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I am studying quantum computing and created the circuit below:

Qiskit Quantum Circuit

In such a circuit, should q2 be at the probability of 25%? Because the Toffoli gate has 2 control inputs that haven't been collapsed yet. So the inputs could be 00, 01, 10, and 11. So, only in the case of 11, the output will be affected.

I see, when q1 is 1, q0 can not be 0; or q1 is 0, q0 can not be 1. So, I think only 00 and 11 sitations are considered. But in super position, isn't it possible to be 0 and 1 at the same time? So, is it right or should other situations be considered ?

Thank you in advance.

Hasan Yetiş
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2 Answers2

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I have the feeling there is some misunderstanding on the way you deal with several qubits. Let's break down the calculations gate by gate :

enter image description here

Now let's take back what you wrote:

I see, when q1 is 1, q0 can not be 0; or q1 is 0, q0 can not be 1. So, I think only 00 and 11 sitations are considered.

You are completely right about this, we have this just before the Toffoli gate.

But in super position, isn't it possible to be 0 and 1 at the same time? So, is it right or should other situations be considered ?

Indeed, a single qubit is by definition in a superposition state between the two ground states, |0> and |1>. I am not sure to understand what you mean by "other situations considered", but maybe this'll help : this superposition state will no longer exists as soon as you measure, and this probability is described via the complex amplitudes of the state, here 1/sqrt(2)

Now here in particular you have an entangled state, meaning that somehow the qubits are "linked" to one another, the value of one is linked to the value of the other. So when you measure only one qubit, you actually know directly all the other qubits. So for q_2, you have 1/2 chances to get 0, 1/2 to get 1, and once you have this value, you will know exactly your measured state even though you did only one measurement.

Is it clear enough? Please tell me if something is too weird in my explanation and I'll try to detail better.

By the way, there is a SO platform especially for quantum computing, feel free to post your questions there next time! https://quantumcomputing.stackexchange.com

Lena
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One way of thinking about it is like this:

In your circuit, q1 has been put into a superposition state and the other qubits have been entangled to it. As there are no other Haddamards applied to q0 and q2 their states are directly tied to the state of q1 and nothing else.

So there are only 2 different scenarios possible for the outcome:

a) If q1 is 0, then q0 is definitely 0 and q2 is definitely 0

b) If q1 is 1, then q0 is definitely 1 and q2 is definitely 1

The probability of q1 collapsing down to 0 or 1 is 50:50, so 50% of the time scenario a) will happen and 50% of the time b) will happen.

QofQ
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