Noise modeling

[jon-wurtz]

Is your feature request related to a problem? Please describe.
With bloqade.jl being deprecated, users are lacking a viable option to do noisy emulation.

Describe the solution you'd like
Reproducing the features of bloqade.jl noise modeling, including stochastic coherent noise averaging, incoherent decay, and measurement error

Describe alternatives you've considered
Continuing to use bloqade.jl

[jon-wurtz]

More requirements on Python noise modeling.

1. Equivalent workflow to noiseless simulation and job submission:

result = program.bloqade.python.run(nshots = 1000) # Noiseless simulator job submission
result = program.quera.custom().run_async(nshots = 1000) # Aquila exclusive access job submission
result = program.braket.aquila().run_async(nshots = 1000) # Aquila braket job submission
result = program.bloqade.python.noisy_run(nshots = 1000, noisemodel = noise) # Prototype interface for noisy results

with the result object being consistent with that submitted to hardware (and possibly accessing stochastic statevector or probability distribution?). noise specifies the noise model (see 3).
2. pip install bloqade-analog or a generally seamless installation
3. Parameterized, user specifiable noise model with a set of "aquila" defaults.
4. At least the noise sources matching the Aquila whitepaper https://arxiv.org/pdf/2306.11727 pp.17. Note that measurement error and finite loading are not included in the Julia noise model. This includes:
Systematic bias (set by each instance of a noise model?)

• Pattern-dependent errors
• Detuning inhomogeneity
• Detuning shift

Coherent, shot-by-shot error in

• qubit position
• Rabi amplitude variance (Gaussian multiplication Omega * e^{w})
• Detuning variance (Gaussian addition Delta + w)
• Finite loading probability

Measurement error

• Mis-measuring ground as Rydberg
• Mis-measuring Rydberg as ground
  Incoherent error of
• Scattering/decay from G to R and from R to G

5. Bonus would be fast caching of intermediate data for inverse modeling and log-likelihood minimization, and/or differentiable values of a generated probability distribution.