Bernstein–Vazirani Encoding

A guided research project in Quantum Computing.

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Question

How can one quantum query recover a hidden binary string?

Quantum interference turns the oracle's phase pattern directly into the hidden string.
Quantum interference turns the oracle's phase pattern directly into the hidden string.

Goals

  • Derive and implement the Bernstein–Vazirani circuit.
  • Explain how phase encoding and interference reveal the string.

Method

Encode the hidden string in an oracle and let interference collect all of its bits.

  • Define the oracle \(f(x)=s\cdot x \pmod 2\).
  • Build the Hadamard–oracle–Hadamard circuit and simulate or run it.
  • Measure the output and test how noise changes the recovered string.