def pauli_represent_minus_plus(e):
"""
Traverse an expression and change all instances of SigmaX and SigmaY
to the corresponding expressions using SigmaMinus and SigmaPlus.
"""
# XXX: todo, make sure that new operators inherit labels
return expression_tree_transform(
e, [(lambda e: isinstance(e, SigmaX),
lambda e: SigmaMinus() + SigmaPlus()),
(lambda e: isinstance(e, SigmaY),
lambda e: I * SigmaMinus() - I * SigmaPlus())])
SigmaX,
SigmaY,
SigmaZ,
SigmaMinus,
SigmaPlus,
qsimplify_pauli,
)
from sympy.physics.quantum.pauli import SigmaZKet, SigmaZBra
from sympy.testing.pytest import raises
sx, sy, sz = SigmaX(), SigmaY(), SigmaZ()
sx1, sy1, sz1 = SigmaX(1), SigmaY(1), SigmaZ(1)
sx2, sy2, sz2 = SigmaX(2), SigmaY(2), SigmaZ(2)
sm, sp = SigmaMinus(), SigmaPlus()
sm1, sp1 = SigmaMinus(1), SigmaPlus(1)
A, B = Operator("A"), Operator("B")
def test_pauli_operators_types():
assert isinstance(sx, SigmaOpBase) and isinstance(sx, SigmaX)
assert isinstance(sy, SigmaOpBase) and isinstance(sy, SigmaY)
assert isinstance(sz, SigmaOpBase) and isinstance(sz, SigmaZ)
assert isinstance(sm, SigmaOpBase) and isinstance(sm, SigmaMinus)
assert isinstance(sp, SigmaOpBase) and isinstance(sp, SigmaPlus)
def test_pauli_operators_commutator():
from sympy import I, Mul
from sympy.physics.quantum import (Dagger, Commutator, AntiCommutator, qapply,
Operator)
from sympy.physics.quantum.pauli import (SigmaOpBase, SigmaX, SigmaY, SigmaZ,
SigmaMinus, SigmaPlus,
qsimplify_pauli)
from sympy.physics.quantum.pauli import SigmaZKet, SigmaZBra
sx, sy, sz = SigmaX(), SigmaY(), SigmaZ()
sx1, sy1, sz1 = SigmaX(1), SigmaY(1), SigmaZ(1)
sx2, sy2, sz2 = SigmaX(2), SigmaY(2), SigmaZ(2)
sm, sp = SigmaMinus(), SigmaPlus()
A, B = Operator("A"), Operator("B")
def test_pauli_operators_types():
assert isinstance(sx, SigmaOpBase) and isinstance(sx, SigmaX)
assert isinstance(sy, SigmaOpBase) and isinstance(sy, SigmaY)
assert isinstance(sz, SigmaOpBase) and isinstance(sz, SigmaZ)
assert isinstance(sm, SigmaOpBase) and isinstance(sm, SigmaMinus)
assert isinstance(sp, SigmaOpBase) and isinstance(sp, SigmaPlus)
def test_pauli_operators_commutator():
assert Commutator(sx, sy).doit() == 2 * I * sz
assert Commutator(sy, sz).doit() == 2 * I * sx
assert Commutator(sz, sx).doit() == 2 * I * sy