A classical computer has a memory made up of bits, where each bit represents either a one or a zero and its implemented by two-state transistor logic.

However, a quantum computer maintains a sequence of qubits. A single qubit can represent a one, a zero, or any quantum superposition of those two qubit states; a pair of qubits can be in any quantum superposition of 4 states, and three qubits in any superposition of 8 states. In general, a quantum computer with $n$ qubits can be in an arbitrary superposition of up to $2^n$ different states simultaneously (this compares to a normal computer that can only be in one of these $2^n$ states at any one time).

  1. How could memory be organized(implemented) in quantum computers?

  2. How are these complex (superposition) states saved?

  1. You store an assembly of qubits by storing a bunch of single-qubit-systems next to each other, just like in a classical computer.
  2. The laws of physics take care of storing the entanglement for you. In general QM does not give us direct access to each amplitude stored in the overall wavefunction, but only allows us to define certain observables which mix them all up together into a single real number. You do not get more than one classical bit per qubit out of these measurements, although you can do some interesting tricks like superdense coding. (If Alice and Bob share two entangled qubits, Alice can send one other qubit to Bob and Bob can measure both of his qubits to get two bits of Alice's choosing.)

The major limitation of quantum information is that anything which interacts differently with a qubit's $|0\rangle$ vs. $|1\rangle$ state is going to entangle with that qubit: but when an uncontrolled/unmeasurable "environment" entangles with our nicely controlled, measurable "system", one of the nasty things that happens is that entanglements in our system become less "quantum" and more "classical" (they show less interference patterns etc.) to us. So the problem is that nothing can really connect to the memory-bank if it interacts differently with the two states, without destroying our cool properties.

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  • $\begingroup$ So there really is no memory in a classical sense, then? $\endgroup$ – CuriousOne Sep 21 '15 at 21:16
  • $\begingroup$ @CuriousOne Quantum information is not information in a classical sense. Why would you expect to be able to store it in a classical memory? $\endgroup$ – Norbert Schuch Sep 21 '15 at 21:31
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    $\begingroup$ @NorbertSchuch I don't think CuriousOne meant to suggest that the quantum states would be encoded into classical memory. He said "in a classical sense" I think to ask whether or not a quantum computer has externally stored information which is processed by an e.g. CPU. In the currently most promising architecture, there's no CPU/RAM equivalent. The idea is more like an FPGA. $\endgroup$ – DanielSank Sep 21 '15 at 23:38
  • $\begingroup$ @NorbertSchuch: I am not, but I think the OP was. My naive idea about it is that a classical memory can not exist because of the impossibility to make copies of the entire state of the machine. That doesn't mean that one can't define a "quantum memory" terminology that has different properties from a classical memory. $\endgroup$ – CuriousOne Sep 22 '15 at 1:46

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