Skip to content

Commit

Permalink
LAtex fix
Browse files Browse the repository at this point in the history
  • Loading branch information
haggaila committed Oct 8, 2024
1 parent 5a69f9a commit b73d32b
Showing 1 changed file with 5 additions and 12 deletions.
17 changes: 5 additions & 12 deletions docs/background.md
Original file line number Diff line number Diff line change
Expand Up @@ -44,18 +44,11 @@ $S_{\rm vN}(i)$ is the von Neumann entropy of the subsystem
$[i+1,\cdots,N]$.


What about mixed states? They can be represented using so-called matrix-product operators (MPO):
$\rho=\sum_{a_1,a_2,\cdots,a_N}{\rm Tr}\left[M^{(a_1)}_1 M^{(a_2)}_2\cdots M^{(a_N)}_N\right]\sigma^a_1 \otimes \sigma^a_2 \otimes \cdots \sigma^a_N$
where each $a_i$ can take four values
$\in\{1,x,y,z\}$,
$\sigma^{a_i}$ is a Pauli matrix or the identity acting on qubit
$i$,
and we have associated four matrices
$M_i^{(1)},
$M_i^{(x)}$,
$M_i^{(y)}$ and
$M_i^{(z)}$ to each qubit.

What about mixed states? They can be represented using so-called matrix-product operators (MPO),
```math
\rho=\sum_{a_1,a_2,\cdots,a_N}{\rm Tr}\left[M^{(a_1)}_1 M^{(a_2)}_2\cdots M^{(a_N)}_N\right]\sigma^a_1 \otimes \sigma^a_2 \otimes \cdots \sigma^a_N
```
where each $a\_i$ can take four values $\in\{1,x,y,z\}$, $\sigma^{a_i}$ is a Pauli matrix or the identity acting on qubit $i$, and we have associated four matrices $M_i^{(1)}, $M_i^{(x)}$, $M_i^{(y)}$ and $M_i^{(z)}$ to each qubit.


### Bond dimension and entanglement
Expand Down

0 comments on commit b73d32b

Please sign in to comment.