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

Abstract

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 O(1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{O}}(1)$$\end{document}, drastically faster than O(N)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{O}}(N)$$\end{document} Clifford simulators or O(2N)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{O}}({2}^{N})$$\end{document} 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.