Faster-than-Clifford simulations of entanglement purification circuits and their full-stack optimization

Generating quantum entanglement is plagued by decoherence. Distillation and error-correction are employed against such noise, but designing a good distillation circuit, especially on today’s imperfect hardware, is challenging. We develop a simulation algorithm for distillation circuits with per-gate complexity of $${\mathcal{O}}(1)$$ , drastically faster than $${\mathcal{O}}(N)$$ Clifford simulators or $${\mathcal{O}}({2}^{N})$$ wavefunction simulators over N qubits. This simulator made it possible to optimize distillation circuits much larger than previously feasible. We design distillation circuits from n raw Bell pairs to k purified pairs and study the use of these circuits in the teleportation of logical qubits. The resulting purification circuits are the best-known for finite-size noisy hardware and can be fine-tuned for specific error-models. Furthermore, we design purification circuits that shape the correlations of errors in the purified pairs such that the performance of potential error-correcting codes is greatly improved.