Is there a quantum computing model that allows you to add different states?

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SUMMARY

The discussion centers on the existence of a quantum computing model that allows for the addition of different quantum states prepared on n qubits. The user presents examples of two qubit states, specifically (|00> + |01>)/√2 and -(|00> + |10>)/√2, and inquires whether these states can be added together in a meaningful way. The consensus indicates that such addition is not feasible due to the non-unitary nature of the operation, although optical quantum computation may offer unique interference opportunities among qubits from the same laser source.

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  • Understanding of quantum states and superposition
  • Familiarity with qubit representation and notation
  • Knowledge of unitary vs. non-unitary operations in quantum mechanics
  • Basic principles of optical quantum computation
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I want to know if a quantum computing model exists where you can prepare two different states on n qubits and interfere (i.e. add) them together. For example, for two qubits, consider the states (|00> + |01>)/√2 and -(|00> + |10>)/√2 (both pretty easy to prepare in most quantum computing models). Adding these two states would give (|01> - |10>)√2. Is there a model where any two states that can be prepared can also be added together?
 
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Just as a follow-up to my own question, I'm guessing no, since addition is a non-unitary operation... but then again it seems to me that in optical quantum computation it would be straightforward to have the qubits interfere with other qubits from the same laser source. An answer to this would be appreciated.
 

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