Hybrid Dependency Hypergraphs for Quantum Computation

· MIT Licensed · · Author: Maria Gragera Garces

Work in Progress - Preparing for 1.0

---

What is HDH?

HDH (Hybrid Dependency Hypergraph) is an intermediate directed hypergraph-based representation designed to encode the dependecies arising in any quantum workload. It provides a unified structure that makes it easier to:

• Translate quantum programs (e.g., a circuit or a mbqc pattern) into a unified hypergraph format
• Analyze and visualize the logical and temporal dependencies within a computation

---

Current Capabilities

• Qiskit, Braket, Cirq and Pennylane circuit mappings to HDHs
• OpenQASM 2.0 file parsing
• 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)

---

Installation

pip install hdh

---

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)

---

Contributing

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

• SDK compatibility
• Frontend tools (visualization, benchmarking)

or if you've found a bug!

---

Citation

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