6.7.2.5. Measurement

As the system ultimately represents the state |a‿, measuring the qubits directly provides the binary representation of ‘a’. This measurement yields the bits a₁, a₂, …, an individually.

This algorithm serves as an example of the superiority of quantum computers over classical computers. Understanding the mathematical foundations of quantum algorithms will help make this technology more broadly applicable in the future. The goals can be summarized as follows:

• Theoretical foundation: Proving the speed advantage of quantum computers.
• Education and research: Serving as an example for learning and teaching quantum algorithms and quantum circuit design.
• Practical value: Although not directly applicable, it can inspire quantum applications in fields such as cryptography and optimization.

The Bernstein-Vazirani algorithm is not a directly applicable algorithm in practice, but it was developed to demonstrate the power of quantum computation. It serves several purposes:

1. Demonstrating the Power of Quantum Computers: The algorithm highlights the speed advantage of quantum computers over classical computers. This is used as a “demonstration” algorithm to prove that quantum computers can revolutionize computing.
2. Quantum Circuit Design and Phase Interference: This algorithm is a fundamental example for understanding how phase interference is used in quantum circuits.
3. Quantum Cryptography: The ability to quickly find secret information using quantum techniques can provide insights for quantum cryptography algorithms.