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Quantum shell game: Finding the hidden pea in a single attempt

Abstract A quantum search of a database of four elements can be carried out in a single run with unit success probability. The classical analogy is to finding a pea hidden under one of four nut shells in a single attempt. We consider the algorithm in a system composed of two qubits, and show how the one and two-qubit search transforms are related to Pauli spin operators. The key search operation, the inversion about the mean, appears as a spatially rotated two-qubit phase shift, which provides some physical intuition for how it is implemented.