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I'm trying to do something similar to this question, where I want to partially measure the system before getting the output. In particular, say I have 4 qubits. I want to measure two of them, and then get the state vector associated with the other two. I know that I can do this the following way:

  1. Measure the 2 qubits.
  2. Perform a partial trace on those two qubits (so that my output vector only has $2^2$ components instead of $2^4$).
  3. Call the statevector function to get the state on my other 2 qubits.

The problem is that I need to actually get the statevector in Step 2 before performing the partial trace. This means the system has to produce the statevector, taking up a lot of memory and limiting the number of qubits I can scale to.

My question is: Is there a way to collapse the wavefunction and then get the statevector out on only the remaining qubits without having the system calculate the whole statevector beforehand?

I don't know if this is a reasonable question, but I was wondering if it could be done.

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