qml.taper

taper(h, generators, paulixops, paulix_sector)

Transform a Hamiltonian with a Clifford operator and then taper qubits.

The Hamiltonian is transformed as \(H' = U^{\dagger} H U\) where \(U\) is a Clifford operator. The transformed Hamiltonian acts trivially on some qubits which are then replaced with the eigenvalues of their corresponding Pauli-X operator. The list of these eigenvalues is defined as the Pauli sector.

Parameters

• h (Operator) – Hamiltonian as a PennyLane operator

• generators (list[Operator]) – generators expressed as PennyLane Hamiltonians

• paulixops (list[Operation]) – list of single-qubit Pauli-X operators

• paulix_sector (list[int]) – eigenvalues of the Pauli-X operators

Returns

the tapered Hamiltonian

Return type

(Operator)

Example

>>> symbols = ["H", "H"]
>>> geometry = np.array([[0.0, 0.0, -0.69440367], [0.0, 0.0, 0.69440367]])
>>> H, qubits = qml.qchem.molecular_hamiltonian(symbols, geometry)
>>> generators = qml.qchem.symmetry_generators(H)
>>> paulixops = paulix_ops(generators, 4)
>>> paulix_sector = [1, -1, -1]
>>> H_tapered = taper(H, generators, paulixops, paulix_sector)
>>> H_tapered
(
    (-0.3210343973331179-2.0816681711721685e-17j) * I(0)
  + (0.7959678504583807+0j) * Z(0)
  + (0.18092702760702645+0j) * X(0)
)

code/api/pennylane.taper

 

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