Lecture 5. Stabilizer circuits simulation using stabilizer tableau

In this Lecture we discussed the application of the stabilizer tableau method to weak and strong simulation of stabilizer circuits. It is convenient to encode each stabilizer state into an extended stabilizer, with freedom in row operationsand the choice of destabilizers. Such a representation of states occupies $\mathcal{O}(n^2)$ bits in memory. The action of local gates on the stabilizer tableau is described by column operations, it takes $\mathcal{O}(n)$ time. A Pauli observable measurement can produce either a deterministic or uniformly random outcome, and takes time $\mathcal{O}(n^2)$. By working out how these operations work in the stabilizer formalism, it is possible to perform both weak and strong simulations of stabilizer circuits.