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joeycarter committed Nov 6, 2024
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# performing :math:`O(\sqrt{N})` queries on the database, whereas a classical search algorithm would
# require :math:`O(N)` queries to perform the same task.
#
# More formally, the *unstructured search problem* is defined as a search for a string of bits in a list containing
# :math:`N` items given an *oracle access function* :math:`f(x).` This function is defined such that
# :math:`f(x) = 1` if :math:`x` is the bitstring we are looking for (the *solution*), and
# :math:`f(x) = 0` otherwise. The generalized form of Grover's algorithm accepts :math:`M`
# solutions, with :math:`1 \leq M \leq N.`
# More formally, the *unstructured search problem* is defined as a search for a string of bits in a
# list containing :math:`N` items given an *oracle access function* :math:`f(x).` This function is
# defined such that :math:`f(x) = 1` if :math:`x` is the bitstring we are looking for (the
# *solution*), and :math:`f(x) = 0` otherwise. The generalized form of Grover's algorithm accepts
# :math:`M` solutions, with :math:`1 \leq M \leq N.`
#
# In this tutorial, we will implement the generalized Grover's algorithm using `Catalyst
# <https://docs.pennylane.ai/projects/catalyst>`__, a quantum just-in-time (QJIT) compiler framework
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