Is it possible to use quantum state to store and read information without destorying it?

Question

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?

Answer 1

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: $$|\psi_2\rangle = \frac{1}{\sqrt{3}}(|000\rangle + |001\rangle + |010\rangle)$$

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