metadata.json

{
  "id": "hhl-algorithm",
  "name": "HHL Algorithm (2\u00d72 Linear System)",
  "category": "simulation",
  "description": "Harrow-Hassidim-Lloyd algorithm: solve Ax=b for a 2\u00d72 system A=diag(1,2), b=|0\u27e9 using 4 qubits.",
  "long_description": "The HHL algorithm solves sparse linear systems Ax=b exponentially faster than classical algorithms in certain regimes. It applies QPE to encode eigenvalues \u03bb, performs a conditional rotation 1/\u03bb on an ancilla, then uncomputes with inverse QPE. Post-selecting ancilla=|1\u27e9 yields |x\u27e9 \u221d A\u207b\u00b9|b\u27e9. For A=diag(1,2) with eigenvalues 1 and 2, b=|0\u27e9 is an eigenstate so x=A\u207b\u00b9b=|0\u27e9. This circuit is a pedagogical 4-qubit simplification.",
  "difficulty": "advanced",
  "qubit_count": 4,
  "clbit_count": 1,
  "gate_count": 18,
  "depth": 12,
  "tags": [
    "hhl",
    "linear-systems",
    "quantum-simulation",
    "exponential-speedup"
  ],
  "circuit_formats": [
    "qasm2"
  ],
  "source_file": "circuit.qasm",
  "expected_output": "Post-select ancilla=1 to obtain |x\u27e9 \u221d A\u207b\u00b9|b\u27e9",
  "references": [
    {
      "title": "Harrow, Hassidim, Lloyd (2009). Quantum Algorithm for Linear Systems of Equations. PRL 103, 150502",
      "url": "https://doi.org/10.1103/PhysRevLett.103.150502"
    }
  ],
  "author": "OpenQC Community",
  "license": "MIT",
  "version": "1.0.0"
}