def test_one_qubit_commutators():
"""Test single qubit gate commutation relations."""
for g1 in (IdentityGate, X, Y, Z, H, T, S):
for g2 in (IdentityGate, X, Y, Z, H, T, S):
e = Commutator(g1(0), g2(0))
a = matrix_to_zero(represent(e, nqubits=1, format='sympy'))
b = matrix_to_zero(represent(e.doit(), nqubits=1, format='sympy'))
assert a == b
e = Commutator(g1(0), g2(1))
assert e.doit() == 0
def test_one_qubit_commutators():
"""Test single qubit gate commutation relations."""
for g1 in (IdentityGate, X, Y, Z, H, T, S):
for g2 in (IdentityGate, X, Y, Z, H, T, S):
e = Commutator(g1(0),g2(0))
a = matrix_to_zero(represent(e, nqubits=1, format='sympy'))
b = matrix_to_zero(represent(e.doit(), nqubits=1, format='sympy'))
assert a == b
e = Commutator(g1(0),g2(1))
assert e.doit() == 0
def test_commutator_identities():
assert Comm(a * A, b * B) == a * b * Comm(A, B)
assert Comm(A, A) == 0
assert Comm(a, b) == 0
assert Comm(A, B) == -Comm(B, A)
assert Comm(A, B).doit() == A * B - B * A
assert Comm(A, B *
C).expand(commutator=True) == Comm(A, B) * C + B * Comm(A, C)
assert (Comm(A * B, C * D).expand(commutator=True) == A * C * Comm(B, D) +
A * Comm(B, C) * D + C * Comm(A, D) * B + Comm(A, C) * D * B)
assert Comm(
A, B**2).expand(commutator=True) == Comm(A, B) * B + B * Comm(A, B)
assert (Comm(A**2, C**2).expand(commutator=True) ==
Comm(A * B, C * D).expand(commutator=True).replace(B, A).replace(
D, C) == A * C * Comm(A, C) + A * Comm(A, C) * C +
C * Comm(A, C) * A + Comm(A, C) * C * A)
assert Comm(A, C**-2).expand(commutator=True) == Comm(
A, (1 / C) * (1 / D)).expand(commutator=True).replace(D, C)
assert Comm(A + B, C + D).expand(
commutator=True) == Comm(A, C) + Comm(A, D) + Comm(B, C) + Comm(B, D)
assert Comm(A, B + C).expand(commutator=True) == Comm(A, B) + Comm(A, C)
assert Comm(A**n, B).expand(commutator=True) == Comm(A**n, B)
e = Comm(A, Comm(B, C)) + Comm(B, Comm(C, A)) + Comm(C, Comm(A, B))
assert e.doit().expand() == 0
def test_commutator_identities():
assert Comm(a*A,b*B) == a*b*Comm(A,B)
assert Comm(A, A) == 0
assert Comm(a, b) == 0
assert Comm(A,B) == -Comm(B,A)
assert Comm(A,B).doit() == A*B - B*A
assert Comm(A,B*C).expand(commutator=True) == Comm(A,B)*C + B*Comm(A,C)
assert Comm(A*B,C).expand(commutator=True) == A*Comm(B,C) + Comm(A,C)*B
assert Comm(A+B,C).expand(commutator=True) == Comm(A,C) + Comm(B,C)
assert Comm(A,B+C).expand(commutator=True) == Comm(A,B) + Comm(A,C)
e = Comm(A,Comm(B,C))+Comm(B,Comm(C,A))+Comm(C,Comm(A,B))
assert e.doit().expand() == 0
def test_commutator_identities():
assert Comm(a * A, b * B) == a * b * Comm(A, B)
assert Comm(A, A) == 0
assert Comm(a, b) == 0
assert Comm(A, B) == -Comm(B, A)
assert Comm(A, B).doit() == A * B - B * A
assert Comm(A, B *
C).expand(commutator=True) == Comm(A, B) * C + B * Comm(A, C)
assert Comm(A * B,
C).expand(commutator=True) == A * Comm(B, C) + Comm(A, C) * B
assert Comm(A + B, C).expand(commutator=True) == Comm(A, C) + Comm(B, C)
assert Comm(A, B + C).expand(commutator=True) == Comm(A, B) + Comm(A, C)
e = Comm(A, Comm(B, C)) + Comm(B, Comm(C, A)) + Comm(C, Comm(A, B))
assert e.doit().expand() == 0