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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.
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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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