# Tag Info

Accepted

### Definition of magic $T$ and $H$ states: are there different definitions for them?

Magic state names are not consistent across papers. For example, the state used to perform T gates via gate teleportation, equal to $\frac{1}{\sqrt{2}}\left(|0\rangle + e^{i \pi/4}|1\rangle\right)$ up ...

### Why are there eight $T$ magic state and twelve $H$ magic states?

It becomes very simple when you look at it in the Bloch representation (Figure by me. Ref: Robustness of Magic and Symmetries of the Stabiliser Polytope) The depicted octahedron is the polytope ...

### Magic state distillation: why is it harder to prepare the encoded $|A_{\pi/4}\rangle$ than $|0 \rangle$

The point is the logical $|0\rangle$ and $|+\rangle$ are (relatively) easy to prepare. You start with any bunch of qubits, it doesn't matter what state. You simply measure the stabilizers of the code ...
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### Why are there eight $T$ magic state and twelve $H$ magic states?

Your reasoning is in the correct direction, but realize that $C_{1}$ permutes the $3$ Paulis, and adds a $\pm 1$ on any of the Paulis. See for instance Table 1 on page 20 of Entanglement in ...
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### Universal Gate Set, Magic States, and costliness of the T gate

The T state $Z^{1/4}|+\rangle$ has four core advantages over most other states: You can physically inject T states at pretty high fidelity. It has a reasonably cheap distillation circuit, as far as ...
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### Is the plus state a magic state for the Hadamard gate?

Start with a state $|\psi\rangle|+\rangle$. Measure the operator $X_1Z_2$ using either lattice surgery or an ancilla qubit and $CZ,CX$ gates. Call this result $m_{xz}$ Then measure the first qubit in ...
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### Good references to learn magic state distillation for fault tolerance

Disclaimer: these links do not all fit the criterion recent. First and foremost, it is important to realize that there is no 'one' magic state, and no 'one' magic state distillation. The term 'magic ...

### Why do magic state consumption circuits work?

First, note that you can phase a qubit by preparing an ancilla equal to it and phasing the ancilla: You can pick $\theta=1/4$ to get a T gate. And because the bottom qubit is being discarded, you can ...

### Magic state distillation: why is it harder to prepare the encoded $|A_{\pi/4}\rangle$ than $|0 \rangle$

To prepare $|0_L\rangle$ in a CSS code, all you have to do is separately initialize all the data qubits into $|0\rangle$ and then start measuring the stabilizers of the code. The reason this works is ...

### Universal Gate Set, Magic States, and costliness of the T gate

Imagine you're interested in implementing a gate $$P_k=\left(\begin{array}{cc} 1 & 0 \\ 0 & e^{i\pi/2^k} \end{array}\right),$$ so $Z=P_0$, $S=P_1$ and $T=P_2$. Now imagine that you're going ...
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### Magic state distillation with the $15$ qubit code. How are the transversal $T$ performed? Also via a (lower level) state injection?

You start with physically injected magic states, expanded into $C_1$. In the case of the surface code you could use e.g. Li injection. The error rate of this part is extremely important, as it limits ...