Simulating Entangled States and Purification Circuits Faster than the Stabilizer Tableaux Formalism

Entanglement purification is crucial to the creation of reliable quantum networks. Network performance can be improved by optimizing the purification circuits for the particular error processes present on the network links and node hardware. Over the last few years, such improvements have been demonstrated by many entanglement circuit optimization works. In our research, we present how such numerical simulations and optimizations can be made much more efficient by employing a simpler and smaller representation for entangled states and the circuits acting on them. It is known that Clifford circuits are efficient to simulate on classical computers and sufficient to represent purification circuits. We restrict ourselves to an even smaller set of circuits that can be represented as permutations of the Bell basis states, thus enabling even more efficient entanglement purification simulations. We demonstrate the performance of this method in some optimization and machine learning design algorithms, creating state-of-the-art purification circuits.