def find_fidelity(graph, critical_time):
cost = hamiltonian.HamiltonianMIS(graph, IS_subspace=True)
driver = hamiltonian.HamiltonianDriver(IS_subspace=True, graph=graph)
def schedule(t, T):
# Linear ramp on the detuning, experiment-like ramp on the driver
k = 50
a = .95
b = 3.1
x = t / T
amplitude = (
-1 / (1 + np.e ** (k * (x - a))) ** b - 1 / (1 + np.e ** (-k * (x - (1 - a)))) ** b + 1) / \
(-1 / ((1 + np.e ** (k * (1 / 2 - a))) ** b) - 1 / (
(1 + np.e ** (-k * (1 / 2 - (1 - a)))) ** b) + 1)
cost.energies = (3 * 2 * (1 / 2 - x), )
driver.energies = (amplitude, )
ad = SimulateAdiabatic(graph=graph,
hamiltonian=[cost, driver],
cost_hamiltonian=cost,
IS_subspace=True)
final_state = ad.run(critical_time, schedule, method='odeint')[0][-1]
cost.energies = (1, )
optimum_indices = np.argwhere(
cost._diagonal_hamiltonian == cost.optimum).T[0]
# Construct an operator that is zero everywhere except at the optimum
optimum = np.zeros(cost._diagonal_hamiltonian.shape)
optimum[optimum_indices] = 1
optimum_overlap = cost.optimum_overlap(final_state)
return final_state, optimum, optimum_overlap
def find_ratio(tails_graph, graph, detuning_plateau, tf):
cost = hamiltonian.HamiltonianMIS(graph, IS_subspace=True)
print('Starting driver')
driver = hamiltonian.HamiltonianDriver(IS_subspace=True, graph=graph)
print('Starting rydberg')
if tails_graph is not None:
rydberg = hamiltonian.HamiltonianRydberg(tails_graph,
graph,
IS_subspace=True,
energies=(2 * np.pi, ))
ad = SimulateAdiabatic(graph=graph,
hamiltonian=[cost, driver, rydberg],
cost_hamiltonian=cost,
IS_subspace=True)
else:
ad = SimulateAdiabatic(graph=graph,
hamiltonian=[cost, driver],
cost_hamiltonian=cost,
IS_subspace=True)
def schedule_cubic(t, T):
cubic_ys = 2 * np.pi * np.array([
11.5, detuning_plateau + .5, detuning_plateau,
detuning_plateau - .5, -11.5
])
cubic_xs = np.array([
.312, (T / 2 - .312) / 1.35 + .312, T / 2,
T - .312 - (T / 2 - .312) / 1.35, T - .312
])
if t < .312:
driver.energies = (2 * np.pi * 2 * t / .312, )
cost.energies = (2 * np.pi * 11.5, )
elif .312 <= t <= T - .312:
driver.energies = (2 * np.pi * 2, )
cost.energies = (scipy.interpolate.interp1d(cubic_xs,
cubic_ys,
kind='cubic')(t), )
else:
driver.energies = (2 * np.pi * 2 * (T - t) / .312, )
cost.energies = (-2 * np.pi * 11.5, )
print('Starting evolution')
states, data = ad.run(tf,
schedule_cubic,
num=int(400 * tf),
method='trotterize',
full_output=False)
np.savez_compressed('{}x{}_{}_{}_{}_trotterize_highres.npz'.format(
size, size, graph_index, np.round(np.abs(detuning_plateau), 2),
np.round(np.abs(tf), 2)),
state=states[-1])
def find_ratio(tails_graph, graph, tf):
cost = hamiltonian.HamiltonianMIS(graph, IS_subspace=True)
driver = hamiltonian.HamiltonianDriver(IS_subspace=True, graph=graph)
def schedule(t, T):
# Linear ramp on the detuning, experiment-like ramp on the driver
k = 50
a = .95
b = 3.1
x = t / T
amplitude = (
-1 / (1 + np.e ** (k * (x - a))) ** b - 1 / (1 + np.e ** (-k * (x - (1 - a)))) ** b + 1) / \
(-1 / ((1 + np.e ** (k * (1 / 2 - a))) ** b) - 1 / (
(1 + np.e ** (-k * (1 / 2 - (1 - a)))) ** b) + 1)
cost.energies = (11 * 2 * (1 / 2 - x), )
driver.energies = (2 * amplitude, )
# Uncomment this to print the schedule at t=0
# schedule(0, 1)
# print(cost.hamiltonian*2*np.pi)
# print(driver.hamiltonian)
if tails_graph is None:
ad = SimulateAdiabatic(graph=graph,
hamiltonian=[cost, driver],
cost_hamiltonian=cost,
IS_subspace=True)
else:
rydberg = hamiltonian.HamiltonianRydberg(tails_graph,
graph,
IS_subspace=True,
energies=(1, ))
ad = SimulateAdiabatic(graph=graph,
hamiltonian=[cost, driver, rydberg],
cost_hamiltonian=cost,
IS_subspace=True)
print('running')
states, data = ad.run(tf, schedule, method='odeint')
print(data)
times = data['t']
is_overlaps = np.zeros((graph.mis_size + 1, len(states)))
cost.energies = (1, )
for j in range(graph.mis_size + 1):
projector = (cost._diagonal_hamiltonian == j)
for i in range(len(states)):
is_overlaps[j, i] = np.sum(np.abs(states[i])**2 * projector)
print(is_overlaps)
for j in range(graph.mis_size + 1):
plt.scatter(times, is_overlaps[j], label=str(j))
plt.legend()
plt.show()
def track_eigenstate_populations(graph, tails_graph, grid, k=2):
n_points = 7
times_exp = 2**np.linspace(-2.5, 4.5 / 6 *
(n_points - 1) - 2.5, n_points) + .312 * 2
t_max = times_exp[6]
cost = hamiltonian.HamiltonianMIS(graph, IS_subspace=True)
# print('Starting driver')
driver = hamiltonian.HamiltonianDriver(IS_subspace=True, graph=graph)
# print('Starting rydberg')
if tails_graph is not None:
rydberg = hamiltonian.HamiltonianRydberg(tails_graph,
graph,
IS_subspace=True,
energies=(2 * np.pi, ))
pulse = np.loadtxt('for_AWG_{}.000000.txt'.format(6))
t_pulse_max = np.max(pulse[:, 0]) - 2 * 0.312
max_detuning = np.max(pulse[:, 2])
def schedule_old(t, T):
# Linear ramp on the detuning, experiment-like ramp on the driver
k = 50
a = .95
b = 3.1
x = t / T
amplitude = (
-1 / (1 + np.e ** (k * (x - a))) ** b - 1 / (1 + np.e ** (-k * (x - (1 - a)))) ** b + 1) / \
(-1 / ((1 + np.e ** (k * (1 / 2 - a))) ** b) - 1 / (
(1 + np.e ** (-k * (1 / 2 - (1 - a)))) ** b) + 1)
cost.energies = (-2 * np.pi * 11 * 2 * (1 / 2 - t / T),
) # (2 * np.pi * (-(11 + 15) / T * t + 15),)
driver.energies = (2 * np.pi * 2 * amplitude,
) # (2 * np.pi * 2 * amplitude,)
def schedule_exp_optimized(t, T):
if t < .312:
driver.energies = (2 * np.pi * 2 * t / .312, )
cost.energies = (2 * np.pi * 15, )
elif .312 <= t <= T - .312:
t_pulse = (t - 0.312) / (T - 2 * 0.312) * t_pulse_max + 0.312
driver.energies = (
2 * np.pi * np.interp(t_pulse, pulse[:, 0], pulse[:, 1] / 2), )
cost.energies = (2 * np.pi *
np.interp(t_pulse, pulse[:, 0], -pulse[:, 2]), )
else:
driver.energies = (2 * np.pi * 2 * (T - t) / .312, )
cost.energies = (-2 * np.pi * max_detuning, )
# print(t, cost.energies)
def schedule_exp_linear(t, T):
if t < .312:
driver.energies = (2 * np.pi * 2 * t / .312, )
cost.energies = (2 * np.pi * 15, )
elif .312 <= t <= T - .312:
driver.energies = (2 * np.pi * 2, )
cost.energies = (2 * np.pi * (-(11 + 15) / (T - 2 * .312) *
(t - .312) + 15), )
else:
driver.energies = (2 * np.pi * 2 * (T - t) / .312, )
cost.energies = (-2 * np.pi * 11, )
def eigs(t):
schedule_exp_linear(t, t_max)
eigval, eigvec = eq.eig(which='S', k=k)
return eigval - eigval[0], eigvec
if tails_graph is not None:
eq = schrodinger_equation.SchrodingerEquation(
hamiltonians=[cost, driver, rydberg])
ad = SimulateAdiabatic(graph=graph,
hamiltonian=[cost, driver, rydberg],
cost_hamiltonian=cost,
IS_subspace=True)
else:
eq = schrodinger_equation.SchrodingerEquation(
hamiltonians=[cost, driver])
ad = SimulateAdiabatic(graph=graph,
hamiltonian=[cost, driver],
cost_hamiltonian=cost,
IS_subspace=True)
print('starting evolution')
states, data = ad.run(t_max,
schedule_exp_linear,
num=int(60 * t_max),
method='odeint',
full_output=True)
print('finished evolution')
times = data['t']
start_index = len(times) // 2
times = times[start_index:]
states = states[start_index:]
populations = np.zeros((len(times), k))
energies = np.zeros((len(times), k))
for (i, time) in enumerate(times):
print(i)
eigval, eigvecs = eigs(time)
populations[i] = (np.abs(eigvecs @ states[i])**2).flatten()
energies[i] = eigval / (2 * np.pi)
populations = np.log10(populations)
from matplotlib.collections import LineCollection
fig, ax = plt.subplots()
norm = plt.Normalize(-5, np.max(populations))
for i in range(energies.shape[1]):
points = np.array([times, energies[:, i]]).T.reshape(-1, 1, 2)
segments = np.concatenate([points[:-1], points[1:]], axis=1)
lc = LineCollection(segments, cmap='coolwarm', norm=norm)
# Set the values used for colormapping
lc.set_array(populations[:-1, i])
lc.set_linewidth(1)
line = ax.add_collection(lc)
cbar = fig.colorbar(line, ax=ax)
cbar.ax.set_ylabel(r'$\log_{10}(\rm{population})$')
ax.set_xlim(np.min(times), np.max(times))
ax.set_xlabel(r'Time ($\mu$s)')
ax.set_ylabel(r'Eigenenergy (MHz)')
ax.set_ylim(np.min(energies) - .3, np.max(energies))
# ax.annotate(r'$r_{0\rightarrow j} = \sum_\mu |\langle j |c_\mu |0\rangle |^2$', xy=(0.4, 0.1), xycoords='data')
plt.show()
fig, ax = plt.subplots()
deltas = np.zeros(len(times))
print(times)
for (i, time) in enumerate(times):
schedule_exp_linear(time, t_max)
deltas[i] = cost.energies[0] / (2 * np.pi)
print(deltas)
norm = plt.Normalize(-5, np.max(populations))
for i in range(energies.shape[1]):
points = np.array([deltas, energies[:, i]]).T.reshape(-1, 1, 2)
segments = np.concatenate([points[:-1], points[1:]], axis=1)
lc = LineCollection(segments, cmap='coolwarm', norm=norm)
# Set the values used for colormapping
lc.set_array(populations[:-1, i])
lc.set_linewidth(1)
line = ax.add_collection(lc)
cbar = fig.colorbar(line, ax=ax)
cbar.ax.set_ylabel(r'$\log_{10}(\rm{population})$')
ax.set_xlim(np.max(deltas), np.min(deltas))
ax.set_xlabel(r'$\Delta$ (MHz)')
ax.set_ylabel(r'Eigenenergy (MHz)')
ax.set_ylim(np.min(energies) - .3, np.max(energies))
# ax.annotate(r'$r_{0\rightarrow j} = \sum_\mu |\langle j |c_\mu |0\rangle |^2$', xy=(0.4, 0.1), xycoords='data')
plt.show()
fig, ax = plt.subplots(3, 5)
probs = np.abs(eigvecs)**2
print(probs[:, :10])
for l in range(k):
i = l // 5
j = l % 5
layout = grid.copy().flatten().astype(float)
layout[layout == 0] = -5
layout[layout == 1] = 0
layout_temp = layout.copy()
for m in range(probs.shape[1]):
layout_temp[layout == 0] = layout_temp[
layout == 0] + (1 - graph.independent_sets[m]) * probs[l, m]
ax[i][j].imshow(layout_temp.reshape(grid.shape))
ax[i][j].set_axis_off()
ax[i][j].text(-0.1,
1.05,
'$\lambda${}'.format(str(l)),
transform=ax[i][j].transAxes,
size=10,
weight='bold')
plt.show()
def find_ratio(tails_graph, graph, tf, graph_index=None, size=None):
cost = hamiltonian.HamiltonianMIS(graph, IS_subspace=True)
# print('Starting driver')
driver = hamiltonian.HamiltonianDriver(IS_subspace=True, graph=graph)
# print('Starting rydberg')
if tails_graph is not None:
rydberg = hamiltonian.HamiltonianRydberg(tails_graph,
graph,
IS_subspace=True,
energies=(2 * np.pi, ))
pulse = np.loadtxt('for_AWG_{}.000000.txt'.format(6))
t_pulse_max = np.max(pulse[:, 0]) - 2 * 0.312
def schedule(t, T):
# Linear ramp on the detuning, experiment-like ramp on the driver
k = 50
a = .95
b = 3.1
x = t / T
amplitude = (
-1 / (1 + np.e ** (k * (x - a))) ** b - 1 / (1 + np.e ** (-k * (x - (1 - a)))) ** b + 1) / \
(-1 / ((1 + np.e ** (k * (1 / 2 - a))) ** b) - 1 / (
(1 + np.e ** (-k * (1 / 2 - (1 - a)))) ** b) + 1)
cost.energies = (2 * np.pi * (-(11 + 15) / T * t + 15), )
driver.energies = (2 * np.pi * 2 * amplitude, )
def schedule_old(t, T):
# Linear ramp on the detuning, experiment-like ramp on the driver
k = 50
a = .95
b = 3.1
x = t / T
amplitude = (
-1 / (1 + np.e ** (k * (x - a))) ** b - 1 / (1 + np.e ** (-k * (x - (1 - a)))) ** b + 1) / \
(-1 / ((1 + np.e ** (k * (1 / 2 - a))) ** b) - 1 / (
(1 + np.e ** (-k * (1 / 2 - (1 - a)))) ** b) + 1)
cost.energies = (-2 * np.pi * 11 * 2 * (1 / 2 - t / T),
) # (2 * np.pi * (-(11 + 15) / T * t + 15),)
driver.energies = (2 * np.pi * 2 * amplitude,
) # (2 * np.pi * 2 * amplitude,)
def schedule_exp_optimized(t, T):
if t < .312:
driver.energies = (2 * np.pi * 2 * t / .312, )
cost.energies = (2 * np.pi * 15, )
elif .312 <= t <= T - .312:
t_pulse = (t - 0.312) / (T - 2 * 0.312) * t_pulse_max + 0.312
driver.energies = (
2 * np.pi * np.interp(t_pulse, pulse[:, 0], pulse[:, 1] / 2), )
cost.energies = (2 * np.pi *
np.interp(t_pulse, pulse[:, 0], -pulse[:, 2]), )
else:
driver.energies = (2 * np.pi * 2 * (T - t) / .312, )
cost.energies = (-2 * np.pi * 11, )
# print(t, cost.energies)
def schedule_exp_linear(t, T):
if t < .312:
driver.energies = (2 * np.pi * 2 * t / .312, )
cost.energies = (2 * np.pi * 15, )
elif .312 <= t <= T - .312:
driver.energies = (2 * np.pi * 2, )
cost.energies = (2 * np.pi * (-(11 + 15) / (T - 2 * .312) *
(t - .312) + 15), )
else:
driver.energies = (2 * np.pi * 2 * (T - t) / .312, )
cost.energies = (-2 * np.pi * 11, )
# print(t, cost.energies)
# Uncomment this to print the schedule at t=0
# schedule(0, 1)
# print(cost.hamiltonian*2*np.pi)
# print(driver.hamiltonian)
if tails_graph is None:
ad = SimulateAdiabatic(graph=graph,
hamiltonian=[cost, driver],
cost_hamiltonian=cost,
IS_subspace=True)
else:
ad = SimulateAdiabatic(graph=graph,
hamiltonian=[cost, driver, rydberg],
cost_hamiltonian=cost,
IS_subspace=True)
# print('Starting evolution')
ars = []
probs = []
for i in range(len(tf)):
states, data = ad.run(tf[i],
schedule_exp_linear,
num=int(20 * tf[i]),
method='odeint',
full_output=False)
cost.energies = (1, )
ar = cost.approximation_ratio(states[-1])
prob = cost.optimum_overlap(states[-1])
# np.savez_compressed('{}x{}_{}_{}.npz'.format(size, size, graph_index, i), state=states[-1])
print(tf[i], ar, prob)
ars.append(ar)
probs.append(prob)
return ars, probs