# Questions tagged [unitarity]

For questions related to the unitarity (unitary evolution) of quantum systems, as applicable to quantum computing or quantum information.

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### Getting a Hermitian operator from a Quantum circuit, and taking its expectation value

I have a circuit $C$, which acting on a state $|\psi \rangle$ is equivalent to a Unitary $U$ acting on the state: $$C(|\psi \rangle) = U|\psi \rangle$$ Now, this circuit is just a Hamiltonian ...
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### Definition of a quantum gate

A quantum gate is usually defined as a unitary transformation, like the definition found in "Mathematics of Quantum Mechanics" by Scherer. According to this definition, can we consider a ...
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### A maximally distant unitary from a parameterized circuit

I have a parameterized circuit that includes a certain number of rotation gates, each parameterized by an angle. By sampling over these angles, I can obtain various unitaries. What are the unitaries ...
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### Axis and Angle of rotation of $\frac{1}{\sqrt{2}}\begin{bmatrix}-i&-1\\1&i\end{bmatrix}$

I have made use of the following formulas, \begin{align} \theta&=2\cos^{-1}\bigg(\frac{e^{-i\alpha}Tr(X)}{2}\bigg)\\ n_i&=\frac{e^{-i\alpha}Tr(X\sigma_x)}{2\sin\theta/2}\\ e^{i\alpha}&=\...
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### How to represent unitary evolution in Python?

How to represent $U(t)$ (a unitary operator) in a code? Is there any package available for that in Python?
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### Understanding notation regarding phase oracle [duplicate]

I am new to quantum computing. I cannot get my head around the following: Consider a finite random variable $X : \Omega \rightarrow E$ on a probability space $(\Omega, 2^{\Omega}, P)$. Let $H_{\Omega}$...
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### How use UnitaryGate to creat a CNOT gate?

This is my code using qiskit below. I am not familiar with Unitarygate, so I tried to creat a cnot-gate. ...
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