{
  "A_coefficient": "a_(k,r)=sum_(m=0)^r choose(k+r-m,k)/m!; 0<=r<=k",
  "allowed_gates": [
    "ry",
    "cx"
  ],
  "amplitude": "exp(p) for p<=-1; exp(-1)*(1-t)^(k+1)*A_k(t)+t^(k+1)*A_k(1-t) for -1<p<0, t=p+1; exp(-p) for p>=0",
  "ancillas": [],
  "checkBackends": {
    "internalCanonicalEvaluator": {
      "method": "independent NumPy primitive statevector",
      "status": "passed"
    },
    "openqasm3RoundTrip": {
      "method": "Qiskit qasm3.loads followed by statevector replay",
      "status": "passed"
    },
    "qiskitOperator": {
      "method": "Qiskit Statevector.from_instruction, not full Operator",
      "status": "passed"
    }
  },
  "circuit": "circuit.qasm",
  "control_order": "low to high",
  "executable_evidence": "acceptance.json",
  "exporter": "executable-exports/SP-HERMITE-001/qiskit/export.py",
  "grid": "p_j=-pi*L+2*pi*L*j/2^n",
  "lean_gate": "separate repository build; this manifest is not build evidence",
  "normalization": "f_j/sqrt(sum_i f_i^2)",
  "parameters": {
    "L": 1.0,
    "k": 1,
    "n": 3
  },
  "registers": [
    {
      "input": "0",
      "integer_bit_weight": 1,
      "name": "q[0]",
      "output": "data amplitude"
    },
    {
      "input": "0",
      "integer_bit_weight": 2,
      "name": "q[1]",
      "output": "data amplitude"
    },
    {
      "input": "0",
      "integer_bit_weight": 4,
      "name": "q[2]",
      "output": "data amplitude"
    }
  ],
  "samples": "samples.csv",
  "schema_version": 1,
  "smoothness": "C^k splice; the k=1 cubic is not asserted to be C^2",
  "source": "https://arxiv.org/abs/2403.19123",
  "source_anchor": "Section 4.3, equations 4.31-4.32 (v3)",
  "task": "SP-HERMITE-001",
  "theorem_links": [
    {
      "declaration": "QuantumBlockEncoding.compileUniformlyControlledRy_eval_controlledRyBlockMatrix",
      "scope": "exact primitive multiplexor compilation",
      "source": "QuantumBlockEncoding/UniformlyControlledRy.lean"
    }
  ]
}