# Qubit reset using Grover iteration

Suppose I’m building a long circuit and I need to reuse a qubit from a previous step but I don’t want to use the reset operation (or I’m not using an IBM computer so I don’t even have the reset option).

Could I apply some Grover-style rotation of the qubit that I want to reset, like if I was searching for the state $$|0\rangle$$?

I know that the Grover algorithm presumes you are starting from a qubit in a uniform superimposition - but what would happen if I tried to do a Grover-like search for $$|0\rangle$$ starting from any arbitrary state instead of a uniform superimposition? Would I still get to $$|0\rangle$$ or would something weird happen?

Unfortunately, as you say, something weird would happen. If you start with a qubit in an unknown quantum state, there are no unitary operations to map it to $$|0\rangle$$ because unitary operations must be reversible. Commonly, initialization in quantum computing is done by measuring the desired reset bit, and then applying $$X$$ to it if $$|1\rangle$$ is measured to get back to $$|0\rangle$$.
• Let's say you have a qubit in an arbitrary state $|\psi_1\rangle$ in one run of your algorithm and $|\psi_2\rangle$ in a second. Then any amplification process $A$ that re-initializes the qubit to $|0\rangle$ must have $A|\psi_1\rangle = A|\psi_2\rangle = |0\rangle$. Then such a process cannot be unitary (otherwise $A^\dagger|0\rangle = |\psi_1\rangle = |\psi_2\rangle$, a contradiction). This means any sort of Grover-like amplification process would be unable to do what you want since they're unitary. To reinitialize a qubit, you need to do something non-unitary like measurement. Oct 26, 2022 at 21:22