Questions on quantum circuit simulation and probability approximation

[ChienKaiMa]

According to the book "Quantum Computer Systems: Research for Noisy Intermediate-Scale Quantum Computers" (https://ieeexplore.ieee.org/document/9122477), there are strong simulation and weak simulation. I want to compare the ability to perform strong simulation on different classical simulators. To match the definition of strong simulation, I found the method to_dense in QuiMB can yield accurate simulation results of full statevector. However, since I'm only curious about part of the statevector (or the probability of some arbitrary states), I'm afraid using to_dense is not a fair comparison. When the qubit number is large, the other simulator I'm experimenting with can still calculate the accurate probability of one or more outcomes. The following questions are my ideas or concerns for my experiments:

1. Is there a quick function in QuiMB such that I can query the state probability of an arbitrary bitstring?
2. The method sample in QuiMB can simulate larger circuits and do the work faster. I wonder if it is possible to obtain the probability amplitude of some states by using _sample_conditionals or other variables used during sample. If it is possible, how accurate is the approximation or how to know how accurate it is?

[jcmgray]

Is maybe Circuit.amplitude what you are looking for? See here & here. It's generally cheaper to compute than either the full state vector and also easier than sampling. If you are investigating performance, you might want to consider some of the things here.

The method sample in QuiMB can simulate larger circuits and do the work faster. I wonder if it is possible to obtain the probability amplitude of some states by using _sample_conditionals or other variables used during sample. If it is possible, how accurate is the approximation or how to know how accurate it is?

Apart from the threshold simplify_atol, which is generally close to the dtype precision, there is no approximation in the sampling.