def ewl_fixed() -> EWL:
i = sp.I
pi = sp.pi
sqrt2 = sp.sqrt(2)
psi = (Qubit('00') + i * Qubit('11')) / sqrt2
alice = U_theta_alpha_beta(theta=pi / 2, alpha=pi / 2, beta=0)
bob = U_theta_alpha_beta(theta=0, alpha=0, beta=0)
return EWL(psi=psi, C=C, D=D, players=[alice, bob])
def ewl_parametrized() -> EWL:
i = sp.I
sqrt2 = sp.sqrt(2)
theta1, alpha1, beta1, theta2, alpha2, beta2 = sp.symbols(
'theta1 alpha1 beta1 theta2 alpha2 beta2', real=True)
psi = (Qubit('00') + i * Qubit('11')) / sqrt2
alice = U_theta_alpha_beta(theta=theta1, alpha=alpha1, beta=beta1)
bob = U_theta_alpha_beta(theta=theta2, alpha=alpha2, beta=beta2)
return EWL(psi=psi, C=C, D=D, players=[alice, bob])
def test_fix(ewl_parametrized_00_11: EWL, ewl: EWL):
ewl_fixed = ewl_parametrized_00_11.fix(theta1=pi / 2,
alpha1=pi / 2,
beta1=0,
theta2=0,
alpha2=0,
beta2=0)
assert ewl_fixed.psi == ewl.psi
assert ewl_fixed.players[0] == ewl.players[0]
assert ewl_fixed.players[1] == ewl.players[1]
def test_amplitudes_parametrized(ewl_parametrized_00_11: EWL):
assert ewl_parametrized_00_11.amplitudes() == Matrix([
cos(alpha1 + alpha2) * cos(theta1 / 2) * cos(theta2 / 2) +
sin(beta1 + beta2) * sin(theta1 / 2) * sin(theta2 / 2),
sin(alpha2 - beta1) * sin(theta1 / 2) * cos(theta2 / 2) +
cos(alpha1 - beta2) * cos(theta1 / 2) * sin(theta2 / 2),
cos(alpha2 - beta1) * sin(theta1 / 2) * cos(theta2 / 2) +
sin(alpha1 - beta2) * cos(theta1 / 2) * sin(theta2 / 2),
-sin(alpha1 + alpha2) * cos(theta1 / 2) * cos(theta2 / 2) +
cos(beta1 + beta2) * sin(theta1 / 2) * sin(theta2 / 2),
])
def test_probs_parametrized(ewl_parametrized_01_10: EWL):
assert ewl_parametrized_01_10.probs() == Matrix([
(cos(alpha1 - alpha2) * cos(theta1 / 2) * cos(theta2 / 2) +
sin(beta1 - beta2) * sin(theta1 / 2) * sin(theta2 / 2))**2,
(sin(alpha2 + beta1) * sin(theta1 / 2) * cos(theta2 / 2) -
cos(alpha1 + beta2) * cos(theta1 / 2) * sin(theta2 / 2))**2,
(cos(alpha2 + beta1) * sin(theta1 / 2) * cos(theta2 / 2) +
sin(alpha1 + beta2) * cos(theta1 / 2) * sin(theta2 / 2))**2,
(-sin(alpha1 - alpha2) * cos(theta1 / 2) * cos(theta2 / 2) +
cos(beta1 - beta2) * sin(theta1 / 2) * sin(theta2 / 2))**2,
])
def make_Quantum_Prisoners_Dilemma_Frackiewicz_Pykacz() -> EWL:
"""
Quantum Prisoner's Dilemma with Frąckiewicz-Pykacz parametrization
from "Quantum games with strategies induced by basis change rules" by Piotr Frąckiewicz and Jarosław Pykacz
(https://www.researchgate.net/publication/317754594_Quantum_Games_with_Strategies_Induced_by_Basis_Change_Rules/fulltext/59601fed0f7e9b8194fc0d96/Quantum-Games-with-Strategies-Induced-by-Basis-Change-Rules.pdf)
"""
alice = U_Frackiewicz_Pykacz(theta=theta_A, phi=phi_A)
bob = U_Frackiewicz_Pykacz(theta=theta_B, phi=phi_B)
C = U_Frackiewicz_Pykacz(theta=0, phi=0)
D = U_Frackiewicz_Pykacz(theta=pi, phi=0)
return EWL(psi=psi, C=C, D=D, players=[alice, bob], payoff_matrix=payoff_matrix)
def make_Quantum_Prisoners_Dilemma_Szopa() -> EWL:
"""
Quantum Prisoner's Dilemma with full SU(2) parametrization
from "Dlaczego w dylemat więźnia warto grać kwantowo?" by Marek Szopa
(https://www.ue.katowice.pl/fileadmin/_migrated/content_uploads/11_M.Szopa__Dlaczego_w_dylemat_wieznia....pdf)
"""
alice = U_theta_phi_alpha(theta=theta_A, phi=phi_A, alpha=alpha_A)
bob = U_theta_phi_alpha(theta=theta_B, phi=phi_B, alpha=alpha_B)
C = U_theta_phi_alpha(theta=0, phi=0, alpha=0)
D = U_theta_phi_alpha(theta=pi, phi=0, alpha=0)
return EWL(psi=psi, C=C, D=D, players=[alice, bob], payoff_matrix=payoff_matrix)
def make_Quantum_Prisoners_Dilemma_Chen() -> EWL:
"""
Quantum Prisoner's Dilemma with full SU(2) parametrization
from "How Well Do People Play a Quantum Prisoner's Dilemma?" by Kay-Yut Chen and Tad Hogg
(https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.73.1344&rep=rep1&type=pdf)
"""
alice = U_theta_phi_alpha(theta=theta_A, phi=phi_A, alpha=alpha_A)
bob = U_theta_phi_alpha(theta=theta_B, phi=phi_B, alpha=alpha_B)
C = U_theta_phi_alpha(theta=0, phi=0, alpha=0)
D = U_theta_phi_alpha(theta=pi, phi=0, alpha=pi / 2)
return EWL(psi=psi, C=C, D=D, players=[alice, bob], payoff_matrix=payoff_matrix)
def make_Quantum_Prisoners_Dilemma_Eisert_Wilkens_Lewenstein() -> EWL:
"""
Quantum Prisoner's Dilemma with original EWL parametrization
from "Quantum Games and Quantum Strategies" by Jens Eisert, Martin Wilkens and Maciej Lewenstein
(https://arxiv.org/pdf/quant-ph/9806088.pdf)
"""
alice = U_Eisert_Wilkens_Lewenstein(theta=theta_A, phi=phi_A)
bob = U_Eisert_Wilkens_Lewenstein(theta=theta_B, phi=phi_B)
C = U_Eisert_Wilkens_Lewenstein(theta=0, phi=0)
D = U_Eisert_Wilkens_Lewenstein(theta=pi, phi=0)
return EWL(psi=psi, C=C, D=D, players=[alice, bob], payoff_matrix=payoff_matrix)
def plot_payoff_function(ewl: EWL, *, player: Optional[int],
x: sp.Symbol, x_min, x_max, y: sp.Symbol, y_min, y_max, n: int = 20,
figsize=(8, 8), cmap=plt.cm.coolwarm, **kwargs) -> plt.Figure:
f = sp.lambdify([x, y], ewl.payoff_function(player=player))
xs = np.linspace(x_min, x_max, n)
ys = np.linspace(y_min, y_max, n)
X, Y = np.meshgrid(xs, ys)
Z = f(X, Y)
fig = plt.figure(figsize=figsize)
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(X, Y, Z, cmap=cmap, antialiased=True)
ax.set(xlim=(x_min, x_max), ylim=(y_min, y_max),
xlabel=f'${sp.latex(x)}$', ylabel=f'${sp.latex(y)}$',
zlabel='expected payoff', **kwargs)
return fig
def check_classical_payoffs(ewl: EWL) -> None:
# from Fig. 1 in https://arxiv.org/pdf/quant-ph/0004076.pdf
assert ewl.play(ewl.C, ewl.C).payoffs() == (3, 3)
assert ewl.play(ewl.C, ewl.D).payoffs() == (0, 5)
assert ewl.play(ewl.D, ewl.C).payoffs() == (5, 0)
assert ewl.play(ewl.D, ewl.D).payoffs() == (1, 1)
def test_calculate_probs(ewl: EWL):
assert ewl.probs() == Matrix([0, 0, 1 / 2, 1 / 2])
def ewl_parametrized_01_10() -> EWL:
psi = (Qubit('01') + i * Qubit('10')) / sqrt2
alice = U_theta_alpha_beta(theta=theta1, alpha=alpha1, beta=beta1)
bob = U_theta_alpha_beta(theta=theta2, alpha=alpha2, beta=beta2)
return EWL(psi=psi, C=C, D=D, players=[alice, bob])
def ewl() -> EWL:
psi = (Qubit('00') + i * Qubit('11')) / sqrt2
alice = U_theta_alpha_beta(theta=pi / 2, alpha=pi / 2, beta=0)
bob = U_theta_alpha_beta(theta=0, alpha=0, beta=0)
return EWL(psi=psi, C=C, D=D, players=[alice, bob])