Hybrid Dependency Hypergraphs for Quantum Computation

· MIT Licensed · · Author: Maria Gragera Garces

Work in Progress - Preparing for 1.0

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What is HDH?

HDH (Hybrid Dependency Hypergraph) is an intermediate representation designed to describe quantum computations in a model-agnostic way. It provides a unified structure that makes it easier to:

• Translate quantum programs (e.g., from Qiskit or QASM) into a common hypergraph format
• Analyze and visualize the logical and temporal dependencies within a computation
• Partition workloads across devices using tools like METIS or KaHyPar, taking into account hardware and network constraints

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Current Capabilities

• Qiskit circuit translation
• OpenQASM 2.0 file parsing
• Graph-based printing and canonical formatting
• Partitioning with METIS using custom HDH-to-graph translation
• Model-specific abstractions for:
  • Quantum Circuits
  • Measurement-Based Quantum Computing (MBQC)
  • Quantum Walks
  • Quantum Cellular Automata (QCA)

Includes test examples for:

• Circuit translation (test_convert_from_qiskit.py)
• QASM import (test_convert_from_qasm.py)
• MBQC (mbqc_test.py)
• Quantum Walks (qw_test.py)
• Quantum Cellular Automata (qca_test.py)
• Protocol demos (teleportation_protocol_logo.py)

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Installation

pip install hdh

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Quickstart

From Qiskit

from qiskit import QuantumCircuit
from hdh.converters.convert_from_qiskit import from_qiskit
from hdh.visualize import plot_hdh

qc = QuantumCircuit(2)
qc.h(0)
qc.cx(0, 1)

hdh = from_qiskit(qc)

plot_hdh(hdh)

From QASM file

from hdh.converters.convert_from_qasm import from_qasm
from hdh.visualize import plot_hdh

qasm_path = os.path.join(os.path.dirname(__file__), 'test_qasm_file.qasm')
hdh = from_qasm('file', qasm_path)

plot_hdh(hdh)

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Example Use Cases

• Visualize quantum protocols (e.g., teleportation)
• Analyze dependencies in quantum walk evolutions
• Explore entanglement flow in MBQC patterns

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Coming Soon

• Compatibility with Cirq, Braket, and Pennylane

• Full graphical UI for HDH visualization

• Native noise-aware binning strategies

• Analysis tools for:

  • Cut cost estimation across partitions
  • Partition size reporting
  • Parallelism tracking by time step

  from hdh.passes.cut import compute_cut, cost, partition_sizes, compute_parallelism_by_time
  
  num_parts = 3
  partitions = compute_cut(hdh, num_parts)
  
  print(f"\nMETIS partition into {num_parts} parts:")
  for i, part in enumerate(partitions):
      print(f"Partition {i}: {sorted(part)}")
      
  # plot_hdh(hdh)
  cut_cost = cost(hdh, partitions)
  sizes = partition_sizes(partitions)
  global_parallelism = compute_parallelism_by_time(hdh, partitions, mode="global")
  parallelism_at_t3 = compute_parallelism_by_time(hdh, partitions, mode="local", time_step=3)
  
  print("\n--- QW Metrics ---")
  print(f"\nCut cost: {cut_cost}")
  print(f"Partition sizes: {sizes}")
  print(f"Parallelism over time: {global_parallelism}")
  print(f"Parallelism at time t=3: {parallelism_at_t3}")

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Tests and Demos

All tests are under tests/ and can be run with:

pytest

If you're interested in the HDH of a specific model, see in manual_tests:

• mbqc_test.py for MBQC circuits
• qca_test.py for Cellular Automata
• qw_test.py for Quantum Walks
• teleportation_protocol_logo.py for a protocol-specific demo

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Contributing

Pull requests welcome. Please open an issue or get in touch if you're interested in:

• SDK compatibility
• Optimization strategies
• Frontend tools (visualization, benchmarking)

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Citation

More formal citation and paper preprint coming soon. Stay tuned for updates.