Get probabilistic state of a quantum circuit using Ry gate

Question

Starting with a 2 qubit (each initialized as $|00\rangle$) I need to apply an $R_y(\theta)$ gate to get the following probabilistics:

• 24% $|00\rangle$
• 56% $|01\rangle$
• 6% $|10\rangle$
• 14% $|11\rangle$

I did the following, however, I am not getting exactly what is being asked for, an anyone help me and tell me where am I wrong?

from math import sqrt, acos, asin
from qiskit import QuantumCircuit, Aer, transpile
from qiskit.visualization import plot_histogram

prob = [0.24, 0.56, 0.06, 0.14]

qc = QuantumCircuit(2)

# Initialize both with state |00>
qc.initialize([1,0], 0)
qc.initialize([1,0], 1)

qc.ry(2 * acos(sqrt(prob[0])), 0)
qc.ry(2 * asin(sqrt(prob[2])), 1)

qc.measure_all()
display(qc.draw('mpl'))

backend = Aer.get_backend('aer_simulator') 

job_sim = backend.run(transpile(qc, backend), shots=1024) 
result = job_sim.result()     
plot_histogram(result.get_counts())

Answer 1

this is how you do it without using vqe or qml, of course, you also can increase shots for accuracy.

from math import sqrt, acos, asin
import numpy as np
from qiskit import QuantumCircuit, Aer, transpile
from qiskit.visualization import plot_histogram

prob = np.sqrt([0.24, 0.56, 0.06, 0.14])

qc = QuantumCircuit(2)

# Initialize both with state |00>
# current initialize gate got reset in it, so is better to just use reset.
#qc.reset([0,1])

initial_state = prob/np.linalg.norm(prob)
qc.initialize(initial_state, [0,1])  

qc.measure_all()
display(transpile(qc, basis_gates=['ry','cx']).draw('mpl'))

backend = Aer.get_backend('aer_simulator') 

job_sim = backend.run(transpile(qc,basis_gates=['ry','cx']), shots=1024) 
result = job_sim.result()     
plot_histogram(result.get_counts())

after transpile:(you can't do basis_gates=['ry'])

you can do this to extract the needed ry params out

from qiskit.converters import circuit_to_dag
dag = circuit_to_dag(transpile(qc, basis_gates=['ry','cx']))
gates_param = []
for node in dag.op_nodes():
    gates_param.append(node.op.params)
for i in range(qc.num_qubits):
    print(gates_param[i][0])

qc.ry(1.98, 0)
qc.ry(0.927, 1)

1024 shots:

200000 shots: