Fault-tolerant Coding for Quantum Communication

Alexander Müller-Hermes, Department of Mathematics, University of Oslo
Abstract: Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error it is usually assumed that these circuits can be implemented using noise-free gates. While this assumption is satisfied for classical machines in many scenarios, it is not expected to be satisfied in the near term future for quantum machines where decoherence leads to faults in the quantum gates. As a result, fundamental questions regarding the practical relevance of quantum channel coding remain open. In this talk I will explain how to combine techniques from fault-tolerant quantum computing with techniques from quantum Shannon theory to prove threshold theorems for the classical and quantum capacity: For every quantum channel T and every ε is bigger than 0 there exists a threshold p(ε,T) for the gate error probability below which rates larger than C − ε are fault-tolerantly achievable with vanishing overall communication error, where C denotes the usual capacity.

Joint work with Matthias Christandl. The talk is based on: https://arxiv.org/pdf/2009.07161.pdf

Видео Fault-tolerant Coding for Quantum Communication канала Gemini Center on Quantum Computing