Non-Markovianity in Quantum Information Processing: Interplay with Quantum Error Mitigation

Abstract: Non-Markovian dynamics are typically present in the dynamics of open quantum systems. Despite the rich structure of non-Markovian dynamics, their relevance to quantum information processing (QIP) has been rarely discussed. In this work, we demonstrate that the negativity of the dynamics, a characteristic of non-Markovian dynamics, naturally arises in quantum error correction (QEC) and quantum teleportation. The negativity in open quantum systems is naturally attributed to the information backflow from the environment. We partition the whole Hilbert space into the logical subsystem and the gauge subsystem. The logical subsystem stores the quantum information for QIP, while the gauge subsystem stores the information for recovery of the logical information, i.e., the syndrome measurement outcomes for quantum error correction and Bell measurement outcomes for successful teleportation. We then show that the negativity in quantum information processing appears as a consequence of the feedback operation based on the measurement outcomes of the gauge subsystem. Finally, we show that the negativity of non-Markovianity in QIP reduces the sampling cost of quantum error mitigation (QEM), shedding light on the importance of combination strategies of QEC and QEM in a practical QIP.