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GadIR: A Spatial-Topology Preserving Compiler for Quantum Many-Body Systems Simulation

Xiangyu Ren, Yuexun Huang, Zhaohui Yang, Yuchen Zhu, Tsung-Wei Huang, Tsung-Yi Ho, Zhiding Liang, Antonio Barbalace

arXiv:2609.01771v1quant-phcs.ARcs.PL

TL;DR

Compiling quantum many-body Hamiltonians is challenging because Pauli-string representations discard spatial topology relevant to compilation overhead. The paper introduces GadIR, a Pauli-gadget intermediate representation with topology-preserving frontend reduction and backend compilation, achieving lower reported overheads than QuCLEAR across four architectures.

  • Problem

    Prior Pauli-string representations flatten Hamiltonians and neglect spatial topology, while existing optimizations are mainly tailored to superconducting hardware.

  • Method

    GadIR represents Hamiltonian terms as Pauli gadgets on a topology graph, enabling group reduction, hardware-independent Trotterization and scheduling, and hardware-native synthesis.

  • Results

    0.56× (#2Q gate for SC), 0.87× (infidelity for neutral-atom), 0.85× (#non-Clifford for FTQC), and 0.75× (#emitter-entanglement for MBQC) of QuCLEAR on average.

  • Takeaways & Limitations

    Evaluations across canonical many-body models and four hardware architectures show significant reductions in dominant compilation overheads.

  • Takeaways & Limitations

    The neutral-atom evaluation models circuit fidelity from specified gate, transfer, and coherence parameters and uses only ZAC’s atom-scheduling module.

Abstract

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Simulating quantum many-body systems has been one of the most important applications of quantum computation. For simulation, the Hamiltonian of a physical system is compiled into quantum programs with native instructions for quantum hardware. In previous works, the Hamiltonian is represented as Pauli strings, then compiled and optimized based on the quantum circuit model. Such representation paradigm neglects the spatial topology of original physical models, which is vital information to reducing the overhead of compiling many-body systems Hamiltonians. To address such neglect, we introduce a spatial-topology preserving compiler for quantum many-body simulation. Using Pauli gadgets as the representations of the Hamiltonian, we introduce our intermediate representation -- GadIR, to preserve the spatial-topology information of original physical models. Our compiler frontend performs the group reduction algorithm based on Pauli gadget model, which is a hardware-independent optimization. Our compiler backend performs trotterization and scheduling on Pauli gadgets, then synthesizes the Pauli gadgets into hardware-native quantum programs. We evaluate our compiler on all the canonical quantum many-body system models, while achieving a significant reduction on compilation overhead regarding four major quantum architectures. Overall, our spatial-topology preserving IR exploits the compilation optimization space for quantum many-body systems Hamiltonian.

1 Introduction

Quantum many-body Hamiltonians encode physical spatial topology, but conventional Pauli-string representations flatten and discard it. GadIR preserves this topology for hardware-independent optimization and hardware-native compilation across architectures.

  • Problem Definition: Quantum many-body simulation compiles physical-model Hamiltonians into hardware-native quantum programs for different quantum architectures.The Hamiltonian evolution is represented as U = e^-iHt before compilation.
  • Prior Works: Prior compilers use flattened Pauli strings and optimize mainly circuit-level metrics such as gate cancellation, SWAP reduction, or Clifford extraction.These approaches include Paulihedral, 2QAN, Tetris, and QuCLEAR.
  • Challenge 1: Preserving topology: Flattening Hamiltonians into Pauli strings loses spatial positional information that could reduce compilation overhead.The lost information originates from the physical model’s particle topology.
  • Challenge 2: Hardware-independent optimization: Prior optimization strategies mainly target superconducting hardware and can be incompatible with architectures such as measurement-based quantum computation.The paper identifies hardware-independent optimization across diverse architectures as desirable.
  • Solution: Spatial-topology preserving IR: GadIR represents Hamiltonians with Pauli gadgets on a graph corresponding to the physical topology, preserving that information through compilation.The frontend performs gadget-group reduction, while the backend performs hardware-independent Trotterization and scheduling before hardware-native synthesis.
  • Evaluation: 0.56× (#2Q gate for SC), 0.87× (infidelity for neutral-atom), 0.85× (#non-Clifford for FTQC), and 0.75× (#emitter-entanglement for MBQC) of QuCLEAR on average.Evaluations cover canonical spin, bosonic, fermionic, and lattice-gauge models across multiple hardware architectures.

2 Background

Quantum many-body models describe particle interactions on spatial structures, whose operators are encoded into qubit Hamiltonians and decomposed for quantum execution. ZX-diagrams and Pauli gadgets provide diagrammatic representations for these operators and Hamiltonian terms.

  • Physical Many-Body Models: Quantum many-body models describe particles occupying spatial structures such as lattice sites and interacting with neighboring particles.These interactions are represented by Hamiltonians for digital quantum simulation.
  • Particle-to-Qubit Encoding: Particle operators are encoded into qubit operators commonly represented with Pauli operators using methods such as Jordan-Wigner or Bravyi-Kitaev.Fermihedral and HATT are also cited as encoding methods.
  • Inherent Topology of Qubit-Hamiltonian: Encoding maps the physical model’s topology into a topology of the qubit Hamiltonian, such as a Fenwick tree or a higher-dimensional lattice.For example, a 2×3 bosonic lattice can map to a 2×3×2 qubit lattice under bosonic linear encoding.
  • Suzuki-Trotter Decomposition: Suzuki-Trotter decomposition approximates Hamiltonian time evolution as a product of exponentials of individual Hamiltonian terms.The compiler performs this trotterization in its backend.
  • ZX-Diagram: ZX-diagrams are diagrammatic quantum representations built from spiders and wires, with Z- and X-spiders associated with coefficients.They represent linear maps between input and output qubits and can encode gates such as CNOT.
  • Pauli Gadget: A Pauli gadget is a high-level ZX-diagram structure representing a Hamiltonian term, with Pauli-specific spiders connected to the term coefficient.X, Y, and Z operators correspond to X-, Y-, and Z-spiders.

3 GadIR Design

GadIR combines a spatial-topology graph with Pauli gadgets to preserve physical-model locality throughout the intermediate representation. This topology-aware representation supports compiler optimizations that flattened Pauli strings miss across canonical many-body models.

  • GadIR Structure: GadIR combines a topology graph as its frame with Pauli gadgets as the body representing Hamiltonian terms.The topology graph captures model structure, while gadgets concisely represent individual terms.
  • Locality: Because Bose-Hubbard terms involve neighboring bosons, locality provides critical information for topology-aware representation and optimization.The physical interactions are associated with neighboring lattice sites.
  • Topology Construction: A 2 × 3 bosonic lattice maps to a 2 × 3 × 2 qubit lattice whose topology becomes GadIR’s spatial information.The mapping preserves the lattice structure after boson-to-qubit conversion.
  • GadIR Syntax: Pauli gadgets store their operators and the topology edges covered by those operators, unlike linearly indexed Pauli strings.An edge is covered when both adjacent topology nodes carry spiders from the gadget.
  • Motivating Example: GadIR captures more gate-cancellation opportunities than Paulihedral on a topology path, yielding more CNOT reductions in the motivating example.The comparison uses the path q2 → q1 and q2 → q3.
  • Model Coverage: The IR generation covers spin-qubit, fermionic, bosonic, and lattice gauge theory models.Fermionic topology combines Fenwick-tree and original-model edges, while lattice-gauge gadgets act on topology squares.

4 Compiler Frontend Design

The GadIR frontend reduces Hamiltonian terms before hardware-specific compilation by exploiting patterns among topology-anchored Pauli gadgets. Its group-reduction algorithm systematically applies exhaustive Clifford-model rules and organizes reductions in a recursive tree.

  • Gadget Reduction: Gadget reduction removes Pauli-gadget spiders when suitable gate sets pass through specified spider patterns.Removing a spider reduces one Pauli operator from the Hamiltonian term.
  • Gadget Group Reduction: Gadget group reduction applies one gate set across multiple gadgets, using locality to reduce groups rather than isolated terms.Multiple gadgets can share topology edges, creating simultaneous reduction opportunities.
  • Reduction Benefit: Applying reduction to a group of n gadgets can reduce 2n−2 CNOTs at a time.The two additional gate sets surrounding the group account for the subtraction of two CNOTs.
  • Reduction Rules: The reduction rules cover all combinations of Pauli operators under a Clifford model and yield six canonical reducible Pauli-pair classes.The rule set enumerates 242 local-Clifford dressings, CNOT directions, Pauli signs, and qubit-order reversals.
  • Reduction Tree: The frontend grows a reduction tree whose nodes store reduced GadIR groups and whose leaves mark states with no further reducible groups.Groups dividing and node updating recursively grow the tree before backend optimization.

5 Compiler Backend Design

The GadIR backend performs hardware-independent Trotterization and scheduling directly on the topology-preserving representation. It then uses preserved topology to synthesize programs for superconducting, neutral-atom, fault-tolerant, and photonic architectures.

  • Hardware Independence: The backend performs Trotterization and scheduling on GadIR to enable target-independent optimization across arbitrary hardware architectures.The design contrasts with prior methods tailored to superconducting hardware.
  • Trotterization: GadIR Trotterization converts Hamiltonian terms into ZX-diagram elements, with reduction-tree leaf nodes supplying the terms.Reduction gate sets are recursively wrapped around the leaf-node subcircuits.
  • Scheduling: Scheduling uses topology subsets to identify disjoint node descendants that commute and can execute in parallel.Nodes from the same layer and parent are grouped when their qubit subsets do not intersect.
  • Native Synthesis: Preserved topology assists initial qubit placement for superconducting and neutral-atom systems and guides ZX-diagram synthesis for MBQC and FTQC.The same topology information is reused during architecture-specific native-program synthesis.
  • Architecture-Specific Backends: Superconducting synthesis maps GadIR topology to a coupling-graph subgraph with minimal graph edit distance.Neutral-atom placement instead uses min-cut partitioning to parallelize movements within SLM rows.
  • Architecture-Specific Backends: FTQC and photonic MBQC syntheses separately process leaf-node subcircuits before stitching or combining them into complete programs.FTQC uses LaSsynth, Stim, and TQEC, while photonic synthesis generates and combines graph states.

6 Experimental Methodology

The evaluation benchmarks GadIR on diverse quantum many-body and molecular Hamiltonians using multiple prior compilers as baselines. Metrics are selected separately for superconducting, neutral-atom, emitter-based MBQC, and FTQC architectures.

  • Benchmarks: The experiments evaluate 8 quantum many-body models across spin, fermionic, bosonic, and lattice-gauge categories.Molecule Hamiltonians for LiH, H2O, and Benzene additionally test compatibility with quantum chemistry and VQE circuits.
  • Baselines: The baseline set includes QuCLEAR, Tetris, 2QAN, PauliEvo-Rustiq, and an additional PyZX-opt implementation.2QAN supports only spin-qubit models because its IR and routing target 2-local Hamiltonians.
  • Metrics: For superconducting architectures, evaluation uses 2Q gate count and circuit depth.These metrics align with those used in prior baseline studies.
  • Metrics: For neutral-atom architectures, evaluation measures 2Q gate count, circuit duration, and fidelity.Fidelity captures noise associated with atom movement.
  • Metrics: Emitter-based MBQC uses emitter CZ operations, while FTQC uses non-Clifford-gate count because these operations dominate their respective execution overheads.The FTQC passage states that non-Clifford gates are approximately 100x slower than other operations.

7 Evaluation

GadIR is evaluated across canonical many-body models and four hardware architectures, reducing compilation overhead while showing stronger benefits for more local and larger-scale systems.

  • Superconducting Architecture: GadIR reduces superconducting compilation overhead in two-qubit gates and circuit depth across IBM heavy-hexagon and Google square-grid layouts.The comparisons use CNOT or CZ counts and circuit depth against multiple baseline compilers.
  • Neutral-Atom Architecture: 0.54×–0.48×: GadIR reduces neutral-atom two-qubit gates relative to four baselines, while achieving 13.7×–6.8× fidelity improvements.Average duration is reduced to 0.44×–0.34× of the same baselines.
  • Early-Fault-Tolerant Architecture: 0.58×: GadIR reduces logical CNOT subroutines relative to QuCLEAR, with average circuit infidelity reduced to 0.64× in the nonsaturated regime and 0.58× in the low-error regime.The FTQC evaluation uses lattice-surgery circuits and code distances 3, 5, and 7.
  • Emitter-Based MBQC: 0.69×–0.56×: GadIR reduces emitter entanglement overhead relative to three baselines on emitter-based MBQC with silicon-dot photon emitters.The compared operation is emitter-emitter CNOT, identified as substantially more expensive than other operations.
  • Runtime and Scalability: t≈3e−5 × x^1.05: compilation runtime scales nearly linearly with x = #qubit × #Hamiltonian, with a 9.1 × 10^3 s smoke-test runtime on FH(30, 30).The authors interpret this scaling as evidence of framework scalability for medium- to large-scale algorithms.
  • Hamiltonian Locality Analysis: GadIR shows larger improvements on many-body benchmarks than on Jellium and Molecular benchmarks, consistent with stronger Hamiltonian locality in many-body models.For a 2 × 3 bosonic model, every Hamiltonian term has maximal internal distance ≤ 2.
  • Ablation Studies: Ablations show that topology captures significantly more gadget-reduction opportunities, while backend modules trade gate count against depth, duration, or atom movement.On neutral-atom hardware, two-qubit gate count remains unchanged because connectivity is all-to-all.

8 Related Work

Related compilers optimize Hamiltonian simulation through circuit, Pauli-string, encoding, or phase-polynomial techniques. GadIR instead preserves physical topology and performs reductions directly on topology-preserving Pauli gadgets.

  • Hamiltonian and Trotterization Optimization: Kernpiler optimizes Trotterization by grouping commutative Hamiltonian terms and Monte Carlo searching for approximate circuits, whereas GadIR reduces Hamiltonian terms before Trotterization.The two optimization strategies are described as orthogonal and potentially integrable.
  • Pauli-Level Optimization: Rustiq synthesizes flattened Pauli-rotation sets through Clifford basis changes, while GadIR discovers reductions from spatial-topology-preserving Pauli gadgets.The distinction is between flattened representations and topology-preserving representations.
  • Other Architectures and Techniques: Genesis targets Fermion-Boson Hamiltonians on CV-DV architectures, and the authors identify integrating GadIR's bosonic topology insight as future work.PhasePoly is cited as exploring phase-polynomial optimization in quantum circuits.
  • Scope: GadIR focuses on quantum many-body simulation and uses physical-model topology as a heuristic within the broader literature on quantum and architecture-aware compilation.The paper distinguishes this focus from general quantum simulation and variational-algorithm optimization.

9 Conclusion

The paper proposes a modular frontend-backend compiler centered on GadIR for quantum many-body simulation. Its topology-preserving representation supports gadget reduction and hardware-native synthesis across four architectures, with evaluations reporting significant overhead reductions.

  • Contribution: GadIR preserves spatial topology in a Pauli-gadget intermediate representation for quantum many-body Hamiltonians.The representation supports a modularized frontend-backend compiler design.
  • Compiler Design: The frontend enables gadget group reduction, while the backend synthesizes hardware-native programs across four different quantum architectures.The conclusion presents these as the compiler's principal capabilities.
  • Evaluation: Evaluations on all canonical many-body models show significant reductions in dominant compilation overheads.This is the paper's stated overall evaluation conclusion.
  • Representation and Synthesis: ZX-diagrams provide the graph-based representation used to relate Pauli gadgets to equivalent quantum circuits.The paper includes gadget decomposition and ZX-diagram rewriting as supporting compilation mechanisms.

B IR Constructions of Benchmark Models

The benchmark suite constructs intermediate representations for spin, fermionic, bosonic, chemistry, and lattice-gauge models, preserving model-specific Hamiltonian structure where described. It also documents GadIR’s topology-aware gadget reduction procedure and evaluation coverage.

  • Benchmark models: The benchmark models include Heisenberg/XY spin systems, Fermi–Hubbard and Jellium fermionic systems, Bose–Hubbard bosonic systems, chemistry models, and Z2 lattice gauge theory.These models are introduced with their Hamiltonians or model-specific mappings for evaluation.
  • Spin-qubit model: Heisenberg interactions are defined over neighboring sites with directional couplings J_x, J_y, J_z and a z-directed magnetic field h_z.Setting J_z = 0 yields the XY model.
  • Bosonic model: The Bose–Hubbard mapping represents a site with maximum n excitation using n + 1 qubits, unlike the one-to-one site-to-qubit fermionic mapping.The bosonic model uses hopping, on-site interaction, and chemical-potential parameters.
  • Lattice gauge theory: The Z2 lattice-gauge model represents electrons at vertices and gauge bosons on links, with Hamiltonian terms covering excitations, electric fields, and gauge-field-assisted hopping.Vertex and plaquette products are integrated over links associated with the lattice structure.
  • Chemistry models: Chemistry benchmarks use LiH, H2O, and Benzene with 3, 4, and 6 active orbits, respectively.Cholesky decomposition can reduce the interaction complexity from N^4 terms to O(N^2) under the stated rank-scaling condition.
  • GadIR construction: GadIR’s reduction-tree algorithm takes a Pauli gadget P_m and topology T, then iterates Clifford sets to identify maximally reducible gadgets.The surrounding figures document gadget representations, Clifford passing rules, and group-reduction rules.

A.3.4 Data sets.

The artifact provides a reproducible evaluation package with fixed environments, dependencies, and scripts for checking bundled results or rebuilding the packaged component.

  • Environment setup: The setup requires Conda, host C/C++ build tools, Rust and Cargo, followed by cloning GadIR and running ./prepare.sh.The preparation script creates the analysis, QuCLEAR, and 2QAN environments and installs the packaged Rustiq extension.
  • Environment setup: Dependency checks use separate interpreters for analysis, QuCLEAR, and 2QAN environments.The listed checks import the relevant packages, including Qiskit, PyZX, Rustiq, Stim, and Sinter.

A.5 Experiment workflow

The experiment workflow first validates packaged tables, then supports reduced smoke tests, full reproduction, and figure generation through a fixed sequence of backend workflows.

  • Execution workflow: The workflow recommends running ./run.sh plot before ./run.sh smoke or ./run.sh reproduce.The plot command redraws PDFs from included tables; smoke writes reduced outputs, while reproduce restores full results.
  • Figure generation: The figure-generation notebook creates Figures 10–15, 17, and 18(d) from completed artifact results.Freshly regenerated figures require running ./run.sh reproduce first when bundled tables are insufficient.
  • Execution workflow: Workflows run in the order superconducting, neutral atom, FTQC, MBQC, and analysis.This ordering is fixed in the documented execution procedure.

A.6 Evaluation and expected results

The evaluation reports architecture-specific compiler metrics, group-reduction behavior, and MPS entanglement scaling from packaged result data and analysis workflows.

  • Superconducting evaluation: Figure 10 reports normalized IBM CNOT/Google CZ counts, while Figure 11 reports normalized circuit depth.These figures evaluate superconducting-backend compilation metrics.
  • Neutral-atom and FTQC evaluation: Figure 12 reports neutral-atom two-qubit count, duration, and fidelity, while Figures 13–14 evaluate FTQC non-Clifford and logical-CNOT error statistics.Figure 14 uses stochastic Stim/Sinter sampling and may vary slightly between runs.
  • MBQC evaluation: Figure 15 compares emitter-entanglement counts for Tetris, QuCLEAR, PauliEvo-Rustiq, and GadIR using the same Suzuki-2 construction.GadIR includes the cost of reconnecting independently compiled leaves.
  • Reduction analysis: Figure 17 reports mean reduction percentages for individual- and group-reduction methods over 1000 random instances at each Hamiltonian-term count.The comparison uses fixed seed 7 and is topology-agnostic.
  • Entanglement analysis: Figure 18(d) reports maximum bipartite entropy over MPS prefix cuts, distinguishing exact packaged-Hamiltonian profiles from dimension-derived bounds.The analysis covers Heisenberg, Bose–Hubbard, Fermi–Hubbard, Jellium, and molecule families.
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