# Questions tagged [matrix-representation]

For questions about matrix representations of quantum gates.

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

If a circuit takes more than one qubit as its input and has quantum gates which take different numbers of qubits as their input, how would we interpret this circuit as a matrix? Here is a toy example:...
1answer
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### Advantage of simulating sparse Hamiltonians

In @DaftWullie's answer to this question he showed how to represent in terms of quantum gates the matrix used as example in this article. However, I believe it to be unlikely to have such well ...
2answers
304 views

### Matrix representation of continuous-variable gates

In the introduction to continuous-variable quantum computing by Strawberry Fields (Xanadu), it lists the primary CV gates (rotation, displacement, squeezing, beamsplitter, cubic phase) along with ...
3answers
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### How to properly write the action of a quantum gate implementing an operator $U$ on the superposition of its eigenvectors?

Let's say, that we are in the possession of a quantum gate, that is implementing the action of such an operator $$\hat{U}|u \rangle = e^{2 \pi i \phi}|u\rangle$$ Moreover, let's say, that this ...
1answer
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1answer
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### Error in showing $\operatorname{CPHASE}_{12}=\operatorname{CPHASE}_{21}$ in the matrix representation

I read that the relation $\operatorname{CPHASE}_{12}=\operatorname{CPHASE}_{21}$ in the matrix representation but when I tried to work it out I don't see how. $\operatorname{CPHASE}_{12}$ acts in the ...
1answer
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### Building a matrix corresponding to the teleportation circuit

I'm trying to build the matrix that corresponds to this quantum teleportation circuit, but it never works when I test it in the quirk simulator, I tried finding the matrix corresponding to every part ...
1answer
133 views

### Matrix representation and CX gate [duplicate]

I am having hard time figuring out how the CX (controlled-NOT) gate is represented in the matrix representation. I understood that tensor product and the identity matrix are the keys, and I ...
1answer
184 views

### What's the matrix representation of this 3 qubit circuit?

How do I calculate the matrix representation of this part of a teleportation circuit? It must be a matrix of dimension 8.
0answers
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### How are multi-qubit gates extended into larger registers? [duplicate]

Implementing a single-qubit gate in a multi-qubit register is relatively easy. For example, this gate: This is equivalent to $I \otimes H \otimes I$. If the $H$ gate was on the first bit, it would be ...