160 lines
4.8 KiB
Python
160 lines
4.8 KiB
Python
from sympy.core.mul import Mul
|
|
from sympy.core.numbers import I
|
|
from sympy.matrices.dense import Matrix
|
|
from sympy.printing.latex import latex
|
|
from sympy.physics.quantum import (Dagger, Commutator, AntiCommutator, qapply,
|
|
Operator, represent)
|
|
from sympy.physics.quantum.pauli import (SigmaOpBase, 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():
|
|
|
|
assert Commutator(sx, sy).doit() == 2 * I * sz
|
|
assert Commutator(sy, sz).doit() == 2 * I * sx
|
|
assert Commutator(sz, sx).doit() == 2 * I * sy
|
|
|
|
|
|
def test_pauli_operators_commutator_with_labels():
|
|
|
|
assert Commutator(sx1, sy1).doit() == 2 * I * sz1
|
|
assert Commutator(sy1, sz1).doit() == 2 * I * sx1
|
|
assert Commutator(sz1, sx1).doit() == 2 * I * sy1
|
|
|
|
assert Commutator(sx2, sy2).doit() == 2 * I * sz2
|
|
assert Commutator(sy2, sz2).doit() == 2 * I * sx2
|
|
assert Commutator(sz2, sx2).doit() == 2 * I * sy2
|
|
|
|
assert Commutator(sx1, sy2).doit() == 0
|
|
assert Commutator(sy1, sz2).doit() == 0
|
|
assert Commutator(sz1, sx2).doit() == 0
|
|
|
|
|
|
def test_pauli_operators_anticommutator():
|
|
|
|
assert AntiCommutator(sy, sz).doit() == 0
|
|
assert AntiCommutator(sz, sx).doit() == 0
|
|
assert AntiCommutator(sx, sm).doit() == 1
|
|
assert AntiCommutator(sx, sp).doit() == 1
|
|
|
|
|
|
def test_pauli_operators_adjoint():
|
|
|
|
assert Dagger(sx) == sx
|
|
assert Dagger(sy) == sy
|
|
assert Dagger(sz) == sz
|
|
|
|
|
|
def test_pauli_operators_adjoint_with_labels():
|
|
|
|
assert Dagger(sx1) == sx1
|
|
assert Dagger(sy1) == sy1
|
|
assert Dagger(sz1) == sz1
|
|
|
|
assert Dagger(sx1) != sx2
|
|
assert Dagger(sy1) != sy2
|
|
assert Dagger(sz1) != sz2
|
|
|
|
|
|
def test_pauli_operators_multiplication():
|
|
|
|
assert qsimplify_pauli(sx * sx) == 1
|
|
assert qsimplify_pauli(sy * sy) == 1
|
|
assert qsimplify_pauli(sz * sz) == 1
|
|
|
|
assert qsimplify_pauli(sx * sy) == I * sz
|
|
assert qsimplify_pauli(sy * sz) == I * sx
|
|
assert qsimplify_pauli(sz * sx) == I * sy
|
|
|
|
assert qsimplify_pauli(sy * sx) == - I * sz
|
|
assert qsimplify_pauli(sz * sy) == - I * sx
|
|
assert qsimplify_pauli(sx * sz) == - I * sy
|
|
|
|
|
|
def test_pauli_operators_multiplication_with_labels():
|
|
|
|
assert qsimplify_pauli(sx1 * sx1) == 1
|
|
assert qsimplify_pauli(sy1 * sy1) == 1
|
|
assert qsimplify_pauli(sz1 * sz1) == 1
|
|
|
|
assert isinstance(sx1 * sx2, Mul)
|
|
assert isinstance(sy1 * sy2, Mul)
|
|
assert isinstance(sz1 * sz2, Mul)
|
|
|
|
assert qsimplify_pauli(sx1 * sy1 * sx2 * sy2) == - sz1 * sz2
|
|
assert qsimplify_pauli(sy1 * sz1 * sz2 * sx2) == - sx1 * sy2
|
|
|
|
|
|
def test_pauli_states():
|
|
sx, sz = SigmaX(), SigmaZ()
|
|
|
|
up = SigmaZKet(0)
|
|
down = SigmaZKet(1)
|
|
|
|
assert qapply(sx * up) == down
|
|
assert qapply(sx * down) == up
|
|
assert qapply(sz * up) == up
|
|
assert qapply(sz * down) == - down
|
|
|
|
up = SigmaZBra(0)
|
|
down = SigmaZBra(1)
|
|
|
|
assert qapply(up * sx, dagger=True) == down
|
|
assert qapply(down * sx, dagger=True) == up
|
|
assert qapply(up * sz, dagger=True) == up
|
|
assert qapply(down * sz, dagger=True) == - down
|
|
|
|
assert Dagger(SigmaZKet(0)) == SigmaZBra(0)
|
|
assert Dagger(SigmaZBra(1)) == SigmaZKet(1)
|
|
raises(ValueError, lambda: SigmaZBra(2))
|
|
raises(ValueError, lambda: SigmaZKet(2))
|
|
|
|
|
|
def test_use_name():
|
|
assert sm.use_name is False
|
|
assert sm1.use_name is True
|
|
assert sx.use_name is False
|
|
assert sx1.use_name is True
|
|
|
|
|
|
def test_printing():
|
|
assert latex(sx) == r'{\sigma_x}'
|
|
assert latex(sx1) == r'{\sigma_x^{(1)}}'
|
|
assert latex(sy) == r'{\sigma_y}'
|
|
assert latex(sy1) == r'{\sigma_y^{(1)}}'
|
|
assert latex(sz) == r'{\sigma_z}'
|
|
assert latex(sz1) == r'{\sigma_z^{(1)}}'
|
|
assert latex(sm) == r'{\sigma_-}'
|
|
assert latex(sm1) == r'{\sigma_-^{(1)}}'
|
|
assert latex(sp) == r'{\sigma_+}'
|
|
assert latex(sp1) == r'{\sigma_+^{(1)}}'
|
|
|
|
|
|
def test_represent():
|
|
assert represent(sx) == Matrix([[0, 1], [1, 0]])
|
|
assert represent(sy) == Matrix([[0, -I], [I, 0]])
|
|
assert represent(sz) == Matrix([[1, 0], [0, -1]])
|
|
assert represent(sm) == Matrix([[0, 0], [1, 0]])
|
|
assert represent(sp) == Matrix([[0, 1], [0, 0]])
|