Measuring of quantum state of a many-body quantum system in computational basis

[shadibeh]

Hi every one.

I would like to measure a quantum state consisted of a large number of spins (around 300 spins) in computational basis. So, the simplest way to do that is to find all the spin configurations in computational basis and find the squared inner product of each possible configuration and the quantum state to find the probability.

However, it requires large memory and takes long time. Would you please let me know if there is any approach in quimb to do it faster. Thanks

[jcmgray]

Hi @shadibeh

However, it requires large memory and takes long time.

Yes 2^300 ~ 10^90 is a very large number!

You don't specify what representation you have of your quantum state? but assuming it is e.g. a tensor network representation, then one performs this generally by computing a series of conditioned marginal probability distributions and sampling from these in a chain. See for example the quimb docs here

• https://quimb.readthedocs.io/en/latest/tensor-circuit.html#Compute-a-marginal-probability-distribution and
• https://quimb.readthedocs.io/en/latest/tensor-circuit.html#Generate-unbiased-samples. however, note this is only possible if the TN representation can be contracted (i.e. is 'close enough to a tree').

[shadibeh]

Thank you very much for the explanations. The links were very helpful.

Thanks