def create_product_testvectors():
"""yield instances of class ``QStateMatrix`` for tests """
for m1_data, m2_data, nqb in qs_matrix_data:
m1 = create_m(*m1_data)
m2 = create_m(*m2_data)
yield m1, m2, nqb
yield qs_unit_matrix(4), qs_unit_matrix(4), 3
for i in range(20):
nqb = randint(0, 2)
yield qs_rand_matrix(2, 0, 3), qs_rand_matrix(2, 0, 3), nqb
for cols1 in range(2, 6):
for cols2 in range(2, 6):
for nqb in range(min(cols1, cols2)):
for n in range(2):
m1 = qs_rand_matrix(0, cols1, cols1 + 3)
rand_mul_scalar(m1)
m2 = qs_rand_matrix(0, cols2, cols2 + 3)
rand_mul_scalar(m2)
yield m1, m2, nqb
# Sparse states
for cols1 in range(2, 6):
for cols2 in range(2, 6):
for nqb in range(min(cols1, cols2)):
for r in range(3):
for n in range(2):
m1 = qs_rand_matrix(0, cols1, r)
m1.mul_scalar(randint(-8, 8), randint(0, 7))
m2 = qs_rand_matrix(0, cols2, r)
m1.mul_scalar(randint(-8, 8), randint(0, 7))
yield m1, m2, nqb
def create_exp_data():
yield qs_unit_matrix(2), 0
yield qs_unit_matrix(4), -3
for n in range(1, 13):
for i in range(10):
m = rand_unitary_matrix(n)
m.mul_scalar(randint(-2, 2))
e = randint(-10000, 10000)
yield m, e
def ref_power(m, e):
if e > 1:
m1 = ref_power(m, e >> 1)
m1 = m1 @ m1
return m1 @ m if e & 1 else m1
if e == 1:
return m
if e == 0:
return qs_unit_matrix(m.shape[0])
if e < 0:
mi = m.inv()
assert m @ mi == qs_unit_matrix(m.shape[0])
return ref_power(mi, -e)
def test_qs_errors(verbose=0):
FORMAT_REDUCED = False
with pytest.raises(ValueError):
QStateMatrix(10000, 10000)
with pytest.raises(ValueError):
QStateMatrix(1, 1, [0, 0, 0xf])
m1, m2 = qs_unit_matrix(1), qs_unit_matrix(2)
with pytest.raises(ValueError):
m1 @ m2
with pytest.raises(ValueError):
m1 * m2
m = QStateMatrix(3, 3, [0, 0, 0xf], 2)
with pytest.raises(ValueError):
m.power(-1)
FORMAT_REDUCED = True
def rand_unitary_matrix(n, scalar=True):
m = qs_unit_matrix(n)
e = randint(-16, 16) if scalar else 0
m.mul_scalar(e, randint(0, 7))
if n == 0:
return m
mask = (1 << n) - 1
for i in range(n + 2):
v = randint(0, mask - 1)
vc = randint(0, mask) & ~v
m.gate_ctrl_not(vc, v)
v1 = randint(0, mask)
v2 = randint(0, mask)
m.gate_ctrl_phi(v1, v2)
m.gate_phi(randint(0, mask), 1)
m.gate_phi(randint(0, mask), 2)
m.gate_h(randint(0, mask))
m.gate_not(randint(0, mask))
for i in range(n + 2):
v = randint(0, mask - 1)
vc = randint(0, mask) & ~v
m.gate_ctrl_not(vc, v)
v1 = randint(0, mask)
v2 = randint(0, mask)
m.gate_ctrl_phi(v1, v2)
return m.echelon()
def create_conjugate_data():
yield rand_unitary_matrix(0), [0, 1, 2, 3]
yield qs_unit_matrix(1), [0, 1, 2, 3]
for n in range(1, 13):
for i in range(10):
m = rand_unitary_matrix(n)
v = rand_pauli_vectors(n, max(10, n))
yield m, v
def test_matrix_power(verbose=0):
MAX_ORDER = (2**8 - 1) * (2**6 - 1) * 2**10
"""Test matrix exponentiation and commputation of trace"""
for ntest, (m, e) in enumerate(create_exp_data()):
# Test exponentiation
me = m.power(e)
me_ref = ref_power(m, e)
ok = me == me_ref
if verbose or not ok:
mm = m.copy()
print("\nTest %d: exponent = %d, " % (ntest, e))
print("m =", m.reduce())
print("Result of exponentiation:", me_ref)
if not ok:
print("Obtained:", me)
raise ValueError("Matrix exponentiation failed")
nqb = m.shape[0]
m.mul_scalar(-m.lb_norm2())
assert m.H == m.inv()
# Test computation of trace
if nqb > 8:
continue
tr = m.trace()
tr_ref = ref_trace(m)
if tr == 0:
ok = tr_ref == 0
else:
ok = abs(tr_ref / tr - 1) < 1.0e-6
if verbose or not ok:
print("\nTrace of m:", tr)
if not ok:
print("m =", m.reduce())
if nqb < 3:
print("m =\n", m.complex())
print("\nTrace expected:", tr_ref)
s, f = m._trace_factor()
print("Low level trace result:", s, hex(f))
print("Intermediate")
m1 = m.copy()
for i in range(nqb):
m1.gate_ctrl_not(1 << i, 1 << (nqb + i))
print(m1)
m1 = m1.restrict(nqb, nqb)
print(m1)
raise ValueError("Computation of trace failed")
# Testing order
if nqb > 4:
continue
order = m.order(MAX_ORDER)
if verbose:
s = print("Scaled matrix m has order %d" % order)
assert m.power(order) == qs_unit_matrix(m.shape[0])
def create_display_testvectors():
"""yield instances of class ``QStateMatrix`` for tests """
for rows, cols, factor, data in qs_matrix_data:
m = QStateMatrix(rows, cols, data)
m.mul_scalar(*factor)
yield m
yield qs_unit_matrix(4)
for i in range(20):
yield qs_rand_matrix(2, 0, 3)
for i in range(20):
yield qs_rand_matrix(1, 0, 2)
for rows in range(6):
for cols in range(5):
for nr in [1, 2] + list(range(rows + cols, rows + cols + 3)):
m = qs_rand_matrix(rows, cols, nr)
m.mul_scalar(randint(-8, 8), randint(0, 7))
yield m
def create_testmatrices():
"""yield instances of class ``QStateMatrix`` for tests """
for m_data in qs_matrix_data:
m = create_m(*m_data)
yield m
yield qs_unit_matrix(4)
for i in range(20):
yield qs_rand_matrix(2, 2, 4)
for cols in range(0,7):
for rows in range(0, 7):
if rows + cols > 9:
break
yield QStateMatrix(rows, cols)
for data_rows in range(1, rows + cols + 3):
for n in range(2):
m = qs_rand_matrix(rows, cols, data_rows)
rand_mul_scalar(m)
yield m
def test_pauli_conjugate(verbose=0):
"""Test the conjugation of Pauli matrix with unitary matrix"""
for ntest, (m, v) in enumerate(create_conjugate_data()):
n = m.shape[0]
p = [qs_pauli_matrix(n, x) for x in v]
pv = [x.pauli_vector() for x in p]
ok = pv == v
if verbose or not ok:
mm = m.copy()
print("\nTest %d: v = %s" % (ntest, binary(v[0], 0, 2 * n + 2)))
print("m =", mm.reduce_matrix(), mm)
print("Pauli matrix of v", p[0])
if not ok:
print("Input and recomputed Pauli vectors:")
for i, x in enumerate(v):
bv = binary(x, 0, 2 * n + 2)
bpv = binary(pv[i], 0, 2 * n + 2)
print(bv, ",", bpv)
if not ok:
err = "Error in recomputation of Pauli vector"
raise ValueError(err)
mi = m.inv()
assert m @ mi == qs_unit_matrix(n), (str(m), str(mi), str(m @ mi))
w = m.pauli_conjugate(v)
w_ref = [(m @ x @ mi).pauli_vector() for x in p]
if verbose or w != w_ref:
for i, w_i in enumerate(w):
w_i_ref = w_ref[i]
if w_i_ref != w_i:
s = "Pauli vector: %s, conjugated: %s, obtained: %s"
print(s % (hex(v[i]), hex(w_i_ref), hex(w_i)))
err = "Pauli vector conjugation error"
raise ValueError(err)
elif verbose:
s = "Pauli vector: %s, conjugated: %s"
print(s % (hex(v[i]), hex(w_i)))
w_noarg = m.pauli_conjugate(v, arg=False)
if verbose:
print("Without arg", [hex(x) for x in w_noarg])
mask = (1 << (2 * n)) - 1
assert w_noarg == [x & mask for x in w]
def test_pauli_multiplication(verbose=0):
for ntest, (n, v1, v2) in enumerate(create_pauli_vectors()):
p1 = qs_pauli_matrix(n, v1)
p2 = qs_pauli_matrix(n, v2)
# Check product v1 * v2
v3 = pauli_vector_mul(n, v1, v2)
p3 = qs_pauli_matrix(n, v3)
v3_ref = (p1 @ p2).pauli_vector()
ok = v3 == v3_ref
if verbose or not ok:
print("Test %d, dim = %d" % (ntest, n))
print("v1 = %s, v2 = %s, v1 * v2 = %s" %
(hex(v1), hex(v2), hex(v3_ref)))
if not ok:
print("m1", p1)
print("m2", p2)
print("m1 * m2", p1 @ p2)
print("pauli vector obtained: ", hex(v3))
err = "Pauli vector multiplication failed"
raise ValueError(err)
# Check powers of v1
p_e_list = [qs_unit_matrix(n), p1, p1 @ p1, p1.H]
v_e_ref_list = [m.pauli_vector() for m in p_e_list]
v_e_list = [pauli_vector_exp(n, v1, e) for e in range(4)]
ok = v_e_list == v_e_ref_list
if verbose or not ok:
print("v1 = ", hex(v1))
for e, v_ref in enumerate(v_e_ref_list):
if ok:
print("v1 ** %d = %s" % (e, hex(v_ref)))
else:
print("v1 ** %d = %s, obtained: %s, v1 = %s" %
(e, hex(v_ref), hex(v_e_list[e]), v1))
if not ok:
err = "Pauli vector exponentiation failed"
raise ValueError(err)