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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?

C Shreve
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  • 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? – D.W. Nov 06 '15 at 07:04
  • 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. – C Shreve Nov 06 '15 at 18:31
  • This seems to be an exact duplicate of http://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 http://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. – D.W. Nov 07 '15 at 10:20

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