One of the potential applications of a quantum computer would be as a coprocessor to a classical computing system, much in the same way as a graphics processing unit (GPU) performs specialized operations that the traditional central processing unit (CPU) cannot do.
I've looked at the main books on quantum computing, and Googled around for research papers, but I'm struggling to find mechanisms that describe the interchange of data between quantum and classical computers.
I imagine it is relatively easy for a classical computer to receive information from a quantum circuit after measurement, but is it possible for a classical computer to send in classical bits through quantum gates for algorithms that mix classical bits and quantum bits?
This question has two parts:
- Theoretical: What is different from a mathematical perspective? Do classical bits mathematically identical to qubits in states $|0\rangle$ or $|1\rangle$?
- Physical: How would the various potential physical implementations of a quantum computer (e.g. trapped ions) have an interface connecting to traditional classical circuits?