Introduction to Quantum Computing
Deutsch's algorithm is one of the first quantum algorithms discovered, and it demonstrates the power of quantum computing by solving a problem exponentially faster than any classical algorithm could.
The problem Deutsch's algorithm solves is a simple one: given a black box that takes a single bit as input and produces a single bit as output, determine whether the box is constant or balanced (returns 0 for half of the possible inputs and 1 for the other half). Classically, this problem would require two queries to the black box, as one would need to check both inputs. But Deutsch's algorithm can solve this problem with just a single query to the black box.
The algorithm begins with two qubits in the state |0⟩, and applies a Hadamard gate to each qubit to create a superposition of all possible input states. The black box is then applied to the qubits, resulting in a phase shift that depends on whether the box is constant or balanced. Finally, another Hadamard gate is applied to each qubit, and the state is measured to determine the answer. If the result is |00⟩, the box is constant, and if it is |01⟩ or |10⟩, the box is balanced.
While the problem Deutsch's algorithm solves is trivial, the algorithm itself is important because it demonstrates the power of quantum computing. It is also the basis for many other quantum algorithms, including Shor's algorithm for factoring large numbers.
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