def find_fidelity(graph, critical_time):
cost = hamiltonian.HamiltonianMIS(graph, IS_subspace=True)
driver = hamiltonian.HamiltonianDriver(IS_subspace=True, graph=graph)
rydberg = hamiltonian.HamiltonianRydberg(tails_graph,
graph,
IS_subspace=True)
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 visualize_low_energy_subspace(graph, tails_graph, k=5):
cost = hamiltonian.HamiltonianMIS(graph, IS_subspace=True)
# print('Starting driver')
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[4]
driver = hamiltonian.HamiltonianDriver(IS_subspace=True, graph=graph)
# print('Starting rydberg')
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)
def gap(t):
schedule_exp_linear(t * t_max, t_max)
eigval, eigvec = eq.eig(which='S', k=k)
return np.abs(eigval - eigval[0]), eigvec
# Uncomment this to print the schedule at t=0
# schedule(0, 1)
# print(cost.hamiltonian*2*np.pi)
# print(driver.hamiltonian)
eq = schrodinger_equation.SchrodingerEquation(
hamiltonians=[cost, driver, rydberg])
fig = plt.figure(tight_layout=True)
k_cutoff = 5
gs = gridspec.GridSpec(k_cutoff, k_cutoff)
ax = fig.add_subplot(gs[:, 0:k_cutoff - 1])
num = 50
print('beginning computation')
for (i, t) in enumerate(np.linspace(.5, .98, num)):
print(i)
g, eigvec = gap(t)
print(g)
if i == num - 1:
probs = np.abs(eigvec)**2
for l in range(k_cutoff):
layout = grid.copy().flatten().astype(float)
layout[layout == 0] = -5
layout[layout == 1] = 0
layout_temp = layout.copy()
ax_im = fig.add_subplot(gs[k_cutoff - l - 1, -1])
for j in range(probs.shape[1]):
layout_temp[layout == 0] = layout_temp[layout == 0] + (
1 - graph.independent_sets[j]) * probs[l, j]
ax_im.imshow(layout_temp.reshape(grid.shape))
ax_im.set_axis_off()
ax.scatter(np.ones(len(g)) * t, g, s=5, color='navy')
ax.set_xlabel(r'$t/T$')
ax.set_ylabel(r'Eigenenergy ($\Omega_{\max} = 1$)')
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
def find_ground_first_excited(graph, tails_graph, t, 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[4]
print('Starting cost')
cost = hamiltonian.HamiltonianMIS(graph, IS_subspace=True)
print('Starting driver')
driver = hamiltonian.HamiltonianDriver(IS_subspace=True, graph=graph)
if tails_graph is not None:
print('Starting rydberg')
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, )
if tails_graph is None:
eq = schrodinger_equation.SchrodingerEquation(
hamiltonians=[cost, driver])
else:
eq = schrodinger_equation.SchrodingerEquation(
hamiltonians=[cost, driver, rydberg])
# Do minimization
schedule = schedule_exp_linear
t = t * t_max
schedule(t, t_max)
eigval, eigvec = eq.eig(which='S', k=k)
print(eigval[0], eigval[1])
return eigval, eigvec
def find_gap(graph, tails_graph, k=2, verbose=False):
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[4]
print('Starting cost')
cost = hamiltonian.HamiltonianMIS(graph, IS_subspace=True)
print('Starting driver')
driver = hamiltonian.HamiltonianDriver(IS_subspace=True, graph=graph)
if tails_graph is not None:
print('Starting rydberg')
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 gap(t):
t = t[0]
t = t * t_max
schedule(t, t_max)
eigval, eigvec = eq.eig(which='S', k=k)
if verbose:
print(np.abs(eigval[1] - eigval[0]), t / t_max)
# print(t/t_max, np.abs(eigval[1] - eigval[0]))
return np.abs(eigval[1] - eigval[0])
if tails_graph is None:
eq = schrodinger_equation.SchrodingerEquation(
hamiltonians=[cost, driver])
else:
eq = schrodinger_equation.SchrodingerEquation(
hamiltonians=[cost, driver, rydberg])
# Do minimization
schedule = schedule_exp_linear
if tails_graph is None:
# Previously .67
upper = 0.8
# Previously .55
lower = .55
init = np.array([.7])
else:
# Default: .77
upper = 0.7860824 # 0.77
lower = 0.7856305 # 0.8161#.77#.6
# Default: .71
init = np.array([0.7860309]) # 0.74
print('Starting gap')
res_linear = scipy.optimize.minimize(gap,
init,
bounds=[(lower, upper)],
method='L-BFGS-B')
terminate = False
while res_linear.x[0] == upper and not terminate:
upper -= .01
if upper <= lower:
upper = .95
res_linear = scipy.optimize.minimize(gap,
init,
bounds=[(lower, upper)],
tol=1e-2)
return res_linear.fun, res_linear.x[0]
def effective_operator_comparison(graph=None,
mis=None,
tf=10,
show_graph=False,
n=3,
gamma=500):
# Generate annealing schedule
def schedule1(t, tf):
return [[t / tf, (tf - t) / tf, 1], [1]]
if graph is None:
graph, mis = line_graph(n=n)
graph = Graph(graph)
if show_graph:
nx.draw(graph)
plt.show()
# Generate the driving and Rydberg Hamiltonians
rabi1 = 1
laser1 = hamiltonian.HamiltonianDriver(transition=(0, 1),
energies=[rabi1],
code=rydberg,
IS_subspace=True,
graph=graph)
rabi2 = 1
laser2 = hamiltonian.HamiltonianDriver(transition=(1, 2),
energies=[rabi2],
code=rydberg,
IS_subspace=True,
graph=graph)
rydberg_hamiltonian_cost = hamiltonian.HamiltonianRydberg(graph,
code=rydberg,
detuning=1,
energy=0,
IS_subspace=True)
# Initialize spontaneous emission
spontaneous_emission_rate = gamma
spontaneous_emission = lindblad_operators.SpontaneousEmission(
transition=(1, 2),
rate=spontaneous_emission_rate,
code=rydberg,
IS_subspace=True,
graph=graph)
strong_spontaneous_emission_rate = (1, 1)
strong_spontaneous_emission = lindblad_operators.StrongSpontaneousEmission(
transition=(0, 2),
rates=strong_spontaneous_emission_rate,
code=rydberg,
IS_subspace=True,
graph=graph)
def schedule2(t, tf):
return [[],
[(2 * t / tf / np.sqrt(spontaneous_emission_rate),
2 * (tf - t) / tf / np.sqrt(spontaneous_emission_rate))]]
# Initialize master equation
master_equation = LindbladMasterEquation(
hamiltonians=[laser2, laser1], jump_operators=[spontaneous_emission])
# Begin with all qubits in the ground codes
psi = np.zeros((rydberg_hamiltonian_cost.hamiltonian.shape[0], 1),
dtype=np.complex128)
psi[-1, -1] = 1
psi = tools.outer_product(psi, psi)
# Integrate the master equation
results1 = master_equation.run_ode_solver(
psi, 0, tf, num_from_time(tf), schedule=lambda t: schedule1(t, tf))
cost_function = [
rydberg_hamiltonian_cost.cost_function(results1[i], is_ket=False) / mis
for i in range(results1.shape[0])
]
# Initialize master equation
master_equation = LindbladMasterEquation(
hamiltonians=[], jump_operators=[strong_spontaneous_emission])
# Integrate the master equation
results2 = master_equation.run_ode_solver(
psi, 0, tf, num_from_time(tf), schedule=lambda t: schedule2(t, tf))
cost_function_strong = [
rydberg_hamiltonian_cost.cost_function(results2[i], is_ket=False) / mis
for i in range(results2.shape[0])
]
print(results2[-1])
times = np.linspace(0, tf, num_from_time(tf))
# Compute the fidelity of the results
fidelities = [
tools.fidelity(results1[i], results2[i])
for i in range(results1.shape[0])
]
plt.plot(times, fidelities, color='r', label='Fidelity')
plt.plot(times,
cost_function,
color='teal',
label='Rydberg EIT approximation ratio')
plt.plot(times,
cost_function_strong,
color='y',
linestyle=':',
label='Effective operator approximation ratio')
plt.hlines(1, 0, max(times), linestyles=':', colors='k')
plt.legend(loc='lower right')
plt.ylim(0, 1.03)
plt.xlabel(r'Annealing time $t$')
plt.ylabel(r'Approximation ratio')
plt.show()
def track_eigenstate_composition(graph, tails_graph, num=1):
cost = hamiltonian.HamiltonianMIS(graph, IS_subspace=True)
# print('Starting driver')
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[4]
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)
def eigs(t):
schedule_exp_linear(t * t_max, t_max)
if num == 0:
eigval, eigvec = eq.eig(which='S', k=num+2)
else:
eigval, eigvec = eq.eig(which='S', k=num+1)
return eigval, eigvec
# 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 not None:
eq = schrodinger_equation.SchrodingerEquation(hamiltonians=[cost, driver, rydberg])
else:
eq = schrodinger_equation.SchrodingerEquation(hamiltonians=[cost, driver])
#gap, loc = find_gap(graph, tails_graph)
loc = 0.6403615396636326
fig, ax = plt.subplots(1, num+2, sharex=True)
print('Beginning computation')
print(graph.mis_size)
colors = ['blue', 'green', 'navy', 'orange', 'firebrick', 'purple', 'magenta', 'cornflowerblue', 'teal',
'grey', 'cyan', 'limegreen', 'red', 'yellow', 'pink', 'orangered', 'salmon', 'violet']
for (i, t) in enumerate(np.linspace(.6, .7, 50)):
print(i)
eigval, eigvec = eigs(t)
ax[0].scatter(t, np.abs(eigval[0] - eigval[1]), color='k')
for n in range(num + 1):
if i == 0:
ax[n+1].vlines(loc, 0, 1)
vec = np.abs(eigvec[n])**2
for j in range(graph.mis_size+1):
population = np.sum(vec*(np.isclose(np.sum(1-graph.independent_sets, axis=1),j)))
ax[n+1].scatter(t, population, color=colors[j])
ax[0].set_xlabel(r'$t/T$')
ax[1].set_xlabel(r'$t/T$')
ax[1].set_ylabel(r'Gap')
ax[0].set_ylabel(r'Population')
for j in range(graph.mis_size):
ax[0].scatter([],[],color=colors[j], label='IS size '+str(j))
ax[0].legend()
plt.show()
def visualize_low_energy_subspace(graph, tails_graph, k=5):
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[4]
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))
max_detuning = np.max(pulse[:, 2])
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 * 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, )
# print(t, cost.energies)
# Uncomment this to print the schedule at t=0
# schedule(0, 1)
# print(cost.hamiltonian*2*np.pi)
def gap(t):
schedule_exp_linear(t, t_max)
eigval, eigvec = eq.eig(which='S', k=k)
return np.abs(eigval - eigval[0]), eigvec
# 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:
eq = schrodinger_equation.SchrodingerEquation(
hamiltonians=[cost, driver])
else:
eq = schrodinger_equation.SchrodingerEquation(
hamiltonians=[cost, driver, rydberg])
fig, ax = plt.subplots(1, 1)
num = 100
print('beginning computation')
for (i, t) in enumerate(np.linspace(.5, .97, num) * t_max):
print(i)
g, eigvec = gap(t)
schedule_exp_linear(t, t_max)
detuning = cost.energies[0] / (2 * np.pi)
g = g / (2 * np.pi)
ax.scatter(-np.ones(len(g)) * detuning, g, s=3, color='navy')
ax.set_xlabel(r'Detuning (MHz)')
ax.set_ylabel(r'Eigenenergy (MHz))')
plt.show()
