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Structural Diagnostics of IBM Heavy-Hex Architectures Using Layer I and Layer II

Pedro Pelegrini

Published Jun 7, 2026• 0 citations
Publisher

Abstract

Technical benchmark of IBM Heavy-Hex quantum architectures using the AlgebraQ Layer I and Layer II diagnostic frameworks. The study evaluates spectral admissibility, structural coherence, mediation costs, amplification behavior and structural risk using publicly reproducible Qiskit coupling maps.
DOI
10.5281/zenodo.20581376

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This technical note investigates whether Layer II structural diagnostics can predict transpilation costs in IBM Heavy-Hex quantum architectures before compilation is performed. The study evaluates Heavy-Hex coupling maps generated through Qiskit for distances d = 3, 5, 7, and 9. Structural observables are computed directly from the architecture graph and compared against normalized transpilation metrics obtained from Quantum Fourier Transform (QFT), GHZ-state preparation, and Hardware-Efficient Ansatz (HEA) circuits. A leave-one-out validation procedure is used to assess predictive capability on unseen architecture instances. Results indicate that mediation, normalized structural cost, and feasibility observables contain measurable predictive information regarding transpilation overhead. The strongest performance is observed for HEA and GHZ workloads, where several prediction targets achieve low error levels. The benchmark provides preliminary evidence that circuit-independent structural observables may support predictive assessment of compilation costs during early-stage quantum architecture evaluation.
Scalable quantum architectures are increasingly constrained by mesoscopic structural effects that emerge prior to hardware realization. While a foundational admissibility layer establishes spectral consistency of scaling families, admissibility alone doesnot ensure favorable physical scaling behavior as architectures grow. This work introduces a second diagnostic layer aimed at quantifying architecture-level structural risk under controlled growth. Assuming admissibility has been verified, we analyze parametrized architectural graph families and extract a minimal set of physically interpretable observables derived from a symmetric structural operator. By examining the scaling of load concentration, mediation overhead, and perturbationinduced amplification, we estimate global and local growth exponents and define a Relative Structural Risk Index (SRI) for comparative assessment across architectures. The framework is evaluated on multiple architectural families, including linear chains, planar grids, centralized star topologies, modular hierarchical constructions, and a constraintmediated architecture inspired by parity-based encodings. The results indicate that spectrally admissible architectures can nonetheless exhibit substantially different mesoscopic scaling regimes. The proposed diagnostic layer functions as a pre-hardware structural assessment instrument, supporting architecture-level decisions prior to layout optimization, hardware prototyping, or error-correction design.
Scalability remains a central challenge in large-scale quantum architectures. While device-level characterization is essential, many scalability constraints originate at the architectural level, where global coordination limits and asymptotic instabilities emerge prior to layout, compilation, or hardware modeling. We introduce a structural admissibility framework positioned as a pre-hardware diagnostic layer for architecture-level scalability assessment. Architectures are modeled as controlled scaling families, and admissibility is determined by a set of structural functionals governing growth consistency, compositional refinement, and perturbative stability. These functionalsestablish whether a family supports coherent large-scale expansion before physical realization. To obtain measurable diagnostics, each structural instance is associated with a symmetric operator from a minimally specified axiomatic class. The smallest non-zero eigenvalue defines a spectral gap observable whose scaling yields a coherence-like indicator, an effective structural dimension estimate, and a quantitative measure of scaling fragility. Baseline experiments using the normalized graph Laplacian show that purely structural observables already separate distinct scaling regimes—such as mediation-dominated 1D chains and dimension-supported 2D grids—without invoking device-level noise models.
We present a novel architecture-aware transpilation method for exact general unitary gate synthesis on superconducting quantum hardware. Our approach is tightly integrated with the optimized block-ZXZ decomposition, exploiting its recursive structure to make hardware-aware decisions at each level of the recursion rather than treating transpilation as an independent post-processing step. The method introduces three key techniques: a greedy qubit mapping strategy that minimizes pairwise distances between physical qubits, an adaptive Gray code selection combined with qubit swapping that optimizes the construction of uniformly controlled Rz gates for the target topology, and a heuristic for reducing CNOT gates by exploiting the structure of long-range CNOT ladders. We benchmark our method against TKet, Qiskit, and Pennylane on the 20-qubit IQM Garnet (square lattice) and the 156-qubit IBM Marrakesh (heavy-hex) architectures with qubit counts ranging from 3 to 11. Our method achieves CNOT count reductions of up to 36 percent on the IQM Garnet and up to 34 percent on the IBM Marrakesh compared to the best competing transpiler, while simultaneously achieving transpilation speedups of up to 553x. Furthermore, our method is the only one capable of transpiling circuits beyond 10 qubits within a 30-minute time limit across both architectures.