HHL Algorithm based Hermitian Matrix Decomposition

This checkout includes an OpenQASM 3.0 HHL circuit for a 2x2 sparse Hermitian system, A = diag(1, 2) with b = |0>, plus a runner that compiles the circuit with IBM Qiskit, transpiles it for Qiskit Aer, and submits it to the local Aer simulator.

. .venv/bin/activate
python -m pip install --upgrade pip
python -m pip install -r requirements.txt
python scripts/run_hhl_ibm_aer.py

The default run writes:

• outputs/hhl_ibm_aer_transpiled.qasm with the OpenQASM 3.0 circuit emitted after Qiskit transpilation of the pre-measurement unitary circuit.
• outputs/hhl_ibm_aer_result.json with source circuit metrics, compiled simulator metrics, statevector probabilities before ancilla measurement, sampled ancilla shot counts, and the post-selection probability for c[0] == 1.