The quantum query complexity of approximating the median and related statistics
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
Quantum summation with an application to integration
Journal of Complexity
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Quantum Information Processing
Classical and Quantum Computation
Classical and Quantum Computation
Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Classical and Quantum Complexity of the Sturm--Liouville Eigenvalue Problem
Quantum Information Processing
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We design an adiabatic quantum algorithm for the counting problem, i.e., approximating the proportion, 驴, of the marked items in a given database. As the quantum system undergoes a designed cyclic adiabatic evolution, it acquires a Berry phase 2驴驴. By estimating the Berry phase, we can approximate 驴, and solve the problem. For an error bound $${\epsilon}$$ , the algorithm can solve the problem with cost of order $${(\frac{1}{\epsilon})^{3/2}}$$ , which is not as good as the optimal algorithm in the quantum circuit model, but better than the classical random algorithm. Moreover, since the Berry phase is a purely geometric feature, the result may be robust to decoherence and resilient to certain noise.