-native A* formulation routes layer by layer and prioritizes states using

$f(s)=g(s)+h_i(s),$

where $g(s)$ is the number of SWAPs used so far and $h_i(s)$ is a shortest-path-distance heuristic over the current layer; a discounted lookahead extends this to future layers (Reumann et al., 1 Jul 2026). In block-based mapping, PAS+PAM replaces gate-level reasoning with fixed-width blocks, boundary permutations, and an overview-cost table

$C[b][G_b][(P_i,P_o)],$

so that mapping is guided by both current block cost and the effect of the chosen output permutation on future routing (Liu et al., 2023).

For neutral-atom quantum computers, the representation shifts from adjacency-constrained gate routing to stagewise movement optimization. The circuit is divided into stages, instruction flow is encoded as a digraph, and maximum weighted matchings between adjacent stages yield a lower bound on the minimum number of required transfers. The mapped problem then becomes a nonlinear integer optimization over stick positions, internal swap variables, total traveled distance, and the number of parallel transfer operations (Gentil et al., 18 Jun 2026).

A separate line of work argues that pre-mapping circuit characterization itself is a form of guidance preparation. Interaction-graph-based profiling uses average shortest path, maximal node degree, minimal node degree, and adjacency-matrix standard deviation to explain why circuits with similar size descriptors can induce different mapping overheads, especially on sparse hardware (Bandić et al., 2022). This suggests that the representation chosen for a GCM system determines what structural information can be exposed to its guidance mechanism.

3. Guidance in classical technology mapping

In classical technology mapping, guidance has been formulated as cost shaping over cuts, path structure, or library composition. PBMap is an early and explicit example: for dc-biased SFQ logic, it guides cut selection using the balancing cost

$B(L_{C_j}),$

the number of DFFs required to align the logic levels of the cut leaves. Its dynamic program minimizes total balancing overhead first, then depth, then area; for tree-structured subject graphs it is exact, and for DAGs it serves as a heuristic. Experimentally, PBMap reduces balancing overhead by up to 2.7 times and by 21% on average relative to the state-of-the-art academic technology mappers (Pasandi et al., 2018).

GPA redefines guidance around learned timing rather than abstract delay heuristics. It fuses three complementary views of circuit structure—AIG-based functional encoding, post-mapping technology structure, and a path-aware view emphasizing critical timing paths—and is trained exclusively on real cell delays extracted from critical paths of industrial-grade post-mapping netlists. In the reported evaluation on the 19 EPFL combinational benchmarks, GPA achieves average delay reductions of 19.9% over techmap, 2.1% over MCH, and 4.1% over SLAP, without compromising area efficiency (Jiang et al., 14 Jan 2026). The important shift is methodological: the cut cost is no longer a hand-designed abstract surrogate, but a learned predictor tied to post-mapping timing behavior.

MapTune moves guidance outward, from cut scoring to library tuning. Its reinforcement-learning agent constructs a design-specific partial library before each mapping call, with the goal of reducing the mapper’s effective search space and improving Area-Delay Product. The framework reports an average ADP improvement of 22.54% across its exploration settings, with improvements remaining across 7nm, 45nm, 130nm, and 180 nm libraries and across two different mappers (Liu et al., 2024). This suggests a broader interpretation of GCM: the mapping process can be guided not only by ranking decisions inside the search, but also by shaping which implementation choices are available to the search at all.

Taken together, these systems show three distinct classical GCM regimes. PBMap uses analytically defined structural regularization, GPA uses learned cost prediction tied to post-mapping ground truth, and MapTune uses outer-loop action selection over the mapper’s cell universe (Pasandi et al., 2018, Jiang et al., 14 Jan 2026, Liu et al., 2024).

4. Quantum mapping: search, rewrites, and compiler integration

Quantum GCM has been dominated by guided search over layouts and routing actions. QMAP provides a concise reference architecture: an exact backend encodes mapping as a MaxSAT problem solved with Z3 and guarantees minimal SWAP count for small instances, while the heuristic backend uses A* search and scales to hundreds of qubits and hundreds of thousands of gates. The same framework exposes multiple initial-layout modes—identity, static first-layer-aware placement, and dynamic greedy assignment—so guidance begins even before routing (Wille et al., 2023).

The MLIR-native reimplementation of A*-based routing pushes this search model into compiler IR. Its guidance consists of the current-layer distance heuristic, discounted lookahead over future layers, pruning by a closed set keyed on layouts, restricted successor generation near currently blocking qubits, and multi-trial initial-layout refinement. Evaluated on almost-hundred MQT Bench circuits on a $10\times 12$ lattice intended to model IBM’s 120-qubit Nighthawk processor, it reports 5% fewer SWAP insertions and 46% lower runtime than QMAP under matched A* settings, and 13% fewer SWAPs and 74% lower runtime than TKET’s LexiRoute, while still trailing Qiskit SABRE in the reported comparisons (Reumann et al., 1 Jul 2026). Its contribution to GCM is not a new theoretical objective, but a demonstration that guided routing can be encoded natively over SSA-based compiler IR, with wire iterators, direct SWAP insertion, and arena-based A* search.

Another branch of quantum GCM expands the action space by exploiting circuit equivalence. The commutation-and-transformation mapper represents the current frontier through a dependency graph and a set of blocking gates, then chooses between SWAPs and distance-2 Bridge transformations. Its heuristic scores SWAPs by the reduction in a weighted sum of shortest-path distances over unresolved gates, while Bridge is used when no sufficiently improving SWAP is available. On the reported RevLib-derived benchmark set, the proposed heuristic reduces additional gates by 53.2% on average relative to QRAND and by 34.7% relative to ZPW; adding Bridge on top of the earlier no-Bridge formulation yields a further 14.2% average improvement (Itoko et al., 2019). In this formulation, guidance is rewrite-aware: the mapper is not restricted to layout changes, but can also consume a blocked gate through an equivalent circuit transformation.

The broader implication is that quantum GCM need not be confined to shortest-path SWAP routing. It can be compiler-integrated, rewrite-aware, and frontier-sensitive, while still retaining explicit state representations and hard legality constraints (Wille et al., 2023, Reumann et al., 1 Jul 2026, Itoko et al., 2019).

5. Advanced guidance mechanisms: fidelity, symmetry, movement, and synthesis flexibility

Several later systems broaden GCM beyond distance-only routing. Variation-aware multi-agent cooperation formulates both initial placement and routing around a fidelity objective derived from calibration data. Placement is selected by iterated local search on a reduced symmetric circuit, while routing uses front-layer distance reduction, SWAP fidelity estimates, and a cooperative population of agents ranked by a fidelity-oriented proxy. On IBMQ_guadalupe, the method improves PST over the HA baseline by 25.86% on average and 95.42% at maximum, and over its own non-variation-aware variant by 60.95% on average and up to 340.28% on con1_216 (Zhu et al., 2021). An important corrective result follows: fewer extra gates are not always the dominant criterion, because a longer route over better couplers can outperform a shorter route over noisier ones.

PAS+PAM replaces local routing heuristics with block-level synthesis flexibility. Each block is synthesized for multiple input/output permutations and hardware sub-topologies, then mapped using a score

$$P(\pi)=W_P\,C[b][G_b][(P_i,P_o)] + H(P_o(P_i(\pi))),$$

which trades off internal block cost against future routing burden. On the reported benchmark combination, this produces circuits shorter by up to 68% and 18% on average relative to Qiskit, up to 36% and 9% on average relative to TKET, and up to 67% and 21% on average relative to BQSKit (Liu et al., 2023). Here the guidance source is neither learned nor purely geometric; it is synthesis-derived flexibility stored in a cost table.

Symmetry-based remapping introduces a different kind of guidance: hardware automorphisms. Rather than searching all placements of a compiled interaction graph in a large regular coupling graph, the method searches only within a reduced neighborhood induced by a generating set and then generates all equivalent placements by group action. Under bounded-degree assumptions it proves linear scaling in the number of physical qubits, and on an 88,200-qubit octagonal processor it reports about 18× speedup over VF2, about 36× speedup for vectorized scoring, and a runtime reduction from about 279 s for MAPOMATIC to about 11 s (Yu et al., 2023). This is GCM by structural quotienting: symmetry shrinks the candidate set before any calibration-aware ranking is applied.

For neutral-atom architectures, the guidance target becomes physical movement rather than SWAP count. The general circuit mapping algorithm for NAQCs derives a transfer lower bound from instruction-flow graphs, then uses a genetic algorithm to optimize either total traveled distance or the number of parallel transfer operations. In the reported 2-zone experiments, the method consistently finds fewer transfers than ZAC and reaches the theoretical minimum transfer count $\lambda_q$ up to rare cycle penalties $N_C=1$ or $f(s)=g(s)+h_i(s),$0 (Gentil et al., 18 Jun 2026). A related expansion of the action space appears in teleportation-augmented mapping for IBM Q Tokyo, where Bell-pair channels are treated as temporary virtual edges; the case study reports overhead reductions around 20% and nearly 30% in the best cases (Hillmich et al., 2020).

Not all guided quantum optimization is a full mapper. Neural guided sampling predicts reducible regions in a 2D circuit representation and uses the attention map as a sampling prior for local equivalence-preserving rewrites. It improves gate counts relative to Qiskit and prior stochastic baselines on the reported 8-qubit tasks, and its Time To Beat Qiskit level 3 drops from $f(s)=g(s)+h_i(s),$1 s to $f(s)=g(s)+h_i(s),$2 s in one NISQ example, but the method remains topology-agnostic beyond gate-set choice and required several days on a larger factorization benchmark (Rosenhahn et al., 14 Oct 2025). The paper is therefore better placed as adjacent to GCM than as a full placement-and-routing method.

6. Evaluation patterns, misconceptions, and open problems

A persistent misconception is that GCM is synonymous with machine learning. The surveyed work contradicts this directly. PBMap is a dynamic program over balancing cost, PAS+PAM is guided by synthesis-derived tables, symmetry remapping is guided by graph automorphisms, and QMAP includes an exact MaxSAT backend; none of these requires a learned policy or predictor (Pasandi et al., 2018, Liu et al., 2023, Yu et al., 2023, Wille et al., 2023). Conversely, when learning is used, it enters at different layers: GPA predicts cut delays, MapTune tunes library subsets, neural guided sampling proposes reducible regions, and MCTS-guided routing uses a CNN to bias rollouts rather than to replace search (Jiang et al., 14 Jan 2026, Liu et al., 2024, Rosenhahn et al., 14 Oct 2025, He et al., 2020).

A second misconception is that added-gate minimization is the universal objective. In fact, the surveyed objectives are heterogeneous: PBMap minimizes balancing DFFs; GPA targets critical-path delay; MapTune optimizes ADP; multi-agent quantum mapping optimizes a fidelity proxy; neutral-atom mapping trades off total distance and PTO count; interaction-graph characterization studies gate overhead, latency overhead, and fidelity decrease as separate metrics (Pasandi et al., 2018, Jiang et al., 14 Jan 2026, Liu et al., 2024, Zhu et al., 2021, Gentil et al., 18 Jun 2026, Bandić et al., 2022). This suggests that GCM is better viewed as a methodology for steering combinatorial compilation toward a chosen physical objective, not as a fixed optimization problem.

The empirical literature also shows that guidance quality depends strongly on structural priors. Interaction-graph characterization reports that graph-based parameters correlate more strongly with mapping performance on sparser hardware than on more connected hardware, implying that circuit-structure-aware guidance becomes more valuable as architecture constraints tighten (Bandić et al., 2022). MCTS-guided routing demonstrates an analogous point on grid routing: random rollouts yield 0% success in the reported experiments, whereas DNN-guided DFS rollouts reach 100% success by 1000 iterations, and Max-UCT sharply lowers wire redundancy relative to Avg-UCT (He et al., 2020). The common lesson is that large mapping spaces are usually too sparse for unguided exploration.

Open problems recur across domains. Exactness does not scale: QMAP’s exact backend is limited to small architectures and circuits, while heuristic A* and multi-agent methods sacrifice global optimality for tractability (Wille et al., 2023, Reumann et al., 1 Jul 2026, Zhu et al., 2021). Learned local rewrite methods improve proposal quality but may remain computationally heavy at larger scale (Rosenhahn et al., 14 Oct 2025). Neutral-atom placement still relies on heuristic PTO scheduling after exact transfer minimization (Gentil et al., 18 Jun 2026). Symmetry methods require strong regularity in the hardware graph, and fidelity-aware methods depend on current calibration data (Yu et al., 2023, Zhu et al., 2021). A plausible synthesis is that future GCM systems will combine multiple guidance layers—structural characterization, architecture-aware search, calibration-aware ranking, and learned proposal policies—rather than relying on a single heuristic or model.

In that sense, Guided Circuit Mapping is best understood as a broad compiler-design paradigm. Its defining move is to expose latent structure—timing, balancing, symmetry, topology, motion, calibration, or circuit equivalence—and use that structure to bias mapping decisions before combinatorial explosion makes them effectively irreversible.