Hybrid Dependency Hypergraphs for Quantum Computation

· · · MIT Licensed

What is a HDH?

HDH (Hybrid Dependency Hypergraph) is an intermediate directed hypergraph-based representation designed to encode the dependencies 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
• Partition workloads across devices, taking into account hardware and network constraints

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)
• Capability to partition HDHs and evaluate partitions

Installation

pip install hdh

Qiskit conversion works out of the box. Cirq, PennyLane, Amazon Braket, and the KaHyPar/METIS partitioners are optional and installed via extras:

pip install hdh[cirq]        # Cirq conversion (needs Python >=3.11)
pip install hdh[pennylane]   # PennyLane conversion (needs Python >=3.11)
pip install hdh[braket]      # Amazon Braket conversion (needs Python >=3.11)
pip install hdh[kahypar]     # KaHyPar-based partitioning
pip install hdh[metis]       # METIS-based partitioning (metis_telegate)
pip install hdh[all]         # everything above (needs Python >=3.11)

Tested against Cirq 1.7, PennyLane 0.45, and amazon-braket-sdk 1.125 — all three now require Python >=3.11 upstream, so those extras aren't installable on Python 3.10. hdh[metis] installs the Python binding only — it talks to a system-installed METIS C library via ctypes, so METIS itself must already be available on your machine (e.g. via your OS package manager or built from source). Without it, metis_telegate automatically falls back to a Kernighan-Lin partition and reports which method it used.

Upgrading from 0.4? HDH.add_node changed signature in 0.5 — see CHANGELOG.md.

Quickstart

From Qiskit

from qiskit import QuantumCircuit
from hdh.converters 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 OpenQASM 2.0

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

qasm = """
OPENQASM 2.0;
include "qelib1.inc";
qreg q[2];
creg c[2];
h q[0];
cx q[0], q[1];
measure q -> c;
"""

hdh = from_qasm('string', qasm)
# or, from a file: hdh = from_qasm('file', 'path/to/circuit.qasm')

plot_hdh(hdh)

Tests and Demos

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

pytest

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.