# Tag Info

Accepted

### Does every code have transversal Pauli group?

I don't think so - consider e.g. the 'diagonal' representation $$\phi:SU(2) \rightarrow GL((\mathbb{C}^2)^{\otimes 4})$$ $$U \mapsto U^{\otimes 4}.$$ The Clebsch-Gordan series tells us that, for spin ...
• 502

### Does every code have transversal Pauli group?

Every code that can be implemented by a stabilizer circuit (this includes stabilizer codes, gauge codes, floquet codes, etc) has this type of subset-transversal Pauli gate. In such a code, the X, Y, ...
• 28.7k
Accepted

Accepted

### Building universal gate set for $SU(d^n)$ from universal gate set for $SU(d)$

Let $G$ be a finite set of gates, of size $|G|$. Let $<G>$ be the words of $G$. That is, $<G>$ is the group generated by $G$. Suppose that $<G>$ is dense in $SU(d)$. ...
• 2,200
Accepted

### What is the difference between Gate.power() and Gate.repeat()?

The method Gate.repeat() accepts positive integers only. While Gate.power() accepts real values. So, you can use it, for eaxmple,...
• 7,109
Accepted

### Bounding operator norm by total variation distance

No you cannot, here's a counterexample. Let $U=I$ be the identity matrix and let $S = \sum_{i} (-1)^{\delta_{0,i}} |i\rangle \langle i|$ where $\delta_{i,j}$ is the Kronecker delta. That is, $S$ is ...
• 4,516
1 vote