Restoring broken symmetries using quantum search “oracles”
Edgar Andres Ruiz Guzman, Denis Lacroix
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.
Topics & Concepts
OracleHomogeneous spaceQubitHamiltonian (control theory)QuantumProjectorComputer scienceUnitary stateQuantum computerParity (physics)Projection (relational algebra)Theoretical physicsTheoretical computer scienceAlgorithmMathematicsPhysicsQuantum mechanicsArtificial intelligenceMathematical optimizationGeometrySoftware engineeringPolitical scienceLawQuantum Computing Algorithms and ArchitectureQuantum Information and CryptographyQuantum and electron transport phenomena