Dynamical decoupling sequences for multi-qubit dephasing suppression and long-time quantum memory

Abstract

Weconsider a class of multi-qubit dephasing models that combine classical noise sources and linear\ncoupling to a bosonic environment, and are controlled by arbitrary sequences of dynamical\ndecoupling pulses. Building on a general transfer filter-function framework for open-loop control, we\nprovide an exact representation of the controlled dynamics for arbitrary stationary non-Gaussian\nclassical and quantum noise statistics, with analytical expressions emerging when all dephasing\nsources are Gaussian. This exact characterization is used to establish two main results. First, we\nconstruct multi-qubit sequences that ensure maximum high-order error suppression in both the time\nand frequency domain and that can be exponentially more efficient than existing ones in terms of total\npulse number. Next, we show how long-time multi-qubit storage may be achieved by meeting\nappropriate conditions for the emergence of a fidelity plateau under sequence repetition, thereby\ngeneralizing recent results for single-qubit memory under Gaussian dephasing. In both scenarios, the\nkey step is to endow multi-qubit sequences with a suitable displacement anti-symmetry property, which\nis of independent interest for applications ranging from environment-assisted entanglement\ngeneration to multi-qubit noise spectroscopy protocols.