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Like building a ROM device? Please consider the influence of the non-cloning theorem and better show some papers. Thanks!

PS: I heard that error-correction methods might help to achieve this goal. Is it true?

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Reading information from a quantum system is possible only via a measurement, which mathematically can be described as applying a Hermitian operator (also called "observable") on the Hilbert space of the quantum system - an action that causes a "collapsion" of the quantum state to one of the basis states of the measurement. You can think of it as "destroying" information. E.g when measuring a single qubit in the $Z$ basis, we get either a $+1$ or $-1$ eigenvalues, which translates to $0$ or $1$ binary values, and the state of the qubit collapses to $|0\rangle$ or $|1\rangle$ respectively.

What can be done to gain some information without collapsing the entire quantum statevector is using a technique called weak measurement. Still, the act of measurement will cause some collapsion of the quantum state, but not all of it. E.g consider a system of 3 qubits: $q_0, q_1, q_2$. We initialize $q_0, q_1$ in a uniform superposition, and $q_2$ is standardly initialized in the $|0\rangle$ state. Therefore the initial state of the system (little-endian convention) is: $$|\psi_0\rangle = \frac{1}{2}(|000\rangle + |001\rangle + |010\rangle + |011\rangle)$$ Then by applying a Toffoli gate with $q_0, q_1$ as control qubits, and $q_2$ as a target qubit, the quantum statevector evolves to: $$|\psi_1\rangle = \frac{1}{2}(|000\rangle + |001\rangle + |010\rangle + |111\rangle)$$ Now, if we desire to find out if $q_1q_0 = 11$, we can measure only $q_2$ in the $Z$ basis. If $1$ is obtained - done. If $0$ is obtained - that means $q_1q_0 \neq 11$, and the quantum statevector evolves to: $$|\psi_2\rangle = \frac{1}{\sqrt{3}}(|000\rangle + |001\rangle + |010\rangle)$$


About "storing" information - I am not sure what you exactly mean. It is possible to encode information into a quantum state using various methods.

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  • $\begingroup$ Thank you, Ohad! Your help is greatly appreciated! "Storing" enables us to access information repeatedly. However, in order to do so, we must ensure that the measurement process does not destroy the data. $\endgroup$ Mar 8, 2023 at 5:15

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