Restoring broken symmetries using oracles
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Abstract
We present a new method to perform variation after projection in many-body systems on quantum computers that does not require performing explicit projection. The technique employs the notion of “oracle”, generally used in quantum search algorithms. We show how to construct the oracle and the projector associated with a symmetry operator. The procedure is illustrated for the parity, particle number, and total spin symmetries. The oracle is used to restore symmetry by indirect measurements using a single ancillary qubit. An Illustration of the technique is made to obtain the approximate ground state energy for the pairing model Hamiltonian.