Block Encoding

Block encoding is a quantum computing method for representing a classical or quantum matrix (A) as a submatrix of a larger unitary matrix (U). Specifically, (U) is built so that (A = \alpha (\langle 0^k | \otimes I) U (|0^k\rangle \otimes I)) for some scaling factor (\alpha) and number of ancilla qubits (k). This lets quantum algorithms access (A) efficiently using unitary operations, enabling tasks like Hamiltonian simulation or matrix inversion.