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Transpilation-Aware Runtime Prediction for Noisy Quantum Circuit Simulation

Davud Azizov, Javier Vela-Tambo, Tian Guo

arXiv:2609.12980v1quant-phcs.PF

TL;DR

Predicting noisy-simulator runtime matters for scheduling and resource allocation, but backend-specific transpilation can change circuits before simulation and make source-level prediction indirect. The paper compares source, hybrid, and transpiled GNN representations with conventional regressors across backends and optimization levels. The transpiled GNN leads among graph-based representations overall, while conventional regressors match or outperform GNNs in some backend-specific settings.

  • Problem

    Noisy-simulator runtime prediction is challenging because backend-specific transpilation changes circuit structure and backend noise can add runtime variability.

    Source: Introduction · p. 1

  • Method

    The study compares source, hybrid, and transpiled GNN representations with five regression methods across backend configurations and optimization levels.

    Source: Introduction · p. 2

  • Results

    The transpiled GNN is strongest among graph-based representations overall, but conventional regression models match or outperform GNNs in several backend-specific settings.

    Source: Introduction · p. 2, Backend-Specific Predictions · p. 6, Conclusion · p. 7

  • Takeaways & Limitations

    Post-transpilation information is useful for runtime prediction, while explicit graph modeling is not always necessary.

    Source: Conclusion · p. 7

    The transpiled-representation dataset is smaller because circuits with DAGs exceeding the 300K-node threshold are excluded.

    Source: Prediction Comparison Among Models · p. 5

Abstract

from arXiv · show

Predicting the runtime of noisy quantum circuit simulations is important for scheduling, resource allocation, and performance optimization. However, accurate prediction is challenging because backend-aware transpilation can substantially alter the original circuit structure, while the backend-derived noise model and simulator execution behavior can introduce additional runtime variation. We study the effectiveness of graph neural networks (GNNs) and conventional regression methods in predicting Qiskit Aer simulation runtime measured after transpilation. We construct a dataset from a benchmark pool of 1,402 unique circuits spanning 22 circuit families, two Qiskit fake-backend configurations, and four transpiler optimization levels. Specifically, we compare a source GNN using original circuit information, hybrid GNN combining source-level graph with post-transpilation features, and transpiled GNN using only transpiled circuit information, along with five regression models. In the overall-model setting, the transpiled GNN achieves the strongest performance among the graph-based representations at all four optimization levels, obtaining $R^2$ values of 0.974, 0.713, 0.745, and 0.605 for optimization levels 0 through 3, respectively. However, under backend-specific evaluation, the advantage of GNN decreases, with conventional regression models matching or outperforming the GNNs in several settings. These results indicate that post-transpilation information is useful, while the value of explicit graph modeling depends on the backend and optimization level.

Introduction

The paper studies noisy-simulator runtime prediction because backend-specific transpilation can substantially change circuit structure, making source-level properties an indirect predictor. It compares three circuit representations and conventional regressors across backends and optimization levels.

Introduction

  • Runtime estimates can support scheduling, resource allocation, performance optimization, time limits, and resource estimates for batches of circuit simulations.Source: Introduction · p. 1
  • Post-transpilation structure and backend noise make the relationship between source-level circuit properties and runtime indirect, nonlinear, and backend-dependent.Transpilation changes depth, gate composition, and two-qubit operation counts; the backend noise configuration can add runtime variability.Source: Introduction · p. 1
  • The paper addresses a gap in evaluating backend-specific post-transpilation features and circuit graphs across optimization levels and backend settings.The cited prior runtime-prediction approach primarily uses source-level, pre-transpilation representations.Source: Introduction · p. 1
  • The three representations are a source GNN, a hybrid GNN with 13 post-transpilation global features, and a transpiled GNN using the backend-specific transpiled graph and features.Source: Introduction · p. 2
  • The transpiled GNN provides the strongest and most consistent results across optimization levels, outperforming source and hybrid GNNs and ML models in the overall-model setting.The study compares five regression methods and evaluates models across two backend configurations and four optimization levels.Source: Introduction · p. 2
  • The contributions include a dataset and reproducible evaluation pipeline spanning two backend configurations and four transpiler optimization levels.Source: Introduction · p. 2

Background

Quantum circuits encode algorithms as operations on qubits. Before execution, transpilation adapts the circuit to backend constraints, producing a structurally different but functionally equivalent circuit.

Background

  • A quantum circuit represents an algorithm as operations on qubits, including gates that transform the state and measurements that extract classical results.Source: Background · p. 2
  • Transpilation adapts circuits to a backend's native gate set and coupling map by decomposing unsupported gates and routing two-qubit operations between unconnected qubits.Source: Background · p. 2
  • Routing inserts SWAP operations to resolve two-qubit gates between logically connected but physically unconnected qubits, yielding a functionally equivalent but structurally different circuit.Source: Background · p. 2, Figure 1 · p. 2
  • Higher optimization levels may reduce circuit depth or gate count, but can increase compilation time, which may contribute substantially to end-to-end processing time.Source: Background · p. 2

Related Work

Prior work covers benchmarking, resource estimation, backend-aware compilation, and quantum simulation, while this paper focuses on predicting noisy-simulator runtime using source and post-transpilation circuit information.

Related Work

  • Circuit benchmarks and characterization metrics capture structure, connectivity, depth, and parallelism because gate count or qubit count alone does not determine execution cost.The paper uses circuit-level features extracted from both source and transpiled circuits for runtime prediction.Source: Related Work · p. 2
  • Resource-estimation frameworks estimate costs for fault-tolerant quantum hardware, whereas this work predicts measured runtime on noisy simulators.Source: Related Work · pp. 2–3
  • Backend-aware compilation and selection optimize device choice or compiled-circuit quality, whereas this work predicts runtime for transpiled circuits on a noisy simulator.Source: Related Work · p. 3
  • QSimBench supplies noisy-simulation execution traces, while the closest cited runtime-prediction work uses graph structure and global features; this paper adds post-transpilation features and analyzes backends and optimization levels.Source: Related Work · p. 3
  • Circuit structure and simulator-specific optimization can affect simulation cost, motivating analysis of whether backend-aware transpilation adds predictive information.Source: Related Work · p. 3

Quantum Circuit Execution Predictor Design

The predictor estimates fixed-shot Qiskit Aer runtime after backend-specific transpilation. It combines circuit-graph and global-feature representations, varying whether those inputs come from the source circuit, the transpiled circuit, or both.

Quantum Circuit Execution Predictor Design

  • The model predicts measured Qiskit Aer runtime after transpilation at a fixed shot count using a two-branch network.Each circuit is represented by a graph and global features, which are processed to estimate runtime.Source: Quantum Circuit Execution Predictor… · p. 3
  • The source setting uses a source-level DAG and 41 global features, including five SupermarQ metrics for properties such as communication, parallelism, and liveness.Source: Circuit Representation and Feature… · pp. 3–4
  • The hybrid setting retains the source-level DAG and adds 13 post-mapping features, including transpiled depth, operation counts, native gate counts, and recomputed SupermarQ metrics.Source: Circuit Representation and Feature… · p. 4
  • The transpiled setting builds both the graph and global feature vector from the backend-specific transpiled circuit.Source: Circuit Representation and Feature… · p. 4
  • The graph branch encodes the circuit DAG, the MLP branch encodes global features, and their concatenated embeddings pass through fully connected layers to predict runtime.The graph branch uses three TransformerConv layers and global mean pooling; the feature branch is a two-layer MLP.Source: Two-Branch Graph Regression Model · p. 4

Evaluation

Evaluation compares runtime predictors across optimization levels and backend settings, then examines optimization overhead and model inference cost. The Transpiled GNN leads the overall-model comparison, but backend-specific results and added computational costs qualify its advantage.

Evaluation

  • Evaluation uses 1,402 unique circuits from 22 families across two fake backends and four levels; held-out source circuits are selected using distribution-matched splits.Circuits are executed for 1,024 shots, and the transpiled representation excludes circuits whose DAGs exceed 300K nodes.Source: Dataset Construction · p. 4, Data Splitting and Model Selection · p. 5
  • The Transpiled GNN outperforms the other GNNs and the best ML baseline across all optimization levels in the overall-model setting.Figure 4 compares GNN models with the best ML model across optimization levels.Source: Figure 4 · p. 5, Prediction Comparison Among Models · p. 5
  • Matched circuits and identical splits preserve the Transpiled GNN's lead; at Opt 3, lower R2 coincides with a tighter runtime distribution and lower RMSE.The controlled comparison addresses differences in dataset composition between GNN representations.Source: Prediction Comparison Among Models · p. 6
  • Washington favors the overall Transpiled GNN, while Sherbrooke has no consistent R2 winner and RMSE exceptions include backend-specific XGBoost at Opt 2 and overall Random Forest at Opt 3.Washington's overall Transpiled GNN outperforms backend-specific GNNs and the best ML models; Sherbrooke's 90th-percentile absolute error remains below approximately 1.25 s.Source: Backend-Specific Predictions · p. 6, Figure 5 · p. 7
  • Deeper or slower circuits more often benefit from added optimization, but Opt 3 helps 76.1% of Washington's slowest circuits and only 5% or 0% of Sherbrooke's slowest or deepest circuits.The comparison measures the share of circuits with lower total runtime than Opt 0.Source: Optimization Level Impact on… · p. 6, Table 3 · p. 7
  • The Transpiled GNN's graphs are approximately 34.9× larger and inference takes about 7.4× longer, yet inference remains 2.35 ms per circuit and mean R2 is highest.Graph construction has a median one-time cost of 149 ms per circuit.Source: Accuracy and Inference Cost · pp. 6–7, Table 4 · p. 7

Conclusion

The transpiled GNN generally performs best among graph-based representations, while conventional regression models remain competitive with or outperform GNNs in several settings. The findings support post-transpilation information for runtime prediction, but not always explicit graph modeling.

Conclusion

  • The transpiled GNN generally provides the strongest performance among graph-based representations, while conventional ML models remain competitive with or outperform GNNs in several settings.Source: Conclusion · p. 7
  • Post-transpilation information is important for reliable quantum execution-time predictors, but explicit graph modeling is not always necessary.Source: Conclusion · p. 7
  • Runtime predictors can guide job placement and resource allocation in future quantum operating systems and schedulers.Source: Conclusion · p. 7
  • Future work will evaluate broader backends, noise models, simulator configurations, and transpilation strategies.Source: Conclusion · p. 7
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