# Tag Info

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### How to interpret a quantum circuit as a matrix?

Specific Circuit The first gate is a Hadamard gate which is normally represented by $$\frac{1}{\sqrt{2}}\begin{bmatrix}1&1\\1&-1\end{bmatrix}$$ Now, since we're only applying it to the first ...
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### Is there a name for the 3-qubit gate that does NOT NOT NOTHING?

The gate in which you're interested: would more often be called $X_1X_2I_3$ rather than $¬_a ¬_b I_c$, because we use $X$ to denote the NOT gate more often than we use $¬$. However it is very ...
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### How to efficiently calculate the inverse of a Kronecker product?

You specifically ask about qubits, so I'll keep it to that. Imagine you have a state $$|\psi\rangle=\sum_{x\in\{0,1\}^n}a_x|x\rangle.$$ You can choose to look at each qubit. I'll take the first ...
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### Non-unitary matrix decomposition as a sum of unitary matrices

All tensor products of $n$ Pauli operators $\{I,X,Y,Z\}$ (that is $4^n$ combinations) form an orthogonal basis for the vector space of $2^n \times 2^n$ complex matrices. Hence, for every matrix there ...
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### Is there a name for the 3-qubit gate that does NOT NOT NOTHING?

Welcome to QCSE. You seem to have gotten some of the gist of quantum gates but don't be surprised if not every such gate is promoted to having a specific, universally recognized name. A reason some ...
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### How to check if a quantum circuit can be constructed for a given matrix representation?

Right. But when you build a quantum computer, you want to have a certain set of gates that you want to implement, and all other gates (unitary matrices) can be built from that set of gates. This is ...
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### What is the square root of the NOT gate?

As mentioned already, both of those unitaries are the same up to a global phase. It might be useful to think about how you can actually arrive at one of these definitions in terms of the "Not ...
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### Is there a tool that can give you the unitary representing a quantum circuit from just a string?

You can use Python with Qiskit. Say your string representation is written using OpenQASM syntax. ...
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### Solving linear systems represented by NxN matrices with N not power of 2

This is indeed a correct way to solve linear systems with dimension not equal to a power of 2. Solve the smallest possible system of dimension 2$^n$ that contains the system you want to solve, and pad ...
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Whether you use $+i$ or $-i$ is entirely up to you. After all, your definition of $\pm i$ is merely a convention. On the other hand, I think I've only ever seen it with $+i$. On a more general ...