# VQE for Beginners : Using Tutorial and Cirq

I have been following this tutorial: https://dkopczyk.quantee.co.uk/vqe/

I am using Cirq to try to teach myself VQE, replicate their results, and also try to understand more about ansatz for molecular simulations - and just for plain fun!

Here's the thing though, while I can match expectation values, the graph I find for their angle range does not match their result.

What am I doing wrong and\or not getting about minimization? My code:

def small_ansatz(parameter_y, qubit):
ygate = cirq.YPowGate(exponent=parameter_y)
#ygate = cirq.YPowGate(exponent=parameter_y)
#yield xgate(qubit)
yield ygate(qubit)

#wrapping into a circuit

def psi_circuit(parameter):
curr_q = cirq.LineQubit(0)
curr_c = cirq.Circuit()

curr_c.append(small_ansatz(parameter, curr_q))

curr_c.append(cirq.measure(curr_q, key='q0'))
return curr_c

def expectation_value_vqe(param, num_reps):
curr_psi = psi_circuit(param)
print()
#keep the measured keys and values

curr_simulator = cirq.Simulator()
curr_results = curr_simulator.run(curr_psi, repetitions=num_reps)
s_k, s_v= zip(*r.measurements.items())

#convert into booleans from sp|in values
curr_state_values = 1 - 2*np.array(s_v).astype(np.int32)

#get the expectation value (the average of the counts)
#I keep double the variables because I want to remind myself of the distinction between this task and the context
#of Farhi's paper.
curr_predicted_label_value = np.mean(curr_state_values)
return(curr_predicted_label_value)

And the plot I get for my expectation values for the ansatz:

And here is the tutorial:

Edit: I also implemented this on Qiskit and did obtain the plot to match Grove's.

In the tutorial, the RY gate is used. What you are using is different. If you look at the corresponding documentation of that gate, you would see:

Note in particular that this gate has a global phase factor of e^{i·π·t/2} vs the traditionally defined rotation matrices about the Pauli Y axis.

This may explain the difference. You can use instead the cirq.ry operation to reproduce the tutorial.

EDIT

I tried your code by replacing by cirq.ry :

ygate = cirq.ry(parameter_y)

And running the following gave me the correct plot:

params_range = np.linspace(0.0, 2 * np.pi, 25)

data = [expectation_value_vqe(params) for params in params_range]

• even with YPowGate it still shows the same graph tendency. Commented Apr 11, 2020 at 22:37
• @EnriqueSegura If you still want to use the YPowGate, then you should use it this way to get the Ry rotation: ygate = cirq.YPowGate(exponent=parameter_y/ np.pi, global_shift= -.5) Commented Apr 12, 2020 at 6:13
• Thank you!!!!!!! Commented Apr 12, 2020 at 21:41