dependabot: bump pennylane from 0.20.0 to 0.32.0

Bumps pennylane from 0.20.0 to 0.32.0.

Release notes

Release 0.32.0
It is now possible to encode an operator A into a quantum circuit by decomposing it into a linear combination of unitaries using PREP (qml.StatePrep) and SELECT (qml.Select) routines. [(#4431)](PennyLaneAI/pennylane#4431) [(#4437)](PennyLaneAI/pennylane#4437) [(#4444)](PennyLaneAI/pennylane#4444) [(#4450)](PennyLaneAI/pennylane#4450) [(#4506)](PennyLaneAI/pennylane#4506) [(#4526)](PennyLaneAI/pennylane#4526)

Consider an operator A composed of a linear combination of Pauli terms:
>>> A = qml.PauliX(2) + 2 * qml.PauliY(2) + 3 * qml.PauliZ(2)
A decomposable block-encoding circuit can be created:
def block_encode(A, control_wires):
    probs = A.coeffs / np.sum(A.coeffs)
    state = np.pad(np.sqrt(probs, dtype=complex), (0, 1))
    unitaries = A.ops
qml.StatePrep(state, wires=control_wires)
qml.Select(unitaries, control=control_wires)
qml.adjoint(qml.StatePrep)(state, wires=control_wires)
>>> print(qml.draw(block_encode, show_matrices=False)(A, control_wires=[0, 1]))
0: ─╭|Ψ⟩─╭Select─╭|Ψ⟩†─┤
1: ─╰|Ψ⟩─├Select─╰|Ψ⟩†─┤
2: ──────╰Select───────┤
This circuit can be used as a building block within a larger QNode to perform algorithms such as QSVT and Hamiltonian simulation.
Decomposing a Hermitian matrix into a linear combination of Pauli words via qml.pauli_decompose is now faster and differentiable. [(#4395)](PennyLaneAI/pennylane#4395) [(#4479)](PennyLaneAI/pennylane#4479) [(#4493)](PennyLaneAI/pennylane#4493)
def find_coeffs(p):
    mat = np.array([[3, p], [p, 3]])
    A = qml.pauli_decompose(mat)
    return A.coeffs
>>> import jax
>>> from jax import numpy as np
>>> jax.jacobian(find_coeffs)(np.array(2.))
Array([0., 1.], dtype=float32, weak_type=True)

... (truncated)

Commits

a9bc37a Update lightning requirement (#4530)
6c19e49 v0.32 release notes (#4496)
d1b256d Fix incorrect gradient in qml.Select (#4526)
c0bce9a Put defer_measurements back in QNode construction (#4516)
5ea4f3e change links (#4491)
a6bb6f8 bugfixes to unblock teleportation tutorial (#4518)
aa4172f More 0.32 related fixes (#4520)
9d23fe3 correct pyscf link in chemistry doc (#4525)
0901fe2 little fixups from timmysilv for the 0.32 release (#4517)
e295ef7 Change how Select is displayed in circuit drawer (#4506)
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quantum-ods / qmlcourse

dependabot: bump pennylane from 0.20.0 to 0.32.0 #563

Release 0.32.0