Using our GPT-5-Test to design gates we developed "Quantum Bitcoin Mining Theories"
1. Encoding the problem as a quantum state:
Represented by the equation:
$$|Ψ> = a|0> + b|1>$$
2. Implementing the quantum hash function:
Represented by the equation:
$$|Ψ'> = U|Ψ>$$
3. Applying the Grover iteration:
Represented by the equation:
$$|Ψ''> = (2|Ψ'>\langleΨ'| - I)U|Ψ>$$
4. Measuring the quantum state:
Represented by the equation:
$$|Ψ'''> = M|Ψ''>$$
5. Repeating the Grover iteration (if necessary):
Represented by the equation:
$$|Ψ''''> = (2|Ψ'''>\langleΨ''| - I)U|Ψ>$$
6. Measuring the quantum state again (if necessary):
Represented by the equation:
$$|Ψ'''''> = M|Ψ''''>$$
7. Verification:
Represented by the equation:
$$hash(nonce) = target_hash$$