diff --git a/docs/background.md b/docs/background.md index 7ba8f24..de1c580 100644 --- a/docs/background.md +++ b/docs/background.md @@ -23,8 +23,8 @@ An MPS is a particular way to encode a many-body wave-function using a set of matrices. Consider a system made of $N$ qubits, in a pure state $\left|\psi\right\rangle=\sum_{s_1,s_2,\cdots,s_N}\psi\left(s_1,s_2,\cdots,s_N\right)\left|s_1\right\rangle\left|s_2\right\rangle\cdots\left|s_N\right\rangle$. -In this expression the sum runs over the $2^N$ basis states ($s_i\in\{0,1\}$) and the wave-function is encoded -into the function $\psi:\{s_i\}\to\psi\left(s_1,s_2,\cdots,s_N\right)$. An MPS is a state where the wave function is written +In this expression the sum runs over the $2^N$ basis states ($s_i\in\\{0,1\\}$) and the wave-function is encoded +into the function $\psi:\\{s_i\\}\to\psi\left(s_1,s_2,\cdots,s_N\right)$. An MPS is a state where the wave function is written $\psi\left(s_1,s_2,\cdots,s_N\right)={\rm Tr}\left[A^{(s_1)}_1A^{(s_2)}_2\cdots A^{(s_N)}_N\right]$ where, for each qubit $i$ we have introduced two matrices $A^{(0)}_i$ and $A^{(1)}_i$ (for a local Hilbert space of dimension