A major caveat to this algorithm is the preparation of the solution vector “ket b.” For 10 points each:
[10h] Name this triply-eponymous quantum algorithm appealing for its application to fields like machine learning and optimization. This algorithm solves a linear system with time logarithmic in the number of variables.
ANSWER: Harrow–Hassidim–Lloyd algorithm [accept HHL algorithm]
[10e] The HHL algorithm applies quantum phase estimation at every step, which is used to compute these quantities for the exponential of the input matrix A. These quantities are the lambdas in “Ax equals lambda x,” where x is a vector scaled by A.
ANSWER: eigenvalues [or characteristic value or characteristic root]
[10m] The HHL algorithm makes heavy use of quantum amplitude amplification, a technique that generalizes this algorithm. This algorithm, which runs in square root N time, increases the probability of measuring a desired eigenstate via iterative reflections.
ANSWER: Grover’s algorithm [accept quantum search algorithm]
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