Enable qubit-dependent dynamical decoupling sequences as a transpiler pass

[dieris]

What is the expected behavior?

Currently, the PadDynamicalDecoupling scheduling pass can be used to insert a given dynamical decoupling (DD) sequence to all idle qubits in a circuit. This is helpful to suppress low-frequency noise by decoupling the qubits from their environment. However, if the same pulses are applied simultaneously to all qubits, any interaction between them is preserved during the DD sequence, leading to undesired correlations instead of idling.

Instead, having the ability to select different DD sequences (typically, differing in their timing) for different qubits would allow the user to selectively turn on/off interactions between qubits during the idle time. A few proposals to modify the DD scheduling pass in order of increasing complexity:

1. Allow the user to choose a subset of qubits to apply the same DD sequence on. For limited connectivity, one can disable each pairwise interaction by applying the sequence to only one of the qubits in each pair. A disadvantage of this approach is that protection from environment is removed for the qubits without DD.
2. Allow the user to choose between a few different DD sequences for each qubit. This way, timing of the pulses can be engineered to maintain protection from the environment, while at the same time canceling qubit-qubit interactions.
3. Automatically assign a DD sequence to each qubit based on the layout, such that coupled qubits will be assigned different sequences (see 1. or 2. above).