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pVQD.py
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pVQD.py
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import numpy as np
import json
import functools
import itertools
import matplotlib.pyplot as plt
from scipy import linalg as LA
import qiskit
from qiskit import Aer, execute
from qiskit.quantum_info import Pauli
from qiskit.utils import QuantumInstance
from qiskit.opflow import PauliOp, SummedOp, CircuitSampler, StateFn
from qiskit.circuit import ParameterVector
from qiskit.opflow.evolutions import Trotter, PauliTrotterEvolution
from qiskit.opflow.state_fns import CircuitStateFn
from qiskit.opflow.expectations import PauliExpectation, AerPauliExpectation
from qiskit.opflow.primitive_ops import CircuitOp
from qiskit.opflow import Z, I
from pauli_function import *
# This class aims to simulate the dynamics of a quantum system
# approximating it with a variational ansatz whose parameters
# are varied in order to follow the unitary evolution
# Useful functions
def projector_zero(n_qubits):
# This function create the global projector |00...0><00...0|
from qiskit.opflow import Z, I
prj_list = [0.5*(I+Z) for i in range(n_qubits)]
prj = prj_list[0]
for a in range(1,len(prj_list)):
prj = prj^prj_list[a]
return prj
def projector_zero_local(n_qubits):
# This function creates the local version of the cost function
# proposed by Cerezo et al: https://www.nature.com/articles/s41467-021-21728-w
from qiskit.opflow import Z, I
tot_prj = 0
for k in range(n_qubits):
prj_list = [I for i in range(n_qubits)]
prj_list[k] = 0.5*(I+Z)
prj = prj_list[0]
for a in range(1,len(prj_list)):
prj = prj^prj_list[a]
#print(prj)
tot_prj += prj
tot_prj = (1/n_qubits)*tot_prj
return tot_prj
def ei(i,n):
vi = np.zeros(n)
vi[i] = 1.0
return vi[:]
## Actual pVQD class
class pVQD:
def __init__(
self,
hamiltonian,
ansatz,
ansatz_reps,
parameters,
initial_shift,
instance,
shots
):
self.hamiltonian = hamiltonian
self.instance = instance
self.parameters = parameters
self.num_parameters = len(parameters)
self.shift = initial_shift
self.shots = shots
self.depth = ansatz_reps
self.num_qubits = hamiltonian.num_qubits
## Initialize quantities that will be equal all over the calculation
self.params_vec = ParameterVector('p',self.num_parameters)
self.ansatz = ansatz(self.num_qubits,self.depth,self.params_vec)
# ParameterVector for left and right circuit
self.left = ParameterVector('l', self.ansatz.num_parameters)
self.right = ParameterVector('r', self.ansatz.num_parameters)
# ParameterVector for measuring abservables
self.obs_params = ParameterVector('θ',self.ansatz.num_parameters)
def construct_total_circuit(self,time_step):
## This function creates the circuit that will be used to evaluate overlap and its gradient
# First, create the Trotter step
step_h = time_step*self.hamiltonian
trotter = PauliTrotterEvolution(reps=1)
U_dt = trotter.convert(step_h.exp_i()).to_circuit()
l_circ = self.ansatz.assign_parameters({self.params_vec: self.left})
r_circ = self.ansatz.assign_parameters({self.params_vec: self.right})
## Projector
zero_prj = StateFn(projector_zero(self.hamiltonian.num_qubits),is_measurement = True)
state_wfn = zero_prj @ StateFn(r_circ +U_dt+ l_circ.inverse())
return state_wfn
def construct_total_circuit_local(self,time_step):
## This function creates the circuit that will be used to evaluate overlap and its gradient, in a local fashion
# First, create the Trotter step
step_h = time_step*self.hamiltonian
trotter = PauliTrotterEvolution(reps=1)
U_dt = trotter.convert(step_h.exp_i()).to_circuit()
l_circ = self.ansatz.assign_parameters({self.params_vec: self.left})
r_circ = self.ansatz.assign_parameters({self.params_vec: self.right})
## Projector
zero_prj = StateFn(projector_zero_local(self.hamiltonian.num_qubits),is_measurement = True)
state_wfn = zero_prj @ StateFn(r_circ +U_dt+ l_circ.inverse())
return state_wfn
# This function calculate overlap and gradient of the overlap
def compute_overlap_and_gradient(self,state_wfn,parameters,shift,expectator,sampler):
nparameters = len(parameters)
# build dictionary of parameters to values
# {left[0]: parameters[0], .. ., right[0]: parameters[0] + shift[0], ...}
# First create the dictionary for overlap
values_dict = [dict(zip(self.right[:] + self.left[:], parameters.tolist() + (parameters + shift).tolist()))]
# Then the values for the gradient
for i in range(nparameters):
values_dict.append(dict(zip(self.right[:] + self.left[:], parameters.tolist() + (parameters + shift + ei(i,nparameters)*np.pi/2.0).tolist())))
values_dict.append(dict(zip(self.right[:] + self.left[:], parameters.tolist() + (parameters + shift - ei(i,nparameters)*np.pi/2.0).tolist())))
# Now evaluate the circuits with the parameters assigned
results = []
for values in values_dict:
sampled_op = sampler.convert(state_wfn,params=values)
mean = sampled_op.eval().real
#mean = np.power(np.absolute(mean),2)
est_err = 0
if (not self.instance.is_statevector):
variance = expectator.compute_variance(sampled_op).real
est_err = np.sqrt(variance/self.shots)
results.append([mean,est_err])
E = np.zeros(2)
g = np.zeros((nparameters,2))
E[0],E[1] = results[0]
for i in range(nparameters):
rplus = results[1+2*i]
rminus = results[2+2*i]
# G = (Ep - Em)/2
# var(G) = var(Ep) * (dG/dEp)**2 + var(Em) * (dG/dEm)**2
g[i,:] = (rplus[0]-rminus[0])/2.0,np.sqrt(rplus[1]**2+rminus[1]**2)/2.0
self.overlap = E
self.gradient = g
return E,g
## this function does the same thing but uses SPSA
def compute_overlap_and_gradient_spsa(self,state_wfn,parameters,shift,expectator,sampler,count):
nparameters = len(parameters)
# build dictionary of parameters to values
# {left[0]: parameters[0], .. ., right[0]: parameters[0] + shift[0], ...}
# Define hyperparameters
c = 0.1
a = 0.16
A = 1
alpha = 0.602
gamma = 0.101
a_k = a/np.power(A+count,alpha)
c_k = c/np.power(count,gamma)
# Determine the random shift
delta = np.random.binomial(1,0.5,size=nparameters)
delta = np.where(delta==0, -1, delta)
delta = c_k*delta
# First create the dictionary for overlap
values_dict = [dict(zip(self.right[:] + self.left[:], parameters.tolist() + (parameters + shift).tolist()))]
# Then the values for the gradient
values_dict.append(dict(zip(self.right[:] + self.left[:], parameters.tolist() + (parameters + shift + delta).tolist())))
values_dict.append(dict(zip(self.right[:] + self.left[:], parameters.tolist() + (parameters + shift - delta).tolist())))
# Now evaluate the circuits with the parameters assigned
results = []
for values in values_dict:
sampled_op = sampler.convert(state_wfn,params=values)
mean = sampled_op.eval()[0]
mean = np.power(np.absolute(mean),2)
est_err = 0
if (not self.instance.is_statevector):
variance = expectator.compute_variance(sampled_op)[0].real
est_err = np.sqrt(variance/self.shots)
results.append([mean,est_err])
E = np.zeros(2)
g = np.zeros((nparameters,2))
E[0],E[1] = results[0]
# and the gradient
rplus = results[1]
rminus = results[2]
for i in range(nparameters):
# G = (Ep - Em)/2Δ_i
# var(G) = var(Ep) * (dG/dEp)**2 + var(Em) * (dG/dEm)**2
g[i,:] = a_k*(rplus[0]-rminus[0])/(2.0*delta[i]),np.sqrt(rplus[1]**2+rminus[1]**2)/(2.0*delta[i])
self.overlap = E
self.gradient = g
return E,g
def measure_aux_ops(self,obs_wfn,pauli,parameters,expectator,sampler):
# This function calculates the expectation value of a given operator
# Prepare the operator and the parameters
wfn = StateFn(obs_wfn)
op = StateFn(pauli,is_measurement = True)
values_obs = dict(zip(self.obs_params[:], parameters.tolist()))
braket = op @ wfn
grouped = expectator.convert(braket)
sampled_op = sampler.convert(grouped,params = values_obs)
#print(sampled_op.eval())
mean_value = sampled_op.eval().real
est_err = 0
if (not self.instance.is_statevector):
variance = expectator.compute_variance(sampled_op).real
est_err = np.sqrt(variance/self.shots)
res = [mean_value,est_err]
return res
def adam_gradient(self,count,m,v,g):
## This function implements adam optimizer
beta1 = 0.9
beta2 = 0.999
eps = 1e-8
alpha = [0.001 for i in range(len(self.parameters))]
if count == 0:
count = 1
new_shift = [0 for i in range(len(self.parameters))]
for i in range(len(self.parameters)):
m[i] = beta1 * m[i] + (1 - beta1) * g[i]
v[i] = beta2 * v[i] + (1 - beta2) * np.power(g[i],2)
alpha[i] = alpha[i] * np.sqrt(1 - np.power(beta2,count)) / (1 - np.power(beta1,count))
new_shift[i] = self.shift[i] + alpha[i]*(m[i]/(np.sqrt(v[i])+eps))
return new_shift
def run(
self,
ths,
timestep,
n_steps,
obs_dict={},
filename='algo_result.dat',
max_iter = 100,
opt='sgd',
cost_fun='global',
grad='param_shift',
initial_point=None
):
## initialize useful quantities once
if(self.instance.is_statevector and cost_fun == 'local'):
expectation = AerPauliExpectation()
else:
expectation = PauliExpectation()
sampler = CircuitSampler(self.instance)
## Now prepare the state in order to compute the overlap and its gradient
if cost_fun == 'global':
state_wfn = self.construct_total_circuit(timestep)
elif cost_fun == 'local':
state_wfn = self.construct_total_circuit_local(timestep)
state_wfn = expectation.convert(state_wfn)
## Also the standard state for measuring the observables
obs_wfn = self.ansatz.assign_parameters({self.params_vec: self.obs_params})
#######################################################
times = [i*timestep for i in range(n_steps+1)]
tot_steps= 0
if initial_point != None :
if len(initial_point) != len(self.parameters):
print("TypeError: Initial parameters are not of the same size of circuit parameters")
return
print("\nRestart from: ")
print(initial_point)
self.parameters = initial_point
print("Running the algorithm")
#prepare observables for quench
if len(obs_dict) > 0:
obs_measure = {}
obs_error = {}
for (obs_name,obs_pauli) in obs_dict.items():
first_measure = self.measure_aux_ops(obs_wfn,obs_pauli,self.parameters,expectation,sampler)
obs_measure[str(obs_name)] = [first_measure[0]]
obs_error['err_'+str(obs_name)] = [first_measure[1]]
counter = []
initial_fidelities = []
fidelities = []
err_fin_fid = []
err_init_fid = []
params = []
params.append(list(self.parameters))
for i in range(n_steps):
print('\n================================== \n')
print("Time slice:",i+1)
print("Shift before optimizing this step:",self.shift)
print("Initial parameters:", self.parameters)
print('\n================================== \n')
count = 0
self.overlap = [0.01,0]
g_norm = 1
if opt == 'adam':
m = np.zeros(len(self.parameters))
v = np.zeros(len(self.parameters))
if opt == 'momentum':
old_grad = np.zeros(len(self.parameters))
g = np.zeros((len(self.parameters),2))
while self.overlap[0] < ths and count < max_iter:
print("Shift optimizing step:",count+1)
count = count +1
if opt == 'momentum':
old_grad = np.asarray(g[:,0])
## Measure energy and gradient
if grad == 'param_shift':
E,g = self.compute_overlap_and_gradient(state_wfn,self.parameters,self.shift,expectation,sampler)
if grad == 'spsa':
E,g = self.compute_overlap_and_gradient_spsa(state_wfn,self.parameters,self.shift,expectation,sampler,count)
tot_steps = tot_steps+1
if count == 1:
initial_fidelities.append(self.overlap[0])
err_init_fid.append(self.overlap[1])
print('Overlap',self.overlap)
print('Gradient',self.gradient[:,0])
if opt == 'adam':
print("\n Adam \n")
meas_grad = np.asarray(g[:,0])
self.shift = np.asarray(self.adam_gradient(count,m,v,meas_grad))
if opt == 'momentum':
print("Momentum")
m_grad = np.asarray(g[:,0]) + 0.9*old_grad
self.shift = self.shift + m_grad
elif opt== 'sgd':
self.shift = self.shift + g[:,0]
#Norm of the gradient
g_vec = np.asarray(g[:,0])
g_norm = np.linalg.norm(g_vec)
# Update parameters
print('\n---------------------------------- \n')
print("Shift after optimizing:",self.shift)
print("New parameters:" ,self.parameters + self.shift)
print("New overlap: " ,self.overlap[0])
self.parameters = self.parameters + self.shift
# Measure quantities and save them
if len(obs_dict) > 0:
for (obs_name,obs_pauli) in obs_dict.items():
run_measure = self.measure_aux_ops(obs_wfn,obs_pauli,self.parameters,expectation,sampler)
obs_measure[str(obs_name)].append(run_measure[0])
obs_error['err_'+str(obs_name)].append(run_measure[1])
counter.append(count)
fidelities.append(self.overlap[0])
err_fin_fid.append(self.overlap[1])
params.append(list(self.parameters))
print("Total measurements:",tot_steps)
print("Measure per step:", tot_steps/n_steps)
# Save data on file
log_data = {}
if len(obs_dict) > 0:
for (obs_name,obs_pauli) in obs_dict.items():
log_data[str(obs_name)] = obs_measure[str(obs_name)]
log_data['err_'+str(obs_name)] = obs_error['err_'+str(obs_name)]
log_data['init_F'] = initial_fidelities
log_data['final_F'] = fidelities
log_data['err_init_F'] = err_init_fid
log_data['err_fin_F'] = err_fin_fid
log_data['iter_number'] = counter
log_data['times'] = times
log_data['params'] = list(params)
log_data['tot_steps'] = [tot_steps]
json.dump(log_data, open( filename,'w+'))