# Questions tagged [quantum-gate]

For questions regarding usage, performance, implementation, application or theory related to quantum gates.

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### Help Identifying a Gate In Nielsen and Chuang

I am seeking help to identify the oracle gates listed in this example. I understand that the right-most one is a toffoli gate, but what are the other ones? Specifically, I do not understand what a ...
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### In which type of Hamiltonian does the ansatz need an entangler in VQE?

I would like to prepare an ansatz for VQE. I know UCC ansatz is one of the most useful ansatz, but I would like to reduce the number of CNOT. From the matrix of a given Hamiltonian, can we know the ...
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### What do we mean by “derive full operator of a quantum circuit” and to describe the mapping from input quantum registers to output quantum registers?

There is a quantum circuit with several controlled NOT and controlled swap gates, with two 2-qubit input registers $X$ and $Y$ and two 2-qubit output registers $X'$ and $Y'$ where we have to find the ...
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### Show how the Bell state arises from the circuit with Hadamard and CNOT, using matrix notation

I understand that starting with , we can get to $\vert \Phi^+ \rangle$. First, we start with $\vert Q_1 \rangle \otimes \vert Q_2 \rangle = \vert 0 \rangle \otimes \vert 0 \rangle$ and then applying ...
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### Rotations to encode $f(x)$ into ancilla qubit for quantum Monte Carlo

I'm trying to understand the quantum monte-carlo algorithm starting at the most basic version. A key step is rotating (Algorithm 1 p.g 8), an ancilla bit by rotation $R$ with respect to the value of a ...
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### Creating Bell states (a question from tutorial) [closed]

I was going through a Quantum Computation lecture series on YouTube given by Umesh Vazirani. There in Lecture 6.3 he talks about creating a Bell state using a Hadamard and CNOT gate. He seems to be ...
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### S gate vs P gate?

The paper A Fully Fault-Tolerant Representation of Quantum Circuits uses the $P$ gate which is given as: $$P = \begin{bmatrix}1 & 0\\0 & i\\\end{bmatrix}.$$ Nielsen and Chuang Quantum ...
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### Quantum circuit to implement matrix exponential

I want to build a circuit which will implement $e^{iAt}$, where $A= \begin{pmatrix} 1.5 & 0.5\\ 0.5 & 1.5\\ \end{pmatrix}$ and $t= \pi/2$. We see that $A$ can be written as, $A=1.5I+0.5X$. ...
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### Decompose Toffoli gate with minimum cost for IBM quantum computer

The known decomposition of toffoli gate that can be used on IBM quantum computer is : I want to know any other Toffoli gate decompositions that can be used on IBM quantum computer and have a cost ...
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### Qubit in a mix sin/cosine state

The question is pretty simple. How can I get an input qubit $|0⟩$ in the state, say $$\cos{\frac{\pi}{10}}|0⟩ + \sin{\frac{\pi}{10}}|1⟩$$ Or any other sine/cosine mix state? Which gates do I need to ...