The Deutsch–Jozsa algorithm determines whether a given function is constant or balanced using only a single query. In this example, a 3-qubit input register and one ancilla qubit are used. A constant oracle is applied, and the expected measurement outcome on the input qubits is 000, indicating that the function is constant.
Shor’s algorithm is used for integer factorization. Let n be the number to be factored, and m the smallest integer such that 2^m is at least n^2. The quantum function computes t^x mod n, where t is an integer coprime to n. The quantum circuit uses two registers: the first with m qubits for the x values, and the second register to store the result using ancilla qubits. A quantum Fourier transform is then applied, followed by a measurement on the first register.
