Add loss policies to NoiseConfig to express different kinds of behavior on lost qubits

[orpuente-MS]

With this change, users are able to specify how gates should behave if at least one of their qubit operands is lost. Below is a comprehensive example, showing all 5 loss policies.

from qdk.simulation import NoiseConfig, LossPolicy
qir = ...

noise = NoiseConfig() 
noise.cz.on_loss  = LossPolicy.SKIP               # if one of the qubits is lost, skip the unitary
noise.cx.on_loss  = LossPolicy.PROPAGATE          # if one of the qubits is lost, loose the other one
noise.rxx.on_loss = LossPolicy.DEGRADE            # degrade to a single qubit gate: rx
noise.ryy.on_loss = LossPolicy.RESIDUAL_S_DAGGER  # apply an S_DAG to the remaining qubits
noise.rzz.on_loss = LossPolicy.APPLY_ANYWAY       # apply unitary anyways

# Works with all simulator types, in any profile.
run_qir(qir, shots=100, noise=noise, type="clifford")

[billti]

This one is interesting. Worth discussing more. Seems odd you would skip the unitary (which swaps the state) but still swap which is lost. Not sure if that would be physically possible.

[orpuente-MS]

Mmh, maybe the behavior here should be:

• SKIP doesn't apply the unitary nor exchanges loss flags.
• APPLY_ANYWAY applies the unitary and exchanges the loss flags.

[orpuente-MS]

I came up with a simple principle: no matter the policy, we should never recover a qubit that was lost. Following this rule of thumb, I created the following table describing the behavior of SWAP under each policy:

Policy	apply unitary	exchange loss flags	extra behavior
SKIP	no	no	no
PROPAGATE	no	no	loose other qubit
DEGRADE	no	no	no
RESIDUAL_S_DAGGER	yes	yes	apply S_ADJ to survivor
APPLY_ANYWAY	yes	yes	no

[billti]

That table doesn't look right. You do apply the unitary for DEGRADE I thought, just to the other qubit. And 'exchange loss flags' being 'yes' on RESIDUAL_S_DAGGER seems wrong.

[billti]

In a number of these, you're not applying idle noise on the other qubit.

Also, for ApplyAnyway (which we should discuss further as it doesn't make much sense to me), should you also be applying idle noise anyway to the lost qubits?

[orpuente-MS]

Added the missing idle noise applications.

We can discuss removing the ApplyAnyway policy.