Suppose I have 2 qubits in the state a|00>+b|01>+c|10>+d|11>. And suppose I want to perform some operation between only the 1st qubit and a 3rd qubit - for example a CNOT operation. What would be the correct way to do this multiplication?

  • $\begingroup$ What do you mean by the correct way to do this? What kind of answer are you looking for -- a matrix, an algorithm, a description of a physical computer, something else? What approaches have you considered? $\endgroup$
    – D.W.
    Nov 6 '15 at 7:04
  • $\begingroup$ A matrix and process I suppose. I know I could make matrix and fill it in with I for the qubit I don't want to affect and CNOT (just for example) for the qubit I do want to affect. But this would require a 2^3 X 2^3 matrix. This is fine for small numbers of qubits, but I don't see how this could work with large numbers of qubits (say 50). 50 qubits would require a 2^50 X 2^50 matrix which is too large of a matrix to work with for a computer. So I'm trying to understand how mathematically to apply operations to specific qubits without invoke some huge (ie 2^50 X 2^50) matrix. $\endgroup$
    – C Shreve
    Nov 6 '15 at 18:31
  • $\begingroup$ This seems to be an exact duplicate of cs.stackexchange.com/q/48834/755. Please see the explanations there and edit the question if there is some distinction that I missed. As far as 50 qubits requiring a 2^50 x 2^50 matrix, please see cs.stackexchange.com/q/48781/755. I sympathize with your feelings of discomfort about such large matrices, but I don't see what else there is to say than what was written there -- yes such a quantum process is modelled by a 2^50 x 2^50 matrix, but the matrix is just a mathematical construct. Large matrix != unrealizable in practice. $\endgroup$
    – D.W.
    Nov 7 '15 at 10:20