Why is the Measurement Result Always 1? (expected to find uniformly random measurement)

Question

I created a $|0\rangle$ state then applied $H$ gate to get $\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle)$ and then I meausred my state. But I always found 1. I expected to find 0 and 1 uniformly random like the case of beam splitter.

Here is my code:

qubit = cirq.NamedQubit("myqubit")
circuit = cirq.Circuit(cirq.H(qubit))
for i in range(10):
    result2 = cirq.measure(qubit, key='myqubit')
    print(result2)
print(circuit)
# run simulation
result = cirq.Simulator().simulate(circuit)
print("result:")
print(result)
print(result2)

How can I find uniformly random result ?

Answer 1

You are not measuring your qubit. Look at what your print(circuit) is returning

myqubit: ───H───

You need to add the measurement gate to the circuit like so:

circuit = cirq.Circuit(cirq.H(qubit), cirq.measure(qubit, key='myqubit'))

Printing this circuit returns myqubit: ───H───M───

In your case, with the loop; you can append the gates:

for i in range(10):
    circuit.append(cirq.measure(qubit, key='myqubit'))

Printing this one returns myqubit: ───H───M───M───M───M───M───M───M───M───M───M───M───

Both programs will get you the expected uniform random measurements.

Answer 2

@Victory Omole already answered the question.

But here is the fixed code if you are interested.

qubit = cirq.NamedQubit("myqubit")
circuit = cirq.Circuit()
circuit = cirq.Circuit(cirq.H(qubit))
circuit.append(cirq.measure(qubit, key='result'))
print(circuit)
s=cirq.Simulator()
samples=s.run(circuit, repetitions=1000)
print('Single measurement result:' ,samples.histogram(key='result'))

print('****************************************')
circuit2 = cirq.Circuit(cirq.H(qubit))
for i in range(10):
    circuit2.append(cirq.measure(qubit, key='myqubit'))
print(circuit2)
samples2 = s.run(circuit, repetitions=1000)
print('Hadamard follows by 10 measurements result:' ,samples2.histogram(key='result'))

The output would be something like:

myqubit: ───H───M('result')───
Single measurement result: Counter({0: 501, 1: 499})
****************************************
myqubit: ───H───M───M───M───M───M───M───M───M───M───M───
Hadamard follows by 10 measurements result: Counter({1: 502, 0: 498})

Update: If you want to print out the counter, that is, accessing the result at each shot/experiment then you can do the following: (There is a better to do this probabbly but I don't really use cirq...)

samples2 = [s.run(circuit, repetitions=1) for i in range(10) ]
samples2

The output would be something like:

[result=1,
 result=0,
 result=1,
 result=1,
 result=1,
 result=0,
 result=1,
 result=0,
 result=0,
 result=0]