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A stored programming computer model is that where a central memory is used to store both instructions and data that they operate on. Basically all the classical computers of today that follow the von Neumann architecture use the stored programming model. During program execution the CPU reads instructions or data from the RAM and places it in the various registers such as Instruction Register (IR) and other general purpose registers.

My question is whether such a stored programming model is applicable to a Quantum Computer or not, since because of the no-cloning theorem it is not possible to clone any arbitrary quantum state.

It means that if we have some qubits in some state stored in a memory register then because of the no-cloning theorem the Quantum Computer processor will not be able to read or copy those qubits from the memory to some internal registers.

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Yes, you can encode a program into your qubits in exactly the same way you'd encode a program into bits and then run circuits that interpret the program. One might hope that you could encode the program in some fancy exponentially efficient way, but in Mike&Ike they prove that's not possible. Because there's no exponential advantage, and because the operations needed to read and decode the program are billions of time more expensive on a quantum computer, you want to store the program in the classical control computer in almost all cases.

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  • $\begingroup$ Link to relevant Mike&Ike $\endgroup$
    – AHusain
    Sep 15, 2018 at 15:57
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    $\begingroup$ "My question is whether such a stored programming model is applicable to a Quantum Computer or not, since because of the no-cloning theorem it is not possible to clone any arbitrary quantum state." Your answer seems to be "yes the model is applicable" but with no reference to the "since" part of the question. Can you tell the asker why his/her belief that the no-cloning theorem would make the answer "no", is false? $\endgroup$
    – user1271772
    Sep 15, 2018 at 17:25
  • $\begingroup$ @user1271772 The no cloning theorem doesn't apply to qubits that are in a known state, or in a basis state of a known orthonormal basis such as the computational basis. So you can encode the program into the computational basis states. The "no exponential efficiency" limitations I mentioned could be thought of as being related to the no cloning theorem. $\endgroup$
    – Craig Gidney
    Sep 15, 2018 at 19:37
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    $\begingroup$ @user1271772 If the states are computational basis states, you can measure them without decohering them and generally make all the copies you want. $\endgroup$
    – Craig Gidney
    Sep 15, 2018 at 23:00
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    $\begingroup$ You say that "One might hope that you could encode the program in some fancy exponentially efficient way" but Mike&Ike prove it's not possible. This covers the "instructions" part of "During program execution the CPU reads instructions or data from the RAM" but not the "data" part. According to @Peter Shor's answer having instructions in superposition "is orders of magnitude more difficult experimentally than just having the memory in superposition," but what about the idea of having the data in the memory superposition? You'd have to copy superposition states from RAM to IRs. NCT violation? $\endgroup$
    – user1271772
    Sep 16, 2018 at 0:21

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