def test_tex_symbolic_labels():
"""Test tex representation of symbols with symbolic labels"""
i = IdxSym('i')
j = IdxSym('j')
hs0 = LocalSpace(0)
hs1 = LocalSpace(1)
Psi = IndexedBase('Psi')
with configure_printing(tex_use_braket=True):
assert latex(BasisKet(FockIndex(2 * i), hs=hs0)) == r'\Ket{2 i}^{(0)}'
assert latex(KetSymbol(StrLabel(2 * i), hs=hs0)) == r'\Ket{2 i}^{(0)}'
assert (latex(KetSymbol(StrLabel(Psi[i, j]), hs=hs0 *
hs1)) == r'\Ket{\Psi_{i j}}^{(0 \otimes 1)}')
expr = BasisKet(FockIndex(i), hs=hs0) * BasisKet(FockIndex(j), hs=hs1)
assert latex(expr) == r'\Ket{i,j}^{(0 \otimes 1)}'
assert (latex(Bra(BasisKet(FockIndex(2 * i),
hs=hs0))) == r'\Bra{2 i}^{(0)}')
assert (latex(LocalSigma(FockIndex(i), FockIndex(j),
hs=hs0)) == r'\Ket{i}\!\Bra{j}^{(0)}')
alpha = symbols('alpha')
expr = CoherentStateKet(alpha, hs=1).to_fock_representation()
assert (latex(expr) == r'e^{- \frac{\alpha \overline{\alpha}}{2}} '
r'\left(\sum_{n \in \mathcal{H}_{1}} '
r'\frac{\alpha^{n}}{\sqrt{n!}} \Ket{n}^{(1)}\right)')
assert (latex(
expr, conjg_style='star') == r'e^{- \frac{\alpha {\alpha}^*}{2}} '
r'\left(\sum_{n \in \mathcal{H}_{1}} '
r'\frac{\alpha^{n}}{\sqrt{n!}} \Ket{n}^{(1)}\right)')
tls = SpinSpace(label='s', spin='1/2', basis=('down', 'up'))
Sig = IndexedBase('sigma')
n = IdxSym('n')
Sig_n = OperatorSymbol(StrLabel(Sig[n]), hs=tls)
assert latex(Sig_n, show_hs_label=False) == r'\hat{\sigma}_{n}'
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_primed_IdxSym():
"""Test that primed IdxSym are rendered correctly not just in QAlgebra's
printing system, but also in SymPy's printing system"""
ipp = IdxSym('i').prime.prime
assert qalgebra.ascii(ipp) == "i''"
assert qalgebra.latex(ipp) == r'{i^{\prime\prime}}'
assert qalgebra.srepr(ipp) == "IdxSym('i', integer=True, primed=2)"
assert qalgebra.unicode(ipp) == "i''"
assert sympy.printing.sstr(ipp) == qalgebra.ascii(ipp)
assert sympy.printing.latex(ipp) == qalgebra.latex(ipp)
assert sympy.printing.srepr(ipp) == qalgebra.srepr(ipp)
assert sympy.printing.pretty(ipp) == qalgebra.unicode(ipp)
def test_repr_latex():
H_0 = OperatorSymbol('H_0', hs=0)
ω, E0 = sympy.symbols('omega, E_0')
Eq.latex_renderer = staticmethod(latex)
eq0 = Eq(H_0, ω * Create(hs=0) * Destroy(hs=0) + E0, tag='0')
repr1 = eq0._repr_latex_()
repr2 = latex(eq0)
assert repr1 == repr2
def test_tex_spin_arrows_multi_sigma():
# when fixed, combine with test_tex_spin_arrows
tls1 = SpinSpace('1', spin='1/2', basis=("down", "up"))
tls2 = SpinSpace('2', spin='1/2', basis=("down", "up"))
tls3 = SpinSpace('3', spin='1/2', basis=("down", "up"))
sig1 = LocalSigma("up", "down", hs=tls1)
sig2 = LocalSigma("up", "up", hs=tls2)
sig3 = LocalSigma("down", "down", hs=tls3)
assert latex(sig1 * sig2 * sig3) == r''
def test_tex_hilbert_elements():
"""Test the tex representation of "atomic" Hilbert space algebra
elements"""
assert latex(LocalSpace(1)) == r'\mathcal{H}_{1}'
assert latex(LocalSpace(1, dimension=2)) == r'\mathcal{H}_{1}'
assert latex(LocalSpace(1, basis=(r'g', 'e'))) == r'\mathcal{H}_{1}'
assert latex(LocalSpace('local')) == r'\mathcal{H}_{\text{local}}'
assert latex(LocalSpace('kappa')) == r'\mathcal{H}_{\kappa}'
assert latex(TrivialSpace) == r'\mathcal{H}_{\text{null}}'
assert latex(FullSpace) == r'\mathcal{H}_{\text{total}}'
assert latex(LocalSpace(StrLabel(IdxSym('i')))) == r'\mathcal{H}_{i}'
def test_tex_spin_arrows():
"""Test the representation of spin-1/2 spaces with special labels "down",
"up" as arrows"""
tls1 = SpinSpace('1', spin='1/2', basis=("down", "up"))
tls2 = SpinSpace('2', spin='1/2', basis=("down", "up"))
tls3 = SpinSpace('3', spin='1/2', basis=("down", "up"))
down1 = BasisKet('down', hs=tls1)
up1 = BasisKet('up', hs=tls1)
down2 = BasisKet('down', hs=tls2)
up3 = BasisKet('up', hs=tls3)
assert latex(down1) == r'\left\lvert \downarrow \right\rangle^{(1)}'
assert latex(up1) == r'\left\lvert \uparrow \right\rangle^{(1)}'
ket = down1 * down2 * up3
assert (
latex(ket) == r'\left\lvert \downarrow\downarrow\uparrow \right\rangle'
r'^{(1 \otimes 2 \otimes 3)}')
sig = LocalSigma("up", "down", hs=tls1)
assert (latex(sig) == r'\left\lvert \uparrow \middle\rangle\!'
r'\middle\langle \downarrow \right\rvert^{(1)}')
def test_tex_equation():
"""Test printing of the Eq class"""
eq_1 = Eq(lhs=OperatorSymbol('H', hs=0), rhs=Create(hs=0) * Destroy(hs=0))
# fmt: off
eq = (eq_1.apply_to_lhs(lambda expr: expr + 1).apply_to_rhs(
lambda expr: expr + 1).apply_to_rhs(lambda expr: expr**2).tag(
3).transform(lambda eq: eq + 1).tag(4).apply_to_rhs('expand').
apply_to_lhs(lambda expr: expr**2).tag(5).apply(
'expand').apply_to_lhs(lambda expr: expr**2).tag(6).apply_to_lhs(
'expand').apply_to_rhs(lambda expr: expr + 1))
# fmt: on
assert latex(eq_1).split("\n") == [
r'\begin{equation}',
r' \hat{H}^{(0)} = \hat{a}^{(0)\dagger} \hat{a}^{(0)}',
r'\end{equation}',
'',
]
assert latex(eq_1.tag(1).reset()).split("\n") == [
r'\begin{equation}',
r' \hat{H}^{(0)} = \hat{a}^{(0)\dagger} \hat{a}^{(0)}',
r'\tag{1}\end{equation}',
'',
]
tex_lines = latex(eq, show_hs_label=False,
tex_op_macro=r'\Op{{{name}}}').split("\n")
expected = [
r'\begin{align}',
r' \Op{H} &= \Op{a}^{\dagger} \Op{a}\\',
r' \mathbb{1} + \Op{H} &= \Op{a}^{\dagger} \Op{a}\\',
r' &= \mathbb{1} + \Op{a}^{\dagger} \Op{a}\\',
r' &= \left(\mathbb{1} + \Op{a}^{\dagger} \Op{a}\right) \left(\mathbb{1} + \Op{a}^{\dagger} \Op{a}\right)\tag{3}\\',
r' 2 + \Op{H} &= \mathbb{1} + \left(\mathbb{1} + \Op{a}^{\dagger} \Op{a}\right) \left(\mathbb{1} + \Op{a}^{\dagger} \Op{a}\right)\tag{4}\\',
r' &= 2 + \Op{a}^{\dagger} \Op{a}^{\dagger} \Op{a} \Op{a} + 3 \Op{a}^{\dagger} \Op{a}\\',
r' \left(2 + \Op{H}\right) \left(2 + \Op{H}\right) &= 2 + \Op{a}^{\dagger} \Op{a}^{\dagger} \Op{a} \Op{a} + 3 \Op{a}^{\dagger} \Op{a}\tag{5}\\',
r' 4 + 4 \Op{H} + \Op{H} \Op{H} &= 2 + \Op{a}^{\dagger} \Op{a}^{\dagger} \Op{a} \Op{a} + 3 \Op{a}^{\dagger} \Op{a}\\',
r' \left(4 + 4 \Op{H} + \Op{H} \Op{H}\right) \left(4 + 4 \Op{H} + \Op{H} \Op{H}\right) &= 2 + \Op{a}^{\dagger} \Op{a}^{\dagger} \Op{a} \Op{a} + 3 \Op{a}^{\dagger} \Op{a}\tag{6}\\',
r' 16 + 32 \Op{H} + \Op{H} \Op{H} \Op{H} \Op{H} + 8 \Op{H} \Op{H} \Op{H} + 24 \Op{H} \Op{H} &= 2 + \Op{a}^{\dagger} \Op{a}^{\dagger} \Op{a} \Op{a} + 3 \Op{a}^{\dagger} \Op{a}\\',
r' &= 3 + \Op{a}^{\dagger} \Op{a}^{\dagger} \Op{a} \Op{a} + 3 \Op{a}^{\dagger} \Op{a}',
r'\end{align}',
r'',
]
for i, line in enumerate(tex_lines):
assert line == expected[i]
def test_tex_bra_operations():
"""Test the tex representation of bra operations"""
hs1 = LocalSpace('q_1', dimension=2)
hs2 = LocalSpace('q_2', dimension=2)
psi1 = KetSymbol("Psi_1", hs=hs1)
psi2 = KetSymbol("Psi_2", hs=hs1)
psi2 = KetSymbol("Psi_2", hs=hs1)
bra_psi1 = KetSymbol("Psi_1", hs=hs1).dag()
bra_psi2 = KetSymbol("Psi_2", hs=hs1).dag()
bra_psi2 = KetSymbol("Psi_2", hs=hs1).dag()
bra_psi3 = KetSymbol("Psi_3", hs=hs1).dag()
bra_phi = KetSymbol("Phi", hs=hs2).dag()
A = OperatorSymbol("A_0", hs=hs1)
gamma = symbols('gamma', positive=True)
phase = exp(-I * gamma)
assert (latex(
(psi1 +
psi2).dag()) == r'\left\langle \Psi_{1} \right\rvert^{(q_{1})} + '
r'\left\langle \Psi_{2} \right\rvert^{(q_{1})}')
assert (latex((psi1 + psi2).dag(), tex_use_braket=True) ==
r'\Bra{\Psi_{1}}^{(q_{1})} + \Bra{\Psi_{2}}^{(q_{1})}')
assert (
latex(bra_psi1 +
bra_psi2) == r'\left\langle \Psi_{1} \right\rvert^{(q_{1})} + '
r'\left\langle \Psi_{2} \right\rvert^{(q_{1})}')
assert (
latex(bra_psi1 - bra_psi2 +
bra_psi3) == r'\left\langle \Psi_{1} \right\rvert^{(q_{1})} - '
r'\left\langle \Psi_{2} \right\rvert^{(q_{1})} + '
r'\left\langle \Psi_{3} \right\rvert^{(q_{1})}')
assert (latex(
bra_psi1 *
bra_phi) == r'\left\langle \Psi_{1} \right\rvert^{(q_{1})} \otimes '
r'\left\langle \Phi \right\rvert^{(q_{2})}')
assert (latex(bra_psi1 * bra_phi, tex_use_braket=True) ==
r'\Bra{\Psi_{1}}^{(q_{1})} \otimes \Bra{\Phi}^{(q_{2})}')
assert (latex(Bra(
phase *
psi1)) == r'e^{i \gamma} \left\langle \Psi_{1} \right\rvert^{(q_{1})}')
assert (latex(
(A * psi1).dag()) == r'\left\langle \Psi_{1} \right\rvert^{(q_{1})} '
r'\hat{A}_{0}^{(q_{1})\dagger}')
def test_ascii_scalar():
"""Test rendering of scalar values"""
assert latex(2) == '2'
latex.printer.cache = {}
# we always want 2.0 to be printed as '2'. Without this normalization, the
# state of the cache might introduce non-reproducible behavior, as 2==2.0
assert latex(2.0) == '2'
assert latex(1j) == '1i'
assert latex('foo') == 'foo'
i = IdxSym('i')
alpha = IndexedBase('alpha')
assert latex(i) == 'i'
assert latex(alpha[i]) == r'\alpha_{i}'
def test_tex_sop_elements():
"""Test the tex representation of "atomic" Superoperators"""
hs1 = LocalSpace('q1', dimension=2)
hs2 = LocalSpace('q2', dimension=2)
alpha, beta = symbols('alpha, beta')
assert latex(SuperOperatorSymbol("A", hs=hs1)) == r'\mathrm{A}^{(q_{1})}'
assert (latex(SuperOperatorSymbol(
"A_1", hs=hs1 * hs2)) == r'\mathrm{A}_{1}^{(q_{1} \otimes q_{2})}')
assert (latex(SuperOperatorSymbol(
"Xi", alpha, beta,
hs=hs1)) == r'\mathrm{\Xi}^{(q_{1})}\left(\alpha, \beta\right)')
assert (latex(SuperOperatorSymbol(
"Xi_2",
hs=('q1', 'q2'))) == r'\mathrm{\Xi}_{2}^{(q_{1} \otimes q_{2})}')
assert (latex(SuperOperatorSymbol(
"Xi_full", hs=1)) == r'\mathrm{\Xi}_{\text{full}}^{(1)}')
assert latex(IdentitySuperOperator) == r'\mathbb{1}'
assert latex(ZeroSuperOperator) == r'\mathbb{0}'
def test_tex_render_string():
"""Test rendering of ascii to latex strings"""
printer = QalgebraLatexPrinter()
assert printer._render_str('a') == r'a'
assert printer._render_str('A') == r'A'
assert printer._render_str('longword') == r'\text{longword}'
assert printer._render_str('alpha') == r'\alpha'
assert latex('alpha') == r'\alpha'
assert printer._render_str('Alpha') == r'A'
assert printer._render_str('Beta') == r'B'
assert printer._render_str('Gamma') == r'\Gamma'
assert printer._render_str('Delta') == r'\Delta'
assert printer._render_str('Epsilon') == r'E'
assert printer._render_str('Zeta') == r'Z'
assert printer._render_str('Eta') == r'H'
assert printer._render_str('Theta') == r'\Theta'
assert printer._render_str('Iota') == r'I'
assert printer._render_str('Kappa') == r'K'
assert printer._render_str('Lambda') == r'\Lambda'
assert printer._render_str('Mu') == r'M'
assert printer._render_str('Nu') == r'N'
assert printer._render_str('Xi') == r'\Xi'
assert printer._render_str('Omicron') == r'O'
assert printer._render_str('Pi') == r'\Pi'
assert printer._render_str('Rho') == r'P'
assert printer._render_str('Sigma') == r'\Sigma'
assert printer._render_str('Tau') == r'T'
assert printer._render_str('Ypsilon') == r'\Upsilon'
assert printer._render_str('Upsilon') == r'\Upsilon'
assert printer._render_str('ypsilon') == r'\upsilon'
assert printer._render_str('upsilon') == r'\upsilon'
assert printer._render_str('Phi') == r'\Phi'
assert printer._render_str('Chi') == r'X'
assert printer._render_str('Psi') == r'\Psi'
assert printer._render_str('Omega') == r'\Omega'
assert printer._render_str('xi_1') == r'\xi_{1}'
assert printer._render_str('xi_1^2') == r'\xi_{1}^{2}'
assert printer._render_str('Xi_1') == r'\Xi_{1}'
assert printer._render_str('Xi_long') == r'\Xi_{\text{long}}'
assert printer._render_str('Xi_1+2') == r'\Xi_{1+2}'
assert printer._render_str('Lambda_i,j') == r'\Lambda_{i,j}'
assert printer._render_str('epsilon_mu,nu') == r'\epsilon_{\mu,\nu}'
def test_tex_matrix():
"""Test tex representation of the Matrix class"""
A = OperatorSymbol("A", hs=1)
B = OperatorSymbol("B", hs=1)
C = OperatorSymbol("C", hs=1)
D = OperatorSymbol("D", hs=1)
assert latex(OperatorSymbol("A", hs=1)) == r'\hat{A}^{(1)}'
assert (latex(Matrix(
[[A, B], [C,
D]])) == r'\begin{pmatrix}\hat{A}^{(1)} & \hat{B}^{(1)} \\'
r'\hat{C}^{(1)} & \hat{D}^{(1)}\end{pmatrix}')
assert (latex(Matrix(
[A, B, C, D])) == r'\begin{pmatrix}\hat{A}^{(1)} \\\hat{B}^{(1)} \\'
r'\hat{C}^{(1)} \\\hat{D}^{(1)}\end{pmatrix}')
assert (latex(Matrix(
[[A, B, C, D]])) == r'\begin{pmatrix}\hat{A}^{(1)} & \hat{B}^{(1)} & '
r'\hat{C}^{(1)} & \hat{D}^{(1)}\end{pmatrix}')
assert (latex(Matrix([[0, 1], [-1, 0]
])) == r'\begin{pmatrix}0 & 1 \\-1 & 0\end{pmatrix}')
assert latex(Matrix([[], []])) == r'\begin{pmatrix} \\\end{pmatrix}'
assert latex(Matrix([])) == r'\begin{pmatrix} \\\end{pmatrix}'
def test_tex_sop_operations():
"""Test the tex representation of super operator algebra operations"""
hs1 = LocalSpace('q_1', dimension=2)
hs2 = LocalSpace('q_2', dimension=2)
A = SuperOperatorSymbol("A", hs=hs1)
B = SuperOperatorSymbol("B", hs=hs1)
C = SuperOperatorSymbol("C", hs=hs2)
L = SuperOperatorSymbol("L", hs=1)
M = SuperOperatorSymbol("M", hs=1)
A_op = OperatorSymbol("A", hs=1)
gamma = symbols('gamma', positive=True)
assert latex(A + B) == r'\mathrm{A}^{(q_{1})} + \mathrm{B}^{(q_{1})}'
assert latex(A * B) == r'\mathrm{A}^{(q_{1})} \mathrm{B}^{(q_{1})}'
assert latex(A * C) == r'\mathrm{A}^{(q_{1})} \mathrm{C}^{(q_{2})}'
assert latex(2 * A) == r'2 \mathrm{A}^{(q_{1})}'
assert latex(2j * A) == r'2i \mathrm{A}^{(q_{1})}'
assert latex((1 + 2j) * A) == r'(1+2i) \mathrm{A}^{(q_{1})}'
assert latex(gamma**2 * A) == r'\gamma^{2} \mathrm{A}^{(q_{1})}'
assert (latex(-(gamma**2) / 2 *
A) == r'- \frac{\gamma^{2}}{2} \mathrm{A}^{(q_{1})}')
assert latex(SuperAdjoint(A)) == r'\mathrm{A}^{(q_{1})\dagger}'
assert (latex(SuperAdjoint(A + B)) == r'\left(\mathrm{A}^{(q_{1})} + '
r'\mathrm{B}^{(q_{1})}\right)^\dagger')
assert latex(A - B) == r'\mathrm{A}^{(q_{1})} - \mathrm{B}^{(q_{1})}'
assert (latex(A - B +
C) == r'\mathrm{A}^{(q_{1})} - \mathrm{B}^{(q_{1})} + '
r'\mathrm{C}^{(q_{2})}')
assert (latex(2 * A - sqrt(gamma) *
(B + C)) == r'2 \mathrm{A}^{(q_{1})} - \sqrt{\gamma} '
r'\left(\mathrm{B}^{(q_{1})} + \mathrm{C}^{(q_{2})}\right)')
assert latex(SPre(A_op)) == r'\mathrm{SPre}\left(\hat{A}^{(1)}\right)'
assert latex(SPost(A_op)) == r'\mathrm{SPost}\left(\hat{A}^{(1)}\right)'
assert (latex(SuperOperatorTimesOperator(
L, A_op)) == r'\mathrm{L}^{(1)}\left[\hat{A}^{(1)}\right]')
assert (latex(SuperOperatorTimesOperator(
L,
sqrt(gamma) *
A_op)) == r'\mathrm{L}^{(1)}\left[\sqrt{\gamma} \hat{A}^{(1)}\right]')
assert (latex(SuperOperatorTimesOperator(
(L + 2 * M),
A_op)) == r'\left(\mathrm{L}^{(1)} + 2 \mathrm{M}^{(1)}\right)'
r'\left[\hat{A}^{(1)}\right]')
def test_tex_hilbert_operations():
"""Test the tex representation of Hilbert space algebra operations"""
H1 = LocalSpace(1)
H2 = LocalSpace(2)
assert latex(H1 * H2) == r'\mathcal{H}_{1} \otimes \mathcal{H}_{2}'
def _latex(self, *args, **kwargs):
return "%s(%s)" % (
self._name,
", ".join([latex(sym) for sym in self._sym_args]),
)
def test_tex_ket_elements():
"""Test the tex representation of "atomic" kets"""
hs1 = LocalSpace('q1', basis=('g', 'e'))
hs2 = LocalSpace('q2', basis=('g', 'e'))
alpha, beta = symbols('alpha, beta')
psi = KetSymbol('Psi', hs=hs1)
assert latex(psi) == r'\left\lvert \Psi \right\rangle^{(q_{1})}'
assert (latex(KetSymbol('Psi', alpha, beta, hs=1)) ==
r'\left\lvert \Psi\left(\alpha, \beta\right) \right\rangle^{(1)}')
assert latex(psi, tex_use_braket=True) == r'\Ket{\Psi}^{(q_{1})}'
assert (latex(psi, tex_use_braket=True,
show_hs_label='subscript') == r'\Ket{\Psi}_{(q_{1})}')
assert (latex(psi, tex_use_braket=True,
show_hs_label=False) == r'\Ket{\Psi}')
assert (latex(KetSymbol('Psi',
hs=1)) == r'\left\lvert \Psi \right\rangle^{(1)}')
assert (latex(KetSymbol(
'Psi',
hs=(1, 2))) == r'\left\lvert \Psi \right\rangle^{(1 \otimes 2)}')
assert (latex(KetSymbol(
'Psi', hs=hs1 *
hs2)) == r'\left\lvert \Psi \right\rangle^{(q_{1} \otimes q_{2})}')
assert (latex(KetSymbol('Psi',
hs=1)) == r'\left\lvert \Psi \right\rangle^{(1)}')
assert latex(ZeroKet) == '0'
assert latex(TrivialKet) == '1'
assert (latex(BasisKet(
'e', hs=hs1)) == r'\left\lvert e \right\rangle^{(q_{1})}')
hs_tls = LocalSpace('1', basis=('excited', 'ground'))
assert (latex(BasisKet(
'excited',
hs=hs_tls)) == r'\left\lvert \text{excited} \right\rangle^{(1)}')
assert latex(BasisKet(1, hs=1)) == r'\left\lvert 1 \right\rangle^{(1)}'
spin = SpinSpace('s', spin=(3, 2))
assert (latex(SpinBasisKet(
-3, 2, hs=spin)) == r'\left\lvert -3/2 \right\rangle^{(s)}')
assert (latex(SpinBasisKet(
1, 2, hs=spin)) == r'\left\lvert +1/2 \right\rangle^{(s)}')
assert (latex(SpinBasisKet(-3, 2, hs=spin), tex_frac_for_spin_labels=True)
== r'\left\lvert -\frac{3}{2} \right\rangle^{(s)}')
assert (latex(SpinBasisKet(1, 2, hs=spin), tex_frac_for_spin_labels=True)
== r'\left\lvert +\frac{1}{2} \right\rangle^{(s)}')
assert (latex(CoherentStateKet(
2.0, hs=1)) == r'\left\lvert \alpha=2 \right\rangle^{(1)}')
def test_tex_operator_operations():
"""Test the tex representation of operator algebra operations"""
hs1 = LocalSpace('q_1', dimension=2)
hs2 = LocalSpace('q_2', dimension=2)
A = OperatorSymbol("A", hs=hs1)
B = OperatorSymbol("B", hs=hs1)
C = OperatorSymbol("C", hs=hs2)
psi = KetSymbol('Psi', hs=hs1)
gamma = symbols('gamma', positive=True)
assert latex(A.dag()) == r'\hat{A}^{(q_{1})\dagger}'
assert latex(A + B) == r'\hat{A}^{(q_{1})} + \hat{B}^{(q_{1})}'
assert latex(A * B) == r'\hat{A}^{(q_{1})} \hat{B}^{(q_{1})}'
assert latex(A * C) == r'\hat{A}^{(q_{1})} \hat{C}^{(q_{2})}'
assert latex(2 * A) == r'2 \hat{A}^{(q_{1})}'
assert latex(2j * A) == r'2i \hat{A}^{(q_{1})}'
assert latex((1 + 2j) * A) == r'(1+2i) \hat{A}^{(q_{1})}'
assert latex(gamma**2 * A) == r'\gamma^{2} \hat{A}^{(q_{1})}'
assert (latex(-(gamma**2) / 2 *
A) == r'- \frac{\gamma^{2}}{2} \hat{A}^{(q_{1})}')
assert (latex(tr(
A * C,
over_space=hs2)) == r'{\rm tr}_{q_{2}}\left[\hat{C}^{(q_{2})}\right] '
r'\hat{A}^{(q_{1})}')
assert latex(Adjoint(A)) == r'\hat{A}^{(q_{1})\dagger}'
assert (latex(Adjoint(
A**2)) == r'\left(\hat{A}^{(q_{1})} \hat{A}^{(q_{1})}\right)^\dagger')
assert (latex(
Adjoint(A)**2) == r'\hat{A}^{(q_{1})\dagger} \hat{A}^{(q_{1})\dagger}')
assert latex(Adjoint(Create(hs=1))) == r'\hat{a}^{(1)}'
assert (latex(Adjoint(A + B)) ==
r'\left(\hat{A}^{(q_{1})} + \hat{B}^{(q_{1})}\right)^\dagger')
assert latex(PseudoInverse(A)) == r'\left(\hat{A}^{(q_{1})}\right)^+'
assert (latex(
PseudoInverse(A)**2
) == r'\left(\hat{A}^{(q_{1})}\right)^+ \left(\hat{A}^{(q_{1})}\right)^+')
assert (latex(NullSpaceProjector(A)) ==
r'\hat{P}_{Ker}\left(\hat{A}^{(q_{1})}\right)')
assert latex(A - B) == r'\hat{A}^{(q_{1})} - \hat{B}^{(q_{1})}'
assert (latex(A - B + C) ==
r'\hat{A}^{(q_{1})} - \hat{B}^{(q_{1})} + \hat{C}^{(q_{2})}')
assert (latex(2 * A - sqrt(gamma) * (B + C)) ==
r'2 \hat{A}^{(q_{1})} - \sqrt{\gamma} \left(\hat{B}^{(q_{1})} + '
r'\hat{C}^{(q_{2})}\right)')
assert (latex(Commutator(
A, B)) == r'\left[\hat{A}^{(q_{1})}, \hat{B}^{(q_{1})}\right]')
expr = (Commutator(A, B) * psi).dag()
assert (latex(expr, show_hs_label=False) ==
r'\left\langle \Psi \right\rvert \left[\hat{A}, '
r'\hat{B}\right]^{\dagger}')
def test_tex_operator_elements():
"""Test the tex representation of "atomic" operator algebra elements"""
hs1 = LocalSpace('q1', dimension=2)
hs2 = LocalSpace('q2', dimension=2)
alpha, beta = symbols('alpha, beta')
fock1 = LocalSpace(1,
local_identifiers={
'Create': 'b',
'Destroy': 'b',
'Phase': 'Phi'
})
spin1 = SpinSpace(1,
spin=1,
local_identifiers={
'Jz': 'Z',
'Jplus': 'Jp',
'Jminus': 'Jm'
})
assert latex(OperatorSymbol("A", hs=hs1)) == r'\hat{A}^{(q_{1})}'
assert (latex(OperatorSymbol(
"A_1", hs=hs1 * hs2)) == r'\hat{A}_{1}^{(q_{1} \otimes q_{2})}')
assert (latex(OperatorSymbol(
"Xi_2", hs=(r'q1', 'q2'))) == r'\hat{\Xi}_{2}^{(q_{1} \otimes q_{2})}')
assert (latex(OperatorSymbol("Xi_full",
hs=1)) == r'\hat{\Xi}_{\text{full}}^{(1)}')
assert latex(
OperatorSymbol("Xi", alpha, beta,
hs=1)) == (r'\hat{\Xi}^{(1)}\left(\alpha, \beta\right)')
assert latex(IdentityOperator) == r'\mathbb{1}'
assert latex(IdentityOperator, tex_identity_sym='I') == 'I'
assert latex(ZeroOperator) == r'\mathbb{0}'
assert latex(Create(hs=1)) == r'\hat{a}^{(1)\dagger}'
assert latex(Create(hs=fock1)) == r'\hat{b}^{(1)\dagger}'
assert latex(Destroy(hs=1)) == r'\hat{a}^{(1)}'
assert latex(Destroy(hs=fock1)) == r'\hat{b}^{(1)}'
assert latex(Jz(hs=SpinSpace(1, spin=1))) == r'\hat{J}_{z}^{(1)}'
assert latex(Jz(hs=spin1)) == r'\hat{Z}^{(1)}'
assert latex(Jplus(hs=SpinSpace(1, spin=1))) == r'\hat{J}_{+}^{(1)}'
assert latex(Jplus(hs=spin1)) == r'\text{Jp}^{(1)}'
assert latex(Jminus(hs=SpinSpace(1, spin=1))) == r'\hat{J}_{-}^{(1)}'
assert latex(Jminus(hs=spin1)) == r'\text{Jm}^{(1)}'
assert (latex(Phase(Rational(
1, 2), hs=1)) == r'\text{Phase}^{(1)}\left(\frac{1}{2}\right)')
assert latex(Phase(0.5, hs=1)) == r'\text{Phase}^{(1)}\left(0.5\right)'
assert latex(Phase(0.5, hs=fock1)) == r'\hat{\Phi}^{(1)}\left(0.5\right)'
assert latex(Displace(0.5, hs=1)) == r'\hat{D}^{(1)}\left(0.5\right)'
assert latex(Squeeze(0.5, hs=1)) == r'\text{Squeeze}^{(1)}\left(0.5\right)'
hs_tls = LocalSpace('1', basis=('g', 'e'))
sig_e_g = LocalSigma('e', 'g', hs=hs_tls)
assert latex(sig_e_g, sig_as_ketbra=False) == r'\hat{\sigma}_{e,g}^{(1)}'
assert (
latex(sig_e_g) ==
r'\left\lvert e \middle\rangle\!\middle\langle g \right\rvert^{(1)}')
hs_tls = LocalSpace('1', basis=('excited', 'ground'))
sig_excited_ground = LocalSigma('excited', 'ground', hs=hs_tls)
assert (latex(sig_excited_ground, sig_as_ketbra=False) ==
r'\hat{\sigma}_{\text{excited},\text{ground}}^{(1)}')
assert (latex(sig_excited_ground) ==
r'\left\lvert \text{excited} \middle\rangle\!'
r'\middle\langle \text{ground} \right\rvert^{(1)}')
hs_tls = LocalSpace('1', basis=('mu', 'nu'))
sig_mu_nu = LocalSigma('mu', 'nu', hs=hs_tls)
assert (latex(sig_mu_nu) == r'\left\lvert \mu \middle\rangle\!'
r'\middle\langle \nu \right\rvert^{(1)}')
hs_tls = LocalSpace('1', basis=('excited', 'ground'))
sig_excited_excited = LocalProjector('excited', hs=hs_tls)
assert (latex(sig_excited_excited,
sig_as_ketbra=False) == r'\hat{\Pi}_{\text{excited}}^{(1)}')
hs_tls = LocalSpace('1', basis=('g', 'e'))
sig_e_e = LocalProjector('e', hs=hs_tls)
assert latex(sig_e_e, sig_as_ketbra=False) == r'\hat{\Pi}_{e}^{(1)}'
def test_repr_latex():
"""Test the automatic representation in the notebook"""
A = OperatorSymbol("A", hs=1)
B = OperatorSymbol("B", hs=1)
assert A._repr_latex_() == "$%s$" % latex(A)
assert (A + B)._repr_latex_() == "$%s$" % latex(A + B)
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 test_tex_derivative(MyScalarFunc):
s, s0, t, t0, gamma = symbols('s, s_0, t, t_0, gamma', real=True)
m = IdxSym('m')
n = IdxSym('n')
S = IndexedBase('s')
T = IndexedBase('t')
f = partial(MyScalarFunc, "f")
g = partial(MyScalarFunc, "g")
expr = f(s, t).diff(t)
assert latex(expr) == r'\frac{\partial}{\partial t} f(s, t)'
expr = f(s, t).diff(s, n=2).diff(t)
assert latex(expr) == (
r'\frac{\partial^{3}}{\partial s^{2} \partial t} f(s, t)')
expr = f(s, t).diff(s, n=2).diff(t).evaluate_at({s: s0})
assert latex(expr) == (
r'\left. \frac{\partial^{3}}{\partial s^{2} \partial t} f(s, t) '
r'\right\vert_{s=s_{0}}')
expr = f(S[m], T[n]).diff(S[m], n=2).diff(T[n]).evaluate_at({S[m]: s0})
assert latex(expr) == (
r'\left. \frac{\partial^{3}}{\partial s_{m}^{2} \partial t_{n}} '
r'f(s_{m}, t_{n}) \right\vert_{s_{m}=s_{0}}')
expr = f(s, t).diff(s, n=2).diff(t).evaluate_at({s: 0})
assert latex(expr) == (
r'\left. \frac{\partial^{3}}{\partial s^{2} \partial t} f(s, t) '
r'\right\vert_{s=0}')
expr = f(gamma, t).diff(gamma, n=2).diff(t).evaluate_at({gamma: 0})
assert latex(expr) == (
r'\left. \frac{\partial^{3}}{\partial \gamma^{2} \partial t} '
r'f(\gamma, t) \right\vert_{\gamma=0}')
expr = f(s, t).diff(s, n=2).diff(t).evaluate_at({s: s0, t: t0})
assert latex(expr) == (
r'\left. \frac{\partial^{3}}{\partial s^{2} \partial t} f(s, t) '
r'\right\vert_{s=s_{0}, t=t_{0}}')
D = expr.__class__
expr = D(f(s, t) + g(s, t), derivs={s: 2, t: 1}, vals={s: s0, t: t0})
assert latex(expr) == (
r'\left. \frac{\partial^{3}}{\partial s^{2} \partial t} '
r'\left(f(s, t) + g(s, t)\right) \right\vert_{s=s_{0}, t=t_{0}}')
expr = D(2 * f(s, t), derivs={s: 2, t: 1}, vals={s: s0, t: t0})
assert latex(expr) == (
r'\left. \frac{\partial^{3}}{\partial s^{2} \partial t} '
r'\left(2 f(s, t)\right) \right\vert_{s=s_{0}, t=t_{0}}')
expr = f(s, t).diff(t) * g(s, t)
assert latex(expr) == (
r'\left(\frac{\partial}{\partial t} f(s, t)\right) g(s, t)')
expr = f(s, t).diff(t).evaluate_at({t: 0}) * g(s, t)
assert latex(expr) == (r'\left(\left. \frac{\partial}{\partial t} f(s, t) '
r'\right\vert_{t=0}\right) g(s, t)')
expr = f(s, t).diff(t) + g(s, t)
assert latex(expr) == r'\frac{\partial}{\partial t} f(s, t) + g(s, t)'
f = MyScalarFunc("f", S[m], T[n])
series = f.series_expand(T[n], about=0, order=3)
assert latex(series) == (
r'\left(f(s_{m}, 0), \left. \frac{\partial}{\partial t_{n}} '
r'f(s_{m}, t_{n}) \right\vert_{t_{n}=0}, \frac{1}{2} \left(\left. '
r'\frac{\partial^{2}}{\partial t_{n}^{2}} f(s_{m}, t_{n}) '
r'\right\vert_{t_{n}=0}\right), \frac{1}{6} \left(\left. '
r'\frac{\partial^{3}}{\partial t_{n}^{3}} f(s_{m}, t_{n}) '
r'\right\vert_{t_{n}=0}\right)\right)')
f = MyScalarFunc("f", s, t)
series = f.series_expand(t, about=0, order=2)
assert (latex(series) ==
r'\left(f(s, 0), \left. \frac{\partial}{\partial t} f(s, t) '
r'\right\vert_{t=0}, \frac{1}{2} \left(\left. '
r'\frac{\partial^{2}}{\partial t^{2}} f(s, t) '
r'\right\vert_{t=0}\right)\right)')
expr = ( # nested derivative
MyScalarFunc("f", s, t).diff(s, n=2).diff(t).evaluate_at({
t: t0
}).diff(t0))
assert latex(expr) == (
r'\frac{\partial}{\partial t_{0}} \left(\left. '
r'\frac{\partial^{3}}{\partial s^{2} \partial t} f(s, t) '
r'\right\vert_{t=t_{0}}\right)')
def test_tex_ket_operations():
"""Test the tex representation of ket operations"""
hs1 = LocalSpace('q_1', basis=('g', 'e'))
hs2 = LocalSpace('q_2', basis=('g', 'e'))
ket_g1 = BasisKet('g', hs=hs1)
ket_e1 = BasisKet('e', hs=hs1)
ket_g2 = BasisKet('g', hs=hs2)
ket_e2 = BasisKet('e', hs=hs2)
psi1 = KetSymbol("Psi_1", hs=hs1)
psi2 = KetSymbol("Psi_2", hs=hs1)
psi2 = KetSymbol("Psi_2", hs=hs1)
psi3 = KetSymbol("Psi_3", hs=hs1)
phi = KetSymbol("Phi", hs=hs2)
A = OperatorSymbol("A_0", hs=hs1)
gamma = symbols('gamma', positive=True)
alpha = symbols('alpha')
beta = symbols('beta')
phase = exp(-I * gamma)
i = IdxSym('i')
assert (latex(psi1 +
psi2) == r'\left\lvert \Psi_{1} \right\rangle^{(q_{1})} + '
r'\left\lvert \Psi_{2} \right\rangle^{(q_{1})}')
assert (latex(psi1 - psi2 +
psi3) == r'\left\lvert \Psi_{1} \right\rangle^{(q_{1})} - '
r'\left\lvert \Psi_{2} \right\rangle^{(q_{1})} + '
r'\left\lvert \Psi_{3} \right\rangle^{(q_{1})}')
assert (latex(
psi1 * phi) == r'\left\lvert \Psi_{1} \right\rangle^{(q_{1})} \otimes '
r'\left\lvert \Phi \right\rangle^{(q_{2})}')
assert (latex(phase * psi1) ==
r'e^{- i \gamma} \left\lvert \Psi_{1} \right\rangle^{(q_{1})}')
assert (latex((alpha + 1) * KetSymbol('Psi', hs=0)) ==
r'\left(\alpha + 1\right) \left\lvert \Psi \right\rangle^{(0)}')
assert (latex(
A * psi1
) == r'\hat{A}_{0}^{(q_{1})} \left\lvert \Psi_{1} \right\rangle^{(q_{1})}')
braket = BraKet(psi1, psi2)
assert (
latex(braket, show_hs_label='subscript') ==
r'\left\langle \Psi_{1} \middle\vert \Psi_{2} \right\rangle_{(q_{1})}')
assert (latex(braket, show_hs_label=False) ==
r'\left\langle \Psi_{1} \middle\vert \Psi_{2} \right\rangle')
expr = BraKet(KetSymbol('Psi_1', alpha, hs=hs1),
KetSymbol('Psi_2', beta, hs=hs1))
assert (latex(expr) ==
r'\left\langle \Psi_{1}\left(\alpha\right) \middle\vert '
r'\Psi_{2}\left(\beta\right) \right\rangle^{(q_{1})}')
assert (latex(
ket_e1 *
ket_e2) == r'\left\lvert ee \right\rangle^{(q_{1} \otimes q_{2})}')
assert latex(ket_e1.dag() * ket_e1) == r'1'
assert latex(ket_g1.dag() * ket_e1) == r'0'
ketbra = KetBra(psi1, psi2)
assert (latex(ketbra) == r'\left\lvert \Psi_{1} \middle\rangle\!'
r'\middle\langle \Psi_{2} \right\rvert^{(q_{1})}')
assert (latex(
ketbra,
show_hs_label='subscript') == r'\left\lvert \Psi_{1} \middle\rangle\!'
r'\middle\langle \Psi_{2} \right\rvert_{(q_{1})}')
assert (latex(
ketbra,
show_hs_label=False) == r'\left\lvert \Psi_{1} \middle\rangle\!'
r'\middle\langle \Psi_{2} \right\rvert')
expr = KetBra(KetSymbol('Psi_1', alpha, hs=hs1),
KetSymbol('Psi_2', beta, hs=hs1))
assert (
latex(expr) ==
r'\left\lvert \Psi_{1}\left(\alpha\right) \middle\rangle\!'
r'\middle\langle \Psi_{2}\left(\beta\right) \right\rvert^{(q_{1})}')
bell1 = (ket_e1 * ket_g2 - I * ket_g1 * ket_e2) / sqrt(2)
bell2 = (ket_e1 * ket_e2 - ket_g1 * ket_g2) / sqrt(2)
assert (latex(bell1) ==
r'\frac{1}{\sqrt{2}} \left(\left\lvert eg \right\rangle^{(q_{1} '
r'\otimes q_{2})} - i \left\lvert ge \right\rangle'
r'^{(q_{1} \otimes q_{2})}\right)')
assert (latex(bell2) ==
r'\frac{1}{\sqrt{2}} \left(\left\lvert ee \right\rangle^{(q_{1} '
r'\otimes q_{2})} - \left\lvert gg \right\rangle'
r'^{(q_{1} \otimes q_{2})}\right)')
assert (latex(bell2, show_hs_label=False) ==
r'\frac{1}{\sqrt{2}} \left(\left\lvert ee \right\rangle - '
r'\left\lvert gg \right\rangle\right)')
assert BraKet.create(bell1, bell2).expand() == 0
assert (latex(BraKet.create(
bell1, bell2)) == r'\frac{1}{2} \left(\left\langle eg \right\rvert'
r'^{(q_{1} \otimes q_{2})} + i \left\langle ge \right\rvert'
r'^{(q_{1} \otimes q_{2})}\right) '
r'\left(\left\lvert ee \right\rangle^{(q_{1} \otimes q_{2})} '
r'- \left\lvert gg \right\rangle^{(q_{1} \otimes q_{2})}\right)')
assert (
latex(KetBra.create(
bell1, bell2)) == r'\frac{1}{2} \left(\left\lvert eg \right\rangle'
r'^{(q_{1} \otimes q_{2})} - i \left\lvert ge \right\rangle'
r'^{(q_{1} \otimes q_{2})}\right)\left(\left\langle ee \right\rvert'
r'^{(q_{1} \otimes q_{2})} - \left\langle gg \right\rvert'
r'^{(q_{1} \otimes q_{2})}\right)')
with configure_printing(tex_use_braket=True):
expr = KetBra(KetSymbol('Psi', hs=0), BasisKet(FockIndex(i), hs=0))
assert latex(expr) == r'\Ket{\Psi}\!\Bra{i}^{(0)}'
expr = KetBra(BasisKet(FockIndex(i), hs=0), KetSymbol('Psi', hs=0))
assert latex(expr) == r'\Ket{i}\!\Bra{\Psi}^{(0)}'
expr = BraKet(KetSymbol('Psi', hs=0), BasisKet(FockIndex(i), hs=0))
assert latex(expr) == r'\Braket{\Psi | i}^(0)'
expr = BraKet(BasisKet(FockIndex(i), hs=0), KetSymbol('Psi', hs=0))
assert latex(expr) == r'\Braket{i | \Psi}^(0)'
def _repr_latex_(self):
from qalgebra import latex
return "$" + latex(self) + "$"
def test_tex_bra_elements():
"""Test the tex representation of "atomic" kets"""
hs1 = LocalSpace('q1', basis=('g', 'e'))
hs2 = LocalSpace('q2', basis=('g', 'e'))
alpha, beta = symbols('alpha, beta')
bra = Bra(KetSymbol('Psi', hs=hs1))
assert latex(bra) == r'\left\langle \Psi \right\rvert^{(q_{1})}'
assert latex(Bra(KetSymbol('Psi', alpha, beta, hs=hs1))) == (
r'\left\langle \Psi\left(\alpha, \beta\right) \right\rvert^{(q_{1})}')
assert latex(bra, tex_use_braket=True) == r'\Bra{\Psi}^{(q_{1})}'
assert (latex(bra, tex_use_braket=True,
show_hs_label='subscript') == r'\Bra{\Psi}_{(q_{1})}')
assert (latex(bra, tex_use_braket=True,
show_hs_label=False) == r'\Bra{\Psi}')
assert (latex(Bra(KetSymbol(
'Psi', hs=1))) == r'\left\langle \Psi \right\rvert^{(1)}')
assert (latex(Bra(KetSymbol(
'Psi',
hs=(1, 2)))) == r'\left\langle \Psi \right\rvert^{(1 \otimes 2)}')
assert (latex(Bra(KetSymbol(
'Psi', hs=hs1 *
hs2))) == r'\left\langle \Psi \right\rvert^{(q_{1} \otimes q_{2})}')
assert (latex(KetSymbol(
'Psi', hs=1).dag()) == r'\left\langle \Psi \right\rvert^{(1)}')
assert latex(Bra(ZeroKet)) == '0'
assert latex(Bra(TrivialKet)) == '1'
assert (latex(BasisKet(
'e', hs=hs1).adjoint()) == r'\left\langle e \right\rvert^{(q_{1})}')
assert (latex(BasisKet(
1, hs=1).adjoint()) == r'\left\langle 1 \right\rvert^{(1)}')
assert (latex(CoherentStateKet(
2.0, hs=1).dag()) == r'\left\langle \alpha=2 \right\rvert^{(1)}')
