Dynamic T-decomposition for classical simulation of quantum circuits

Understand

It is known that a quantum circuit may be simulated with classical hardware via stabilizer state (T-)decomposition in $O(2^{\alpha t})$ time, given $t$ non-Clifford gates and a decomposition efficiency $\alpha$.

• The past years have seen a number of papers presenting new decompositions of lower $\alpha$ to reduce this runtime and enable simulation of ever larger circuits.
• More recently, it has been demonstrated that well placed applications of apparently weaker (higher $\alpha$) decompositions can in fact result in better overall efficiency when paired with the circuit simplification strategies of ZX-calculus.
• In this work, we take the most generalized T-decomposition (namely vertex cutting), which achieves a poor efficiency of $\alpha=1$, and identify common structures to which applying this can, after simplification via ZX-calculus rewriting, yield very strong effective efficiencies $\alpha_{\text{eff}}\ll1$.