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

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?

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