Unitary operators are mathematical functions used in quantum mechanics that preserve the inner product of vectors in a complex vector space. This means they maintain the total probability when transforming quantum states, ensuring that the sum of probabilities remains equal to one. Unitary operators are represented by unitary matrices, which have the property that their inverse is equal to their conjugate transpose. These operators play a crucial role in quantum computing and quantum information theory, where they are used to describe the evolution of quantum states. Examples of unitary operators include the Hadamard gate and Pauli gates, which manipulate qubits in quantum circuits.