0

From what I understand, any circuit can be combined to make a gate, which has a square, unitary matrix form that acts on the $2^n$ row of the qubits state column vector. For example, the circuit

```
┌───┐
q_0: ┤ H ├──■──
├───┤┌─┴─┐
q_1: ┤ H ├┤ X ├
└───┘└───┘
```

has the matrix form $\begin{bmatrix}
\tfrac{1}{2} & \tfrac{1}{2} & \tfrac{1}{2} & \tfrac{1}{2} \\
\tfrac{1}{2} & -\tfrac{1}{2} & -\tfrac{1}{2} & \tfrac{1}{2} \\
\tfrac{1}{2} & \tfrac{1}{2} & -\tfrac{1}{2} & -\tfrac{1}{2} \\
\tfrac{1}{2} & -\tfrac{1}{2} & \tfrac{1}{2} & -\tfrac{1}{2} \\
\end{bmatrix}$
which acts on the vector $\begin{bmatrix}1 \\ 0 \\ 0 \\ 0 \end{bmatrix}$ of the initial $|0\rangle$ state. But when I try to `get_unitary()`

a circuit with a reset gate, Qiskit tells me that reset instruction is not unitary and therefore it cannot give me any matrix form. My question is, in general, how do a reset gate affect the matrix form of a multi-qubit gate/circuit?

Thank you!

Edit: The circuit I'm trying to find the matrix form for is i.e. like this:

```
┌───┐
q_0: ┤ H ├──■───────
├───┤┌─┴─┐
q_1: ┤ H ├┤ X ├─|0>─
└───┘└───┘
```

Can you introduce me to where I can learn to describe the circuit like that, that can include even non-unitary instructions (book, paper)? – Kim Dong – 2020-11-17T18:46:42.113

1It's covered in nielsen and Chiang when they describe channels iirc – Craig Gidney – 2020-11-17T21:28:36.300