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Mini Shell
Mini Shell
from sympy import exp, symbols, sqrt, I, pi, Mul, Integer, Wild, Rational
from sympy.matrices import Matrix, ImmutableMatrix
from sympy.physics.quantum.gate import (XGate, YGate, ZGate, random_circuit,
CNOT, IdentityGate, H, X, Y, S, T, Z, SwapGate, gate_simp, gate_sort,
CNotGate, TGate, HadamardGate, PhaseGate, UGate, CGate)
from sympy.physics.quantum.commutator import Commutator
from sympy.physics.quantum.anticommutator import AntiCommutator
from sympy.physics.quantum.represent import represent
from sympy.physics.quantum.qapply import qapply
from sympy.physics.quantum.qubit import Qubit, IntQubit, qubit_to_matrix, \
matrix_to_qubit
from sympy.physics.quantum.matrixutils import matrix_to_zero
from sympy.physics.quantum.matrixcache import sqrt2_inv
from sympy.physics.quantum import Dagger
def test_gate():
"""Test a basic gate."""
h = HadamardGate(1)
assert h.min_qubits == 2
assert h.nqubits == 1
i0 = Wild('i0')
i1 = Wild('i1')
h0_w1 = HadamardGate(i0)
h0_w2 = HadamardGate(i0)
h1_w1 = HadamardGate(i1)
assert h0_w1 == h0_w2
assert h0_w1 != h1_w1
assert h1_w1 != h0_w2
cnot_10_w1 = CNOT(i1, i0)
cnot_10_w2 = CNOT(i1, i0)
cnot_01_w1 = CNOT(i0, i1)
assert cnot_10_w1 == cnot_10_w2
assert cnot_10_w1 != cnot_01_w1
assert cnot_10_w2 != cnot_01_w1
def test_UGate():
a, b, c, d = symbols('a,b,c,d')
uMat = Matrix([[a, b], [c, d]])
# Test basic case where gate exists in 1-qubit space
u1 = UGate((0,), uMat)
assert represent(u1, nqubits=1) == uMat
assert qapply(u1*Qubit('0')) == a*Qubit('0') + c*Qubit('1')
assert qapply(u1*Qubit('1')) == b*Qubit('0') + d*Qubit('1')
# Test case where gate exists in a larger space
u2 = UGate((1,), uMat)
u2Rep = represent(u2, nqubits=2)
for i in range(4):
assert u2Rep*qubit_to_matrix(IntQubit(i, 2)) == \
qubit_to_matrix(qapply(u2*IntQubit(i, 2)))
def test_cgate():
"""Test the general CGate."""
# Test single control functionality
CNOTMatrix = Matrix(
[[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]])
assert represent(CGate(1, XGate(0)), nqubits=2) == CNOTMatrix
# Test multiple control bit functionality
ToffoliGate = CGate((1, 2), XGate(0))
assert represent(ToffoliGate, nqubits=3) == \
Matrix(
[[1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0,
1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 0, 1, 0]])
ToffoliGate = CGate((3, 0), XGate(1))
assert qapply(ToffoliGate*Qubit('1001')) == \
matrix_to_qubit(represent(ToffoliGate*Qubit('1001'), nqubits=4))
assert qapply(ToffoliGate*Qubit('0000')) == \
matrix_to_qubit(represent(ToffoliGate*Qubit('0000'), nqubits=4))
CYGate = CGate(1, YGate(0))
CYGate_matrix = Matrix(
((1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 0, -I), (0, 0, I, 0)))
# Test 2 qubit controlled-Y gate decompose method.
assert represent(CYGate.decompose(), nqubits=2) == CYGate_matrix
CZGate = CGate(0, ZGate(1))
CZGate_matrix = Matrix(
((1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, -1)))
assert qapply(CZGate*Qubit('11')) == -Qubit('11')
assert matrix_to_qubit(represent(CZGate*Qubit('11'), nqubits=2)) == \
-Qubit('11')
# Test 2 qubit controlled-Z gate decompose method.
assert represent(CZGate.decompose(), nqubits=2) == CZGate_matrix
CPhaseGate = CGate(0, PhaseGate(1))
assert qapply(CPhaseGate*Qubit('11')) == \
I*Qubit('11')
assert matrix_to_qubit(represent(CPhaseGate*Qubit('11'), nqubits=2)) == \
I*Qubit('11')
# Test that the dagger, inverse, and power of CGate is evaluated properly
assert Dagger(CZGate) == CZGate
assert pow(CZGate, 1) == Dagger(CZGate)
assert Dagger(CZGate) == CZGate.inverse()
assert Dagger(CPhaseGate) != CPhaseGate
assert Dagger(CPhaseGate) == CPhaseGate.inverse()
assert Dagger(CPhaseGate) == pow(CPhaseGate, -1)
assert pow(CPhaseGate, -1) == CPhaseGate.inverse()
def test_UGate_CGate_combo():
a, b, c, d = symbols('a,b,c,d')
uMat = Matrix([[a, b], [c, d]])
cMat = Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, a, b], [0, 0, c, d]])
# Test basic case where gate exists in 1-qubit space.
u1 = UGate((0,), uMat)
cu1 = CGate(1, u1)
assert represent(cu1, nqubits=2) == cMat
assert qapply(cu1*Qubit('10')) == a*Qubit('10') + c*Qubit('11')
assert qapply(cu1*Qubit('11')) == b*Qubit('10') + d*Qubit('11')
assert qapply(cu1*Qubit('01')) == Qubit('01')
assert qapply(cu1*Qubit('00')) == Qubit('00')
# Test case where gate exists in a larger space.
u2 = UGate((1,), uMat)
u2Rep = represent(u2, nqubits=2)
for i in range(4):
assert u2Rep*qubit_to_matrix(IntQubit(i, 2)) == \
qubit_to_matrix(qapply(u2*IntQubit(i, 2)))
def test_UGate_OneQubitGate_combo():
v, w, f, g = symbols('v w f g')
uMat1 = ImmutableMatrix([[v, w], [f, g]])
cMat1 = Matrix([[v, w + 1, 0, 0], [f + 1, g, 0, 0], [0, 0, v, w + 1], [0, 0, f + 1, g]])
u1 = X(0) + UGate(0, uMat1)
assert represent(u1, nqubits=2) == cMat1
uMat2 = ImmutableMatrix([[1/sqrt(2), 1/sqrt(2)], [I/sqrt(2), -I/sqrt(2)]])
cMat2_1 = Matrix([[Rational(1, 2) + I/2, Rational(1, 2) - I/2],
[Rational(1, 2) - I/2, Rational(1, 2) + I/2]])
cMat2_2 = Matrix([[1, 0], [0, I]])
u2 = UGate(0, uMat2)
assert represent(H(0)*u2, nqubits=1) == cMat2_1
assert represent(u2*H(0), nqubits=1) == cMat2_2
def test_represent_hadamard():
"""Test the representation of the hadamard gate."""
circuit = HadamardGate(0)*Qubit('00')
answer = represent(circuit, nqubits=2)
# Check that the answers are same to within an epsilon.
assert answer == Matrix([sqrt2_inv, sqrt2_inv, 0, 0])
def test_represent_xgate():
"""Test the representation of the X gate."""
circuit = XGate(0)*Qubit('00')
answer = represent(circuit, nqubits=2)
assert Matrix([0, 1, 0, 0]) == answer
def test_represent_ygate():
"""Test the representation of the Y gate."""
circuit = YGate(0)*Qubit('00')
answer = represent(circuit, nqubits=2)
assert answer[0] == 0 and answer[1] == I and \
answer[2] == 0 and answer[3] == 0
def test_represent_zgate():
"""Test the representation of the Z gate."""
circuit = ZGate(0)*Qubit('00')
answer = represent(circuit, nqubits=2)
assert Matrix([1, 0, 0, 0]) == answer
def test_represent_phasegate():
"""Test the representation of the S gate."""
circuit = PhaseGate(0)*Qubit('01')
answer = represent(circuit, nqubits=2)
assert Matrix([0, I, 0, 0]) == answer
def test_represent_tgate():
"""Test the representation of the T gate."""
circuit = TGate(0)*Qubit('01')
assert Matrix([0, exp(I*pi/4), 0, 0]) == represent(circuit, nqubits=2)
def test_compound_gates():
"""Test a compound gate representation."""
circuit = YGate(0)*ZGate(0)*XGate(0)*HadamardGate(0)*Qubit('00')
answer = represent(circuit, nqubits=2)
assert Matrix([I/sqrt(2), I/sqrt(2), 0, 0]) == answer
def test_cnot_gate():
"""Test the CNOT gate."""
circuit = CNotGate(1, 0)
assert represent(circuit, nqubits=2) == \
Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]])
circuit = circuit*Qubit('111')
assert matrix_to_qubit(represent(circuit, nqubits=3)) == \
qapply(circuit)
circuit = CNotGate(1, 0)
assert Dagger(circuit) == circuit
assert Dagger(Dagger(circuit)) == circuit
assert circuit*circuit == 1
def test_gate_sort():
"""Test gate_sort."""
for g in (X, Y, Z, H, S, T):
assert gate_sort(g(2)*g(1)*g(0)) == g(0)*g(1)*g(2)
e = gate_sort(X(1)*H(0)**2*CNOT(0, 1)*X(1)*X(0))
assert e == H(0)**2*CNOT(0, 1)*X(0)*X(1)**2
assert gate_sort(Z(0)*X(0)) == -X(0)*Z(0)
assert gate_sort(Z(0)*X(0)**2) == X(0)**2*Z(0)
assert gate_sort(Y(0)*H(0)) == -H(0)*Y(0)
assert gate_sort(Y(0)*X(0)) == -X(0)*Y(0)
assert gate_sort(Z(0)*Y(0)) == -Y(0)*Z(0)
assert gate_sort(T(0)*S(0)) == S(0)*T(0)
assert gate_sort(Z(0)*S(0)) == S(0)*Z(0)
assert gate_sort(Z(0)*T(0)) == T(0)*Z(0)
assert gate_sort(Z(0)*CNOT(0, 1)) == CNOT(0, 1)*Z(0)
assert gate_sort(S(0)*CNOT(0, 1)) == CNOT(0, 1)*S(0)
assert gate_sort(T(0)*CNOT(0, 1)) == CNOT(0, 1)*T(0)
assert gate_sort(X(1)*CNOT(0, 1)) == CNOT(0, 1)*X(1)
# This takes a long time and should only be uncommented once in a while.
# nqubits = 5
# ngates = 10
# trials = 10
# for i in range(trials):
# c = random_circuit(ngates, nqubits)
# assert represent(c, nqubits=nqubits) == \
# represent(gate_sort(c), nqubits=nqubits)
def test_gate_simp():
"""Test gate_simp."""
e = H(0)*X(1)*H(0)**2*CNOT(0, 1)*X(1)**3*X(0)*Z(3)**2*S(4)**3
assert gate_simp(e) == H(0)*CNOT(0, 1)*S(4)*X(0)*Z(4)
assert gate_simp(X(0)*X(0)) == 1
assert gate_simp(Y(0)*Y(0)) == 1
assert gate_simp(Z(0)*Z(0)) == 1
assert gate_simp(H(0)*H(0)) == 1
assert gate_simp(T(0)*T(0)) == S(0)
assert gate_simp(S(0)*S(0)) == Z(0)
assert gate_simp(Integer(1)) == Integer(1)
assert gate_simp(X(0)**2 + Y(0)**2) == Integer(2)
def test_swap_gate():
"""Test the SWAP gate."""
swap_gate_matrix = Matrix(
((1, 0, 0, 0), (0, 0, 1, 0), (0, 1, 0, 0), (0, 0, 0, 1)))
assert represent(SwapGate(1, 0).decompose(), nqubits=2) == swap_gate_matrix
assert qapply(SwapGate(1, 3)*Qubit('0010')) == Qubit('1000')
nqubits = 4
for i in range(nqubits):
for j in range(i):
assert represent(SwapGate(i, j), nqubits=nqubits) == \
represent(SwapGate(i, j).decompose(), nqubits=nqubits)
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_anticommutators():
"""Test single qubit gate anticommutation relations."""
for g1 in (IdentityGate, X, Y, Z, H):
for g2 in (IdentityGate, X, Y, Z, H):
e = AntiCommutator(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 = AntiCommutator(g1(0), g2(1))
a = matrix_to_zero(represent(e, nqubits=2, format='sympy'))
b = matrix_to_zero(represent(e.doit(), nqubits=2, format='sympy'))
assert a == b
def test_cnot_commutators():
"""Test commutators of involving CNOT gates."""
assert Commutator(CNOT(0, 1), Z(0)).doit() == 0
assert Commutator(CNOT(0, 1), T(0)).doit() == 0
assert Commutator(CNOT(0, 1), S(0)).doit() == 0
assert Commutator(CNOT(0, 1), X(1)).doit() == 0
assert Commutator(CNOT(0, 1), CNOT(0, 1)).doit() == 0
assert Commutator(CNOT(0, 1), CNOT(0, 2)).doit() == 0
assert Commutator(CNOT(0, 2), CNOT(0, 1)).doit() == 0
assert Commutator(CNOT(1, 2), CNOT(1, 0)).doit() == 0
def test_random_circuit():
c = random_circuit(10, 3)
assert isinstance(c, Mul)
m = represent(c, nqubits=3)
assert m.shape == (8, 8)
assert isinstance(m, Matrix)
def test_hermitian_XGate():
x = XGate(1, 2)
x_dagger = Dagger(x)
assert (x == x_dagger)
def test_hermitian_YGate():
y = YGate(1, 2)
y_dagger = Dagger(y)
assert (y == y_dagger)
def test_hermitian_ZGate():
z = ZGate(1, 2)
z_dagger = Dagger(z)
assert (z == z_dagger)
def test_unitary_XGate():
x = XGate(1, 2)
x_dagger = Dagger(x)
assert (x*x_dagger == 1)
def test_unitary_YGate():
y = YGate(1, 2)
y_dagger = Dagger(y)
assert (y*y_dagger == 1)
def test_unitary_ZGate():
z = ZGate(1, 2)
z_dagger = Dagger(z)
assert (z*z_dagger == 1)
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