A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Strengths and Weaknesses of Quantum Computing
SIAM Journal on Computing
Quantum computation and quantum information
Quantum computation and quantum information
Simple Algorithm for Partial Quantum Search
Quantum Information Processing
Quest for Fast Partial Search Algorithm
Quantum Information Processing
Quantum Information Processing
Quantum Partial Search of a Database with Several Target Items
Quantum Information Processing
Tree search and quantum computation
Quantum Information Processing
Exact quantum lower bound for grover's problem
Quantum Information & Computation
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We consider the partial database search problem where given a quantum database f : {0,1}n→{0,1} such that f(x) =1 for a unique x ∈ {0,1}n, we are required to determine only the first k bits of the address x. We present an algorithm and derive a lower bound for this problem. Let q(k,n) be the minimum number of queries needed to find the first k bits of the required address x with certainty (or with very high probability, say 1--O(N--¼)). We show that there exist constants ck (corresponding to the algorithm) and dk (corresponding to the lower bound) such that πover4 (1--dkover√K) √N ≤ q(k,n) ≤ πover4 (1--ckover√K) √N, where K=2k and N=2n. Our algorithm returns the correct answer with probability 1--O(N--½), and can be easily modified to give the correct answer with certainty. The lower bound for algorithms that return the correct answer with certainty is proved by reducing the usual database search problem to this partial search problem, and invoking Zalka's lower bound showing that Grovers algorithm is optimal for the usual database search problem. We then derive a lower bound that is applicable for database search algorithms that err with small probability, and use it to show that our lower bound also applies to partial search algorithms that return the correct answer with probability at least 1--O(N--¼).