Decoupling with random quantum circuits

Understand

Decoupling has become a central concept in quantum information theory with applications including proving coding theorems, randomness extraction and the study of conditions for reaching thermal equilibrium.

• However, our understanding of the dynamics that lead to decoupling is limited.
• In fact, the only families of transformations that are known to lead to decoupling are (approximate) unitary two-designs, i.e., measures over the unitary group which behave like the Haar measure as far as the first two moments are concerned.
• Such families include for example random quantum circuits with O(n^2) gates, where n is the number of qubits in the system under consideration.