def test_qubit_state_bra():
"""Test sum_i alpha_i <i| for TLS"""
i = IdxSym('i')
alpha = IndexedBase('alpha')
alpha_i = alpha[i]
hs_tls = LocalSpace('tls', basis=('g', 'e'))
term = alpha_i * BasisKet(FockIndex(i), hs=hs_tls).dag()
expr = KetIndexedSum.create(term, ranges=IndexOverFockSpace(i, hs=hs_tls))
assert IndexOverFockSpace(i, hs=hs_tls) in expr.ket.kwargs['ranges']
assert ascii(expr) == "Sum_{i in H_tls} alpha_i * <i|^(tls)"
assert expr.ket.term.free_symbols == set([i, symbols('alpha'), alpha_i])
assert expr.free_symbols == set([symbols('alpha'), alpha_i])
assert expr.ket.variables == [i]
assert expr.space == hs_tls
assert len(expr.ket.args) == 1
assert len(expr.ket.operands) == 1
assert len(expr.ket.kwargs) == 1
assert expr.ket.args[0] == term.ket
assert expr.ket.term == term.ket
assert len(expr.kwargs) == 0
expr_expand = Bra.create(expr.ket.doit().substitute({
alpha[0]: alpha['g'],
alpha[1]: alpha['e']
}))
assert expr_expand == (alpha['g'] * BasisKet('g', hs=hs_tls).dag() +
alpha['e'] * BasisKet('e', hs=hs_tls).dag())
assert ascii(expr_expand) == 'alpha_e * <e|^(tls) + alpha_g * <g|^(tls)'
def test_sum_instantiator():
"""Test use of Sum instantiator."""
i = IdxSym('i')
j = IdxSym('j')
ket_i = BasisKet(FockIndex(i), hs=0)
ket_j = BasisKet(FockIndex(j), hs=0)
A_i = OperatorSymbol(StrLabel(IndexedBase('A')[i]), hs=0)
hs0 = LocalSpace('0')
sum = Sum(i)(ket_i)
ful = KetIndexedSum(ket_i, ranges=IndexOverFockSpace(i, hs=hs0))
assert sum == ful
assert sum == Sum(i, hs0)(ket_i)
assert sum == Sum(i, hs=hs0)(ket_i)
sum = Sum(i, 1, 10)(ket_i)
ful = KetIndexedSum(ket_i, ranges=IndexOverRange(i, 1, 10))
assert sum == ful
assert sum == Sum(i, 1, 10, 1)(ket_i)
assert sum == Sum(i, 1, to=10, step=1)(ket_i)
assert sum == Sum(i, 1, 10, step=1)(ket_i)
sum = Sum(i, (1, 2, 3))(ket_i)
ful = KetIndexedSum(ket_i, ranges=IndexOverList(i, (1, 2, 3)))
assert sum == KetIndexedSum(ket_i, ranges=IndexOverList(i, (1, 2, 3)))
assert sum == Sum(i, [1, 2, 3])(ket_i)
sum = Sum(i)(Sum(j)(ket_i * ket_j.dag()))
ful = OperatorIndexedSum(
ket_i * ket_j.dag(),
ranges=(IndexOverFockSpace(i, hs0), IndexOverFockSpace(j, hs0)),
)
assert sum == ful
def test_operator_kronecker_sum():
"""Test that Kronecker delta are eliminiated from indexed sums over
operators"""
i = IdxSym('i')
j = IdxSym('j')
alpha = symbols('alpha')
delta_ij = KroneckerDelta(i, j)
delta_0i = KroneckerDelta(0, i)
delta_1j = KroneckerDelta(1, j)
delta_0j = KroneckerDelta(0, j)
delta_1i = KroneckerDelta(1, i)
def A(i, j):
return OperatorSymbol(StrLabel(IndexedBase('A')[i, j]), hs=0)
term = delta_ij * A(i, j)
sum = OperatorIndexedSum.create(term,
ranges=(IndexOverList(i, (1, 2)),
IndexOverList(j, (1, 2))))
assert sum == OperatorIndexedSum.create(A(i, i),
ranges=(IndexOverList(i,
(1, 2)), ))
assert sum.doit() == (OperatorSymbol("A_11", hs=0) +
OperatorSymbol("A_22", hs=0))
term = alpha * delta_ij * A(i, j)
range_i = IndexOverList(i, (1, 2))
range_j = IndexOverList(j, (1, 2))
sum = OperatorIndexedSum.create(term, ranges=(range_i, range_j))
assert isinstance(sum, ScalarTimesOperator)
expected = alpha * OperatorIndexedSum.create(
A(i, i), ranges=(IndexOverList(i, (1, 2)), ))
assert sum == expected
hs = LocalSpace('0', basis=('g', 'e'))
i_range = IndexOverFockSpace(i, hs)
j_range = IndexOverFockSpace(j, hs)
sig_ij = LocalSigma(FockIndex(i), FockIndex(j), hs=hs)
sig_0j = LocalSigma('g', FockIndex(j), hs=hs)
sig_i1 = LocalSigma(FockIndex(i), 'e', hs=hs)
term = delta_0i * delta_1j * sig_ij
sum = OperatorIndexedSum.create(term, ranges=(i_range, ))
expected = delta_1j * sig_0j
assert sum == expected
sum = OperatorIndexedSum.create(term, ranges=(j_range, ))
expected = delta_0i * sig_i1
assert sum == expected
term = (delta_0i * delta_1j + delta_0j * delta_1i) * sig_ij
sum = OperatorIndexedSum.create(term, ranges=(i_range, j_range))
expected = LocalSigma('g', 'e', hs=hs) + LocalSigma('e', 'g', hs=hs)
assert sum == expected
def test_two_hs_symbol_sum():
"""Test sum_{ij} a_{ij} Psi_{ij}"""
i = IdxSym('i')
j = IdxSym('j')
a = IndexedBase('a')
hs1 = LocalSpace('1', dimension=3)
hs2 = LocalSpace('2', dimension=3)
hs = hs1 * hs2
Psi = IndexedBase('Psi')
a_ij = a[i, j]
Psi_ij = Psi[i, j]
KetPsi_ij = KetSymbol(StrLabel(Psi_ij), hs=hs)
term = a_ij * KetPsi_ij
expr1 = KetIndexedSum(
term,
ranges=(IndexOverFockSpace(i, hs=hs1), IndexOverFockSpace(j, hs=hs2)),
)
expr2 = KetIndexedSum(term,
ranges=(IndexOverRange(i, 0,
2), IndexOverRange(j, 0, 2)))
assert expr1.term.free_symbols == set(
[i, j, symbols('a'), symbols('Psi'), a_ij, Psi_ij])
assert expr1.free_symbols == set(
[symbols('a'), symbols('Psi'), a_ij, Psi_ij])
assert expr1.variables == [i, j]
assert (
ascii(expr1) == 'Sum_{i in H_1} Sum_{j in H_2} a_ij * |Psi_ij>^(1*2)')
assert unicode(expr1) == '∑_{i ∈ ℌ₁} ∑_{j ∈ ℌ₂} a_ij |Ψ_ij⟩^(1⊗2)'
assert (latex(expr1) ==
r'\sum_{i \in \mathcal{H}_{1}} \sum_{j \in \mathcal{H}_{2}} '
r'a_{i j} \left\lvert \Psi_{i j} \right\rangle^{(1 \otimes 2)}')
assert ascii(expr2) == 'Sum_{i,j=0}^{2} a_ij * |Psi_ij>^(1*2)'
assert unicode(expr2) == '∑_{i,j=0}^{2} a_ij |Ψ_ij⟩^(1⊗2)'
assert (latex(expr2) == r'\sum_{i,j=0}^{2} a_{i j} '
r'\left\lvert \Psi_{i j} \right\rangle^{(1 \otimes 2)}')
assert expr1.doit() == expr2.doit()
assert expr1.doit() == KetPlus(
a[0, 0] * KetSymbol('Psi_00', hs=hs),
a[0, 1] * KetSymbol('Psi_01', hs=hs),
a[0, 2] * KetSymbol('Psi_02', hs=hs),
a[1, 0] * KetSymbol('Psi_10', hs=hs),
a[1, 1] * KetSymbol('Psi_11', hs=hs),
a[1, 2] * KetSymbol('Psi_12', hs=hs),
a[2, 0] * KetSymbol('Psi_20', hs=hs),
a[2, 1] * KetSymbol('Psi_21', hs=hs),
a[2, 2] * KetSymbol('Psi_22', hs=hs),
)
def test_indexed_sum_over_scalartimes():
"""Test ScalarIndexedSum over a term that is an ScalarTimes instance"""
i, j = symbols('i, j', cls=IdxSym)
hs = LocalSpace(1, dimension=2)
Psi_i = KetSymbol(StrLabel(IndexedBase('Psi')[i]), hs=hs)
Psi_j = KetSymbol(StrLabel(IndexedBase('Psi')[j]), hs=hs)
term = KroneckerDelta(i, j) * BraKet(Psi_i, Psi_j)
assert isinstance(term, ScalarTimes)
i_range = IndexOverFockSpace(i, hs)
j_range = IndexOverFockSpace(j, hs)
sum = ScalarIndexedSum.create(term, ranges=(i_range, j_range))
assert sum == hs.dimension
def test_ket_indexed_sum_simplify_scalar():
"""Test calling the simplify_scalar method of an KetIndexedSum."""
# This tests originates from some broken behavior when IndexedSum received
# `ranges` as a positional argument instead of a keyword argument.
a, b, ϕ = symbols('a, b, phi')
factor = (a + b) * sympy.exp(I * ϕ)
factor_expand = factor.expand()
hs = LocalSpace(0)
n = symbols('n', cls=IdxSym)
psi_n = hs.basis_state(FockIndex(n))
expr = KetIndexedSum(factor * psi_n,
ranges=(IndexOverFockSpace(n, hs=hs), ))
expr_expand = expr.simplify_scalar(sympy.expand)
expected = factor_expand * KetIndexedSum(
psi_n, ranges=(IndexOverFockSpace(n, hs=hs), ))
assert expr_expand != expected.term # happened when ranges was an argument
assert expr_expand == expected
def test_create_on_fock_expansion():
"""Test ``Create * sum_i alpha_i |i> = sqrt(i+1) * alpha_i * |i+1>``"""
i = IdxSym('i')
alpha = IndexedBase('alpha')
hs = LocalSpace('0', dimension=3)
expr = Create(hs=hs) * KetIndexedSum(
alpha[i] * BasisKet(FockIndex(i), hs=hs),
ranges=IndexOverFockSpace(i, hs),
)
assert expr == KetIndexedSum(
sympy.sqrt(i + 1) * alpha[i] * BasisKet(FockIndex(i + 1), hs=hs),
ranges=IndexOverFockSpace(i, hs),
)
assert expr.doit() == (alpha[0] * BasisKet(1, hs=hs) +
sympy.sqrt(2) * alpha[1] * BasisKet(2, hs=hs))
def test_indexed_sum_over_kronecker_scalarvalue():
"""Test indexed_sum_over_kronecker for a ScalarValue.
This is an auxiliary test to resolve a bug in test_tls_norm
"""
i = IdxSym('i')
ip = i.prime
term = KroneckerDelta(i, ip) / 2
assert isinstance(term, ScalarValue)
hs = LocalSpace('tls', dimension=2)
i_range = IndexOverFockSpace(i, hs)
ip_range = IndexOverFockSpace(ip, hs)
sum = indexed_sum_over_kronecker(
ScalarIndexedSum,
ops=(term,),
kwargs=dict(ranges=(i_range, ip_range)),
)
assert sum == 1
def test_braket_indexed_sum():
"""Test braket product of sums"""
i = IdxSym('i')
hs = LocalSpace(1, dimension=5)
alpha = IndexedBase('alpha')
psi = KetSymbol('Psi', hs=hs)
psi1 = KetIndexedSum(
alpha[1, i] * BasisKet(FockIndex(i), hs=hs),
ranges=IndexOverFockSpace(i, hs),
)
psi2 = KetIndexedSum(
alpha[2, i] * BasisKet(FockIndex(i), hs=hs),
ranges=IndexOverFockSpace(i, hs),
)
expr = Bra.create(psi1) * psi2
assert expr.space == TrivialSpace
assert expr == ScalarIndexedSum.create(
alpha[1, i].conjugate() * alpha[2, i],
ranges=(IndexOverFockSpace(i, hs), ),
)
assert BraKet.create(psi1, psi2) == expr
expr = psi.dag() * psi2
assert expr == ScalarIndexedSum(
alpha[2, i] * BraKet(psi, BasisKet(FockIndex(i), hs=hs)),
ranges=IndexOverFockSpace(i, hs),
)
assert BraKet.create(psi, psi2) == expr
expr = psi1.dag() * psi
assert expr == ScalarIndexedSum(
alpha[1, i].conjugate() * BraKet(BasisKet(FockIndex(i), hs=hs), psi),
ranges=IndexOverFockSpace(i, hs),
)
assert BraKet.create(psi1, psi) == expr
def test_tls_norm():
"""Test that calculating the norm of a TLS state results in 1"""
hs = LocalSpace('tls', dimension=2)
i = IdxSym('i')
ket_i = BasisKet(FockIndex(i), hs=hs)
nrm = BraKet.create(ket_i, ket_i)
assert nrm == 1
psi = KetIndexedSum((1 / sympy.sqrt(2)) * ket_i,
ranges=IndexOverFockSpace(i, hs))
nrm = BraKet.create(psi, psi)
assert nrm == 1
def test_ketbra_indexed_sum():
"""Test ketbra product of sums"""
i = IdxSym('i')
hs = LocalSpace(1, dimension=5)
alpha = IndexedBase('alpha')
psi = KetSymbol('Psi', hs=hs)
psi1 = KetIndexedSum(
alpha[1, i] * BasisKet(FockIndex(i), hs=hs),
ranges=IndexOverFockSpace(i, hs),
)
psi2 = KetIndexedSum(
alpha[2, i] * BasisKet(FockIndex(i), hs=hs),
ranges=IndexOverFockSpace(i, hs),
)
expr = psi1 * psi2.dag()
assert expr.space == hs
expected = OperatorIndexedSum(
alpha[2, i.prime].conjugate() * alpha[1, i] *
KetBra.create(BasisKet(FockIndex(i), hs=hs),
BasisKet(FockIndex(i.prime), hs=hs)),
ranges=(IndexOverFockSpace(i, hs), IndexOverFockSpace(i.prime, hs)),
)
assert expr == expected
assert KetBra.create(psi1, psi2) == expr
expr = psi * psi2.dag()
assert expr.space == hs
expected = OperatorIndexedSum(
alpha[2, i].conjugate() *
KetBra.create(psi, BasisKet(FockIndex(i), hs=hs)),
ranges=IndexOverFockSpace(i, hs),
)
assert expr == expected
assert KetBra.create(psi, psi2) == expr
expr = psi1 * psi.dag()
assert expr.space == hs
expected = OperatorIndexedSum(
alpha[1, i] * KetBra.create(BasisKet(FockIndex(i), hs=hs), psi),
ranges=IndexOverFockSpace(i, hs),
)
assert expr == expected
assert KetBra.create(psi1, psi) == expr
def test_tensor_indexed_sum():
"""Test tensor product of sums"""
i = IdxSym('i')
hs1 = LocalSpace(1)
hs2 = LocalSpace(2)
alpha = IndexedBase('alpha')
psi1 = KetIndexedSum(
alpha[1, i] * BasisKet(FockIndex(i), hs=hs1),
ranges=IndexOverFockSpace(i, hs1),
)
psi2 = KetIndexedSum(
alpha[2, i] * BasisKet(FockIndex(i), hs=hs2),
ranges=IndexOverFockSpace(i, hs2),
)
expr = psi1 * psi2
assert expr.space == hs1 * hs2
rhs = KetIndexedSum(
alpha[1, i] * alpha[2, i.prime] *
(BasisKet(FockIndex(i), hs=hs1) *
BasisKet(FockIndex(i.prime), hs=hs2)),
ranges=(IndexOverFockSpace(i, hs1), IndexOverFockSpace(i.prime, hs2)),
)
assert expr == rhs
psi0 = KetSymbol('Psi', hs=0)
psi3 = KetSymbol('Psi', hs=3)
expr2 = psi0 * psi1 * psi2 * psi3
rhs = KetIndexedSum(
alpha[1, i] * alpha[2, i.prime] *
(psi0 * BasisKet(FockIndex(i), hs=hs1) *
BasisKet(FockIndex(i.prime), hs=hs2) * psi3),
ranges=(IndexOverFockSpace(i, hs1), IndexOverFockSpace(i.prime, hs2)),
)
assert expr2 == rhs
assert TensorKet.create(psi0, psi1, psi2, psi3) == expr2
OperatorPlus(-OpA, -OpB, -OpC),
),
(
ScalarTimesOperator,
'R004',
(2 * gamma, Half * OpA),
{},
ScalarTimesOperator(gamma, OpA),
),
# State Algebra
# ...
(
KetIndexedSum,
'R001',
(KetSymbol(StrLabel(i), hs=0) - KetSymbol(StrLabel(i), hs=0), ),
dict(ranges=(IndexOverFockSpace(i, hs=LocalSpace(0)), )),
ZeroKet,
),
(
KetIndexedSum,
'R002',
(symbols('a') * BasisKet(FockIndex(i), hs=0), ),
dict(ranges=(IndexOverRange(i, 0, 1), )),
symbols('a') * KetIndexedSum(BasisKet(FockIndex(i), hs=0),
ranges=(IndexOverRange(i, 0, 1), )),
),
]
@pytest.mark.parametrize("cls, rule, args, kwargs, expected", TESTS)
def test_rule(cls, rule, args, kwargs, expected, caplog):
def test_qubit_state():
"""Test sum_i alpha_i |i> for TLS"""
i = IdxSym('i')
alpha = IndexedBase('alpha')
alpha_i = alpha[i]
hs_tls = LocalSpace('tls', basis=('g', 'e'))
term = alpha_i * BasisKet(FockIndex(i), hs=hs_tls)
expr1 = KetIndexedSum.create(term, ranges=IndexOverFockSpace(i, hs=hs_tls))
expr2 = KetIndexedSum.create(term, ranges=IndexOverList(i, [0, 1]))
expr3 = KetIndexedSum.create(term,
ranges=IndexOverRange(i, start_from=0, to=1))
assert IndexOverFockSpace(i, hs=hs_tls) in expr1.kwargs['ranges']
assert ascii(expr1) == "Sum_{i in H_tls} alpha_i * |i>^(tls)"
assert unicode(expr1) == "∑_{i ∈ ℌ_tls} α_i |i⟩⁽ᵗˡˢ⁾"
assert (
srepr(expr1) ==
"KetIndexedSum(ScalarTimesKet(ScalarValue(Indexed(IndexedBase(Symbol('alpha')), IdxSym('i', integer=True))), BasisKet(FockIndex(IdxSym('i', integer=True)), hs=LocalSpace('tls', basis=('g', 'e')))), ranges=(IndexOverFockSpace(IdxSym('i', integer=True), LocalSpace('tls', basis=('g', 'e'))),))"
)
with configure_printing(tex_use_braket=True):
assert (latex(expr1) ==
r'\sum_{i \in \mathcal{H}_{tls}} \alpha_{i} \Ket{i}^{(tls)}')
assert ascii(expr2) == 'Sum_{i in {0,1}} alpha_i * |i>^(tls)'
assert unicode(expr2) == '∑_{i ∈ {0,1}} α_i |i⟩⁽ᵗˡˢ⁾'
assert (
srepr(expr2) ==
"KetIndexedSum(ScalarTimesKet(ScalarValue(Indexed(IndexedBase(Symbol('alpha')), IdxSym('i', integer=True))), BasisKet(FockIndex(IdxSym('i', integer=True)), hs=LocalSpace('tls', basis=('g', 'e')))), ranges=(IndexOverList(IdxSym('i', integer=True), (0, 1)),))"
)
with configure_printing(tex_use_braket=True):
assert (
latex(expr2) == r'\sum_{i \in \{0,1\}} \alpha_{i} \Ket{i}^{(tls)}')
assert ascii(expr3) == 'Sum_{i=0}^{1} alpha_i * |i>^(tls)'
assert unicode(expr3) == '∑_{i=0}^{1} α_i |i⟩⁽ᵗˡˢ⁾'
assert (
srepr(expr3) ==
"KetIndexedSum(ScalarTimesKet(ScalarValue(Indexed(IndexedBase(Symbol('alpha')), IdxSym('i', integer=True))), BasisKet(FockIndex(IdxSym('i', integer=True)), hs=LocalSpace('tls', basis=('g', 'e')))), ranges=(IndexOverRange(IdxSym('i', integer=True), 0, 1),))"
)
with configure_printing(tex_use_braket=True):
assert latex(expr3) == r'\sum_{i=0}^{1} \alpha_{i} \Ket{i}^{(tls)}'
for expr in (expr1, expr2, expr3):
assert expr.term.free_symbols == set([i, symbols('alpha'), alpha_i])
assert expr.term.bound_symbols == set()
assert expr.free_symbols == set([symbols('alpha'), alpha_i])
assert expr.variables == [i]
assert expr.bound_symbols == set([i])
assert len(expr) == len(expr.ranges[0]) == 2
assert 0 in expr.ranges[0]
assert 1 in expr.ranges[0]
assert expr.space == hs_tls
assert len(expr.args) == 1
assert len(expr.kwargs) == 1
assert len(expr.operands) == 1
assert expr.args[0] == term
assert expr.term == term
expr_expand = expr.doit().substitute({
alpha[0]: alpha['g'],
alpha[1]: alpha['e']
})
assert expr_expand == (alpha['g'] * BasisKet('g', hs=hs_tls) +
alpha['e'] * BasisKet('e', hs=hs_tls))
assert (
ascii(expr_expand) == 'alpha_e * |e>^(tls) + alpha_g * |g>^(tls)')
with pytest.raises(TypeError) as exc_info:
KetIndexedSum.create(alpha_i * BasisKet(i, hs=hs_tls),
IndexOverFockSpace(i, hs=hs_tls))
assert "label_or_index must be an instance of" in str(exc_info.value)
def r(index_symbol):
return IndexOverFockSpace(index_symbol, hs=hs)