# Questions tagged [quantum-computing]

A computation model which relies on quantum-mechanic phenomena, such as entanglement and superposition. This generalizes the probabilistic model of computation.

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### Intuition behind the Hadamard gate

I'm trying to teach myself about quantum computing, and I have a decent-ish understanding of linear algebra. I got through the NOT gate, which wasn't too bad, but then I got to the Hadamard gate. ...
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### Does the fact that there exists a polynomial time quantum algorithm for integer factorization suggest that integer factorization is in P?

Just as the title says: Does the fact that there exists a polynomial time quantum algorithm for integer factorization suggest that integer factorization is in P? Additionally, if one could show that a ...
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### Constructing the matrix of a controlled quantum operation

How do we construct a matrix that takes into account whether the first qubit is set? I am trying to construct the controlled-V matrix, but there is no quantum computational paper that describes it so ...
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### Why does quantum cost on gates formed from specific qubit gates not factor swap gates into account?

I've been reading a number of quantum computation research papers that claim quantum cost's that do not add up. For instance, in this paper - there is a claim that the MTSG gate is a quantum cost of ...
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### Are qubits written in a big-endian or little-endian order when grouped?

Say for instance you layout a quantum simulator like follows: amps =  * 8 # 3 qubits Therefore you are left with the following in binary: ...
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### Can you take classical code and compile it to quantum code?

Is there anyway for example, to take a trivial program from C such as: int main() { int i = 1 + 1; return 0; } And compile this down to some form of Quantum ...
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### Is there any proof that quantum computers are more efficient than classical computers?

Shor's algorithm is often used as the argument. It can solve the factorization problem faster than any known algorithm for classical computers. Yet, we have no proof classical computers can't also ...
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### 2 qubits, correct way CNOT a 3rd qubit with the 1st? [duplicate]

Suppose I have 2 qubits in the state a|00>+b|01>+c|10>+d|11>. And suppose I want to perform some operation between only the 1st qubit and a 3rd qubit - for example a CNOT operation. What would be ...
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### Applying a multi qubit quantum gate to specific qubits

A controlled not gate matrix looks like this: $$\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ \end{bmatrix}$$ ...
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### Does entangling 100 qubits require a 2^100 X 2^100 Hadamard gate?

Suppose I have 100 qubits that I want to entangle and put into superposition. To do so I construct a Hadamard gate to do this. By definition, the Hadamard is going to be a 2^100 X 2^100 matrix - which ...
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### Looking for interesting unanswered questions within complexity theory for a project [closed]

I'm looking for interesting open questions in complexity theory that someone with an undergraduate degree in math and comp/sci could theoretically tackle. I have strong interest in the polynomial ...
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### Is it possible to entangle more than 2 qubits? If so, is it useful?

With 2 qubits, there are 4 ways to entangle the qubits - the four maximally entangled two-qubit Bell states, of which one is $1/\sqrt{2}(|00\rangle + |11\rangle)$. Is it possible to entangle more ...
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### Why does the Toffoli gate output c XOR (a AND b) instead of just a AND b?

The Toffoli gate takes in three inputs and gives out three outputs, and is often referred to as the quantum AND gate. It takes in a,b,c and gives out a, b, c XOR (a AND b). Why does it do that, ...
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### How do you apply a multi qubit gate to specific qubits in a multi qubit circuit?

Let's say that you have a 6 qubit system and you want to apply a Hadamard gate to qubits 2 and 4. How would you construct a matrix that did that, while leaving the state of the other qubits alone?
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### How are quantum computers able to process certain tasks faster than regular computers? [duplicate]

I've read posts everywhere and watched videos but still I don't understand one part of it. How are they able to process all these operations in parallel. So based on the landscape example here. How ...
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### Must you work with all qubits in a circuit when applying a gate?

When looking at this question: How to apply a 1-qubit gate to a single qubit from an entangled pair? And other questions, it makes it seem like when you have a quantum circuit involving $N$ qubits, ...
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### Does a Hadamard Gate have uses outside of pure and evenly mixed states?

The standard usage cases for the Hadamard gate seem to be passing a pure $|0\rangle$ or $|1\rangle$ state in to get an even amplitude (probability) mixed state which has either matching or mismatching ...
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### How do Quantum Computers destructively interfere the wrong answer? [duplicate]

From various sources (one being this), I've heard that quantum computers find the correct answer in a sea of possible ones by destructively interfering the wrong ones with each other, and the right ...
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### How do quantum computers find the global minimum?

If I understand correctly, quantum computers work by trying multiple methods of solving a problem simultaneously, using quantum superposition. However, if you try to "look" at a superposition-ed atom, ...
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### Where does entanglement fit into quantum computing?

I've been reading up on quantum computing online from various sources, including this link http://twistedoakstudios.com/blog/Post2644_grovers-quantum-search-algorithm. I get how quantum gates work, ...
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### What specifically makes quantum computers useful?

I know that quantum computers are able to process a superposition of all possible states with a single pass through the logic. That seems to be what people point to as being what makes quantum ...
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### Can quantum computer become perfect chess player?

Can quantum computer become perfect chess player? Can it determine whether (when both players are perfect) win white or black? (or is it dead heat?)
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### Quantum computer memory size

Quantum computers are going to have enormous number of operations per second (in some situations exponentially more than classic computers). Does it also hold for memory size? Are QC going to have ...
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