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Grover amplitude amplification
Grover's algorithm searches an unstructured space of N candidates in O(√N) oracle calls. It prepares a superposition, marks target states by phase, and repeatedly reflects amplitudes to amplify the target.
Grover provides a quadratic (not exponential) speedup and assumes an efficient oracle.
Quantum phase estimation
Phase estimation extracts an eigenphase of a unitary when supplied an eigenstate. It underlies order finding, energy estimation, and many fault-tolerant algorithms. Its precision requirements drive circuit depth and qubit resources.
Phase estimation is a central bridge between quantum dynamics and useful numerical answers.
Shor and cryptography
Shor's algorithm reduces factoring and discrete logarithms to period finding and phase-estimation-like procedures. It threatens RSA and elliptic-curve cryptography on sufficiently large fault-tolerant hardware.
The algorithm is known; the remaining uncertainty is the engineering scale and timing of a cryptographically relevant machine.
Applied activity
Complete a simulator or analysis exercise: reproduce the lesson's central example, record assumptions and outputs, and explain one source of error or limitation.
Leggi il testo completo della lezione
1. Grover amplitude amplification
Grover's algorithm searches an unstructured space of N candidates in O(√N) oracle calls. It prepares a superposition, marks target states by phase, and repeatedly reflects amplitudes to amplify the target.
Grover provides a quadratic (not exponential) speedup and assumes an efficient oracle.
2. Quantum phase estimation
Phase estimation extracts an eigenphase of a unitary when supplied an eigenstate. It underlies order finding, energy estimation, and many fault-tolerant algorithms. Its precision requirements drive circuit depth and qubit resources.
Phase estimation is a central bridge between quantum dynamics and useful numerical answers.
3. Shor and cryptography
Shor's algorithm reduces factoring and discrete logarithms to period finding and phase-estimation-like procedures. It threatens RSA and elliptic-curve cryptography on sufficiently large fault-tolerant hardware.
The algorithm is known; the remaining uncertainty is the engineering scale and timing of a cryptographically relevant machine.
4. Applied activity
Complete a simulator or analysis exercise: reproduce the lesson's central example, record assumptions and outputs, and explain one source of error or limitation.
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