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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? Are 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?
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  • $\begingroup$ Can you specify more precisely what you understand about the interaction of a classical with a quantum computer? -- If you have classical control of a quantum computer, you can e.g. initialize qubits in a desired classical state or flip them depending on your classical control. $\endgroup$
    – Norbert Schuch
    Feb 11, 2015 at 17:57
  • $\begingroup$ Regarding the theory, the examples I read in books describe setting qubits in $|0\rangle$ or $|1\rangle$, but never to a specific value like $|0110001\rangle$. I understand that is because it's not useful for any known quantum algorithm, but I'm looking at designing a series of gates where some bits are in superposition and other bits are always 0 or 1. $\endgroup$
    – James Mishra
    Feb 11, 2015 at 18:25
  • $\begingroup$ Regarding the physical perspective, I'm wondering if classical bits need to be made out of the same "material" as qubits, as qubits are hard to maintain. I'd rather not have classical bits get entangled with quantum bits, and worry that the classical bits will cause problems with decoherence. Ideally classical methods of error correction would work on the classical bits as well. $\endgroup$
    – James Mishra
    Feb 11, 2015 at 18:27
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    $\begingroup$ Insert a grad student between the classical computer and the quantum computer. $\endgroup$
    – jayann
    Feb 11, 2015 at 21:46

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I'm no expert on quantum computing, but I had the same question, and found the following to help, a little bit.

http://tph.tuwien.ac.at/~oemer/doc/quprog/node8.html#SECTION00323300000000000000

The gist of it is, first you 'cool' your qbit to the zero state, and then apply a unitary transformation which has the result $U|0\rangle = |S\rangle$, where $|S\rangle$ is your initial string.

Now, as far as I understand,$|S\rangle$ really is a recording of the probabilities of all possible bit strings, so I would assume that your initial $|S\rangle$ value would be something with:

A high probability for your desired, classical string: $$0.9 \cdot |0101010111\rangle$$

and a very low probability for all other possibilities: $$\frac{0.1}{2^{10}-1} \cdot |others\rangle$$

I really don't know if this is a valid assumption to make, though, so please, tell me if I'm wrong.

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  • $\begingroup$ Provided, that we want to pass superposition, this method is quite useless (amount of information stored in superpositions is incomparably greater than in 'classical' states). $\endgroup$
    – Alleo
    Dec 19, 2015 at 2:12

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