Deutsch-Jozsa Algorithm

Fundamentals of Deutsch-Jozsa Algorithm

The Deutsch-Jozsa technique enables the determination of whether a given Boolean function is constant or balanced. Let us consider a binary function that accepts input values of 0 and 1, and produces output values of 0 or 1. A function is deemed to be constant if and only if all of its outputs are either 0 or 1. A function is considered balanced when exactly half of its inputs are zeroes and exactly half of its inputs are ones.

Working Principles

The Deutsch-Jozsa algorithm encompasses several distinct implementations, although with a common 5-step procedure. The initial stage involves the preparation of quantum registers and input states. During the second stage, the qubits are arranged in accordance with the Hadamard Basis. This implies that every qubit possesses an equal probability of being in the state 0 or 1, each with a probability of 50%. The third stage involves the utilisation of an oracle, which encompasses the encoding of a function that establishes the nature of the outputs, whether they are constant or balanced, through the utilisation of quantum entanglement. The fourth phase involves the reversion of the qubits to the measurement basis for the purpose of determining the solution. In the final stage, the qubits undergo measurement in order to get the answer.