What exactly does state preparation mean in quantum computing?

I want to know what exactly state preparation means in a quantum computing. Are preparing a quantum state by applying different operations on it or we are preparing by some other methods?

• Welcome to QCSE. Your question seems very broad. Maybe you can edit it to be more focussed. Often when we talk about state preparation in quantum computing we want to find a circuit (a sequence of quantum operations/gates) that prepares a quantum state $|\psi \rangle$ of interest. Sep 24 at 16:01

Quantum state preparation is similar to initialization of variables in classical computing. At the beginning all qubits are in state $$|0\rangle$$ (similarly classical numerical variables contain zeros, text variables zero length string or null values etc.). To prepare state means that qubits are somehow changed to be in desired state, described generally as superposition $$\sum_{i=0}^{2^n-1} a_i |i\rangle,$$ where $$n$$ is number of qubits, $$a_i$$ are complex numbers (so-called probability amplitudes), $$|i\rangle$$ are basis states (for simplicity, consider basis states to be strings of 0 and 1, but there can be another bases). It must hold that $$\sum_{i=0}^{2^n-1} |a_i|^2 = 1.$$ The reason for this condition is that $$|a_i|^2$$ is probability of measuring qubits to be in state $$|i\rangle$$.
Example of two-qubit quantum state is $$0.5(|00\rangle + |01\rangle + |10\rangle + |11\rangle).$$ In this case you would measure any of strings 00, 01, 10 or 11 with probability 25%.