[Feature Request] Leakage errors

[zhiihan]

Hey,

Would it be possible to simulate general errors e.g. leakage on the computational basis in sdim? e.g. Suppose I have

|0> --> |vac> : 0.05
|1> --> |vac> : 0.05

So there is a p = 0.1 probability that my qubit was lost. In the simulation, we may take |vac> := |2>, and assume the transition is unitary.

If I have some free time, I am interested in helping developing this feature.

[dweebyk]

Gidney discusses some of the challenges of sampling leakage in his Stim workflow here here:
https://quantumcomputing.stackexchange.com/questions/27295/support-for-qubit-leakage-errors-in-stim

In order to achieve the somewhat hacky method he implements above, we'd have to build the following:


1. Probabilistic gates (already achievable in a hacky fashion using ⁨⁨⁨N1⁩⁩⁩ or ⁨⁨⁨N2⁩⁩⁩, but I mean applying a standard Clifford with some probability).
2. Feedforward conditional gates using the measurement record.
3. Both of the above integrated into the Pauli frame sampler.
   
   These would take a while to get off the ground. If you're interested, reach out to me via email, and we can discuss this further.