# Questions tagged [mathematics]

Use this tag for questions about mathematics relevant to quantum computing and/or quantum information theory. DO NOT use this tag for general mathematics questions.

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### Finding the measurement basis for single qubit with given probability of outcome $0$

I have the general state of a single qubit $|\psi \rangle = \alpha|0\rangle + \beta|1\rangle$. Assume I am given a probability $p$ such that $0 < p <1$. Now I need to find the basis in which ...
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### Is every single-qubit unitary just a rotation around some unit vector on the Bloch sphere?

I remember reading this somewhere... Is there an elegant proof for this?
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### Penalty Function for XOR gate

I was reading a paper on Gates for Adiabatic Quantum Computer. In the paper, there were different penalty functions already given in the form of the following table: I do not quite understand the ...
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### Strange binomial formula for operators?

Does the binomial formula $(a+b)^n=\sum_i C_n^ia^ib^{n-i}$ still work when $n$ is replaced by operator $\hat{n}$(an operator), where $a$ and $b$ are numbers? Since it's not the normal binomial formula ...
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### Modeling building blocks for quantum computation

If I would design library for quantum computation I would naively consider a sequences of entangled qudits with unit length as a building blocks. I.e., unit length elements from \mathbb{C}^{d_{1}}\...
### Is the No-Cloning Theorem Violated in $C^\ast$-Circuit Models?
In Cleve, et al., the authors discuss self-embezzlement of a catalyst state $\psi$, making the statement on page 2, [B]y local operations, state $\psi\otimes(\vert 0 \rangle \otimes \vert 0 \rangle)$ ...
### How do I show that $R_z(\theta)=e^{-iZ\theta/2}$?
I know that an $R_z (\theta)$ gate is equivalent to the unitary transformation $e^{-iZ * \theta/2}$ but I'm not sure how we get there. I know that for every Hermitian matrix there is a corresponding ...