def test_trace_out_xy(theta):
a = numpy.sin(theta)
b = numpy.cos(theta)
state = QubitWaveFunction.from_array([a,b])
H1 = QubitHamiltonian.from_string("1.0*X(0)*X(1)*X(100)")
H2 = QubitHamiltonian.from_string("1.0*X(0)*X(100)")
factor = a.conjugate()*b + b.conjugate()*a
assert factor*H2 == H1.trace_out_qubits(qubits=[1,3,5], states=[state]*3)
factor *= factor
H1 = QubitHamiltonian.from_string("1.0*X(0)*X(1)*X(5)*X(100)")
assert factor*H2 == H1.trace_out_qubits(qubits=[1,3,5], states=[state]*3)
H1 = QubitHamiltonian.from_string("1.0*X(0)*Y(1)*X(100)")
H2 = QubitHamiltonian.from_string("1.0*X(0)*X(100)")
factor = -1.0j*(a.conjugate()*b - b.conjugate()*a)
assert factor*H2 == H1.trace_out_qubits(qubits=[1,3,5], states=[state]*3)
factor *= factor
H1 = QubitHamiltonian.from_string("1.0*X(0)*Y(1)*Y(5)*X(100)")
assert factor*H2 == H1.trace_out_qubits(qubits=[1,3,5], states=[state]*3)
H1 = QubitHamiltonian.from_string("1.0*X(0)*X(1)*X(100)")
H2 = QubitHamiltonian.from_string("1.0*X(0)*X(100)")
factor = a.conjugate()*b + b.conjugate()*a
assert factor*H2 == H1.trace_out_qubits(qubits=[1,3,5], states=[state]*3)
factor *= -1.0j*(a.conjugate()*b - b.conjugate()*a)
H1 = QubitHamiltonian.from_string("1.0*X(0)*X(1)*Y(5)*X(100)")
assert factor*H2 == H1.trace_out_qubits(qubits=[1,3,5], states=[state]*3)
def test_projectors(qubits):
real = numpy.random.uniform(0.0, 1.0, 2**qubits)
imag = numpy.random.uniform(0.0, 1.0, 2**qubits)
array = real + 1.j * imag
wfn = QubitWaveFunction.from_array(arr=array)
P = paulis.Projector(wfn=wfn.normalize())
assert (P.is_hermitian())
assert (wfn.apply_qubitoperator(P) == wfn)
PM = P.to_matrix()
assert ((PM.dot(PM) == PM).all)
def test_ketbra_random(n_qubits):
ket = numpy.random.uniform(0.0, 1.0, 2**n_qubits)
bra = QubitWaveFunction.from_int(0, n_qubits=n_qubits)
operator = paulis.KetBra(ket=ket, bra=bra)
result = operator * bra
assert result == QubitWaveFunction.from_array(ket)