# Questions tagged [quantum-gate]

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

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### How to simulate a $CNOT$ only using a single qubit?

I am looking to do a $CNOT$ on itself, i.e., if the qubit is in $|0\rangle$ it stays in $|0\rangle$ and if it is in $|1\rangle$ it becomes $|0\rangle$. We are allowed to use $H$, $X$, $Z$, and $CNOT$ ...
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### What are necessary and sufficient conditions for the output of a parametrized unitary $U(\theta)$ to be smooth?

Let us consider a unitary $U$ parameterised by $\theta \in \mathbb{R}$, i.e, $U(\theta)$. What are the necessary and sufficient conditions for the output states of this unitary to be smooth? One ...
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### Sufficient conditions for a single-qubit unitary to be the identity

Say I have a unitary $U = e^{-iHt}$ where $H = \alpha X + Z$. First, suppose $U = I$. Then it rotates a set of initial states to themselves. Say I'm working on a computational basis, then on the Bloch ...
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### CNOT and quantum entanglement

I have the following problem: "Consider two parties: Alice in possession of the one-qubit state |ψ⟩ = α|0⟩ + β|1⟩, and Bob who starts with a qubit in the state |0⟩ Show that Alice can teleport ...
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### Implementation of two qubit gate decomposition in local operations

My questions is regards to this paper: https://arxiv.org/abs/1909.07534 The above is the decomposition of a two qubit gate into local operations. Please note they are using a Super Operator formalism....